Patent Publication Number: US-8537131-B2

Title: Method and device for converting sensing information

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 12/923,805, filed Oct. 8, 2010, which claims the benefit of U.S. Provisional Application No. 61/298,252, filed on Jan. 26, 2010, Provisional Application No. 61/298,243, filed on Jan. 26, 2010 and U.S. Provisional Application No. 61/250,051, filed on Oct. 9, 2009, which is herein incorporated by reference for all intents and purposes. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method and device for converting sensing information, and more particularly, to a method and device for partially converting sensing information. 
     2. Description of the Prior Art 
     Touch displays have been widely used in the various electronic devices. One approach is to employ a touch sensitive panel to define a 2-D touch area on the touch display, where sensing information is obtained by scanning along horizontal and vertical axes of the touch panel for determining the touch or proximity of an external object (e.g. a finger) on or near the touch panel. U.S. Pat. No. 4,639,720 discloses a capacitive touch display. 
     Sensing information can be converted into a plurality of continuous signal values by an analog-to-digital converter (ADC). By comparing signal values before and after the touch or approaching of the external object, the location touched or approached by the external object can be determined. 
     Generally, a controller controlling the touch panel will first obtain sensing information when there is no external object touching or approaching as a baseline. For example, in a capacitive touch panel, each conductive line corresponds to a respective baseline. The controller determines whether there is an external object touching or approaching by comparing sensing information obtained subsequently with the baseline, and further determines the position of the external object. For example, when there is no external object touching or approaching the touch panel, subsequent sensing information with respect to the baseline will be or close to zero. Thus, the controller can determine whether there is an external object touching or approaching by determining whether the sensing information with respect to the baseline is or close to zero. 
     As shown in  FIG. 1A , when an external object  12  (e.g. a finger) touches or approaches a sensing device  120  of a touch display  10 , sensing information of sensors  140  on an axis (e.g. x axis) is converted into signal values as shown in  FIG. 1B . Corresponding to the appearance of the finger, the signal values show a waveform or finger profile. The location of the peak  14  of the finger profile indicates the position touched or approached by the finger. 
     However, the surface of the touch display will continuously gives out various noises. These noises vary with time and position and directly or indirectly affect the signal values, causing errors in position detection, or even positive detections at untouched locations. Furthermore, human body carries many noises, which could equally affect the signal values directly or indirectly. 
     From the above it is clear that prior art still has shortcomings. In order to solve these problems, efforts have long been made in vain, while ordinary products and methods offering no appropriate structures and methods. Thus, there is a need in the industry for a novel technique that solves these problems. 
     SUMMARY OF THE INVENTION 
     The present invention provides a method and device for converting sensing information. The present invention first detects each first touch related sensing information of a first sensing information, and then at least one of the first touch related sensing information is replaced by a corresponding second touch related sensing information to generate a second sensing information. 
     Traditionally, the process of transmitting signals of sensing devices to a controller may be interfered by noises. During conversion of sensing information, these noises may cause severe errors. For example, when performing an accumulation calculation, noises will also be accumulated. The amount of this accumulated noise may be significant when noise interference is strong, i.e. at low signal-to-noise ratio (SNR). Moreover, when the size of a sensing device is increased, the amount of sensors also increases, and this in turn raises the cost of converting sensing information. 
     The present invention includes at least the following objectives: 
     1. achieving quasi conversion of all of a sensing information by converting only a part of the sensing information; 
     2. selecting touch related sensing information with dissimilar all signal values and converting it into touch related sensing information with similar all signal values, so that the entire sensing information forms a sensing information with quasi all signal values; and 
     3. converting sensing information with not all signal values into sensing information with quasi all signal values to be applicable in touch-detection method and device for sensing information with all signal values. 
     The objectives of the present invention can be achieved by the following technical schemes. A method for converting sensing information proposed by the present invention includes: obtaining a first sensing information; detecting each first touch related sensing information of the first sensing information; and generating a second sensing information based on the first sensing information, the second sensing information being generated by replacing at least one of first touch related sensing information of the first sensing information with a second touch related sensing information. In addition, a device for converting sensing information proposed by the present invention includes a controller or a host for performing the following operations: obtaining a first sensing information; detecting each first touch related sensing information of the first sensing information; and generating a second sensing information based on the first sensing information, the second sensing information being generated by replacing at least one of first touch related sensing information of the first sensing information with a second touch related sensing information. 
     The objectives of the present invention can also be achieved by the following technical schemes. A method for converting sensing information proposed by the present invention includes: obtaining a dual-differential sensing information; detecting each touch related sensing information having two peaks in a pair of zero-crossings in the dual-differential sensing information; and converting the dual-differential sensing information into a sensing information with quasi all signal values, including: converting each touch related sensing information having two peaks in a pair of zero-crossings into signal values. In addition, a device for converting sensing information proposed by the present invention includes a controller or a host for performing the following operations: obtaining a dual-differential sensing information; detecting each touch related sensing information having two peaks in a pair of zero-crossings in the dual-differential sensing information; and converting the dual-differential sensing information into a sensing information with quasi all signal values, including: converting each touch related sensing information having two peaks in a pair of zero-crossings into signal values. 
     By aforementioned technical schemes, the present invention achieves at least the following advantages and benefits: 
     1. Compared to conversion of the entire sensing information, conversion of partial sensing information exhibits a better performance; 
     2. Compared to accumulation calculation of the entire sensing information, accumulation calculation of partial sensing information significantly reduces noise accumulation issue. 
     3. The present invention converts differential sensing information into traditional sensing information with all signal values, so that it can be applied in traditional methods for position analysis, while achieving a better SNR. 
     The above description is only an outline of the technical schemes of the present invention. Preferred embodiments of the present invention are provided below in conjunction with the attached drawings to enable one with ordinary skill in the art to better understand said and other objectives, features and advantages of the present invention and to make the present invention accordingly. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention can be more fully understood by reading the following detailed description of the preferred embodiments, with reference made to the accompanying drawings, wherein: 
         FIG. 1A  is a schematic diagram depicting a prior-art touch sensitive device; 
         FIG. 1B  is a schematic diagram illustrating prior-art signal values; 
         FIG. 1C  is a schematic diagram illustrating differences according to the present invention; 
         FIGS. 1D and 1E  are schematic diagrams illustrating dual differences according to the present invention; 
         FIG. 1F  is a schematic diagram illustrating a sensing device according to the present invention; 
         FIG. 1G  is a block diagram illustrating functions of a computing system according to the present invention; 
         FIGS. 2A and 2B  are schematic diagrams illustrating a driving/detecting unit and a sensing device according to the present invention; 
         FIG. 3A  is a block diagram illustrating functions of a detecting unit according to the present invention; 
         FIGS. 3B to 3D  are circuit diagrams illustrating detectors according to the present invention; 
         FIGS. 3E to 3J  are diagrams showing connections between a detecting circuit and an ADC circuit according to the present invention; 
         FIG. 4A  is a diagram illustrating position detection using binary differences according to the present invention; 
         FIGS. 4B to 4D  are diagrams illustrating examples for detecting centroid positions according to the present invention; 
         FIGS. 5A and 5B  are schematic diagrams depicting basins and hills according to the present invention; 
         FIG. 6  is a flowchart illustrating a method for converting sensing information according to a first embodiment of the present invention; and 
         FIG. 7  is a flowchart illustrating a method for converting sensing information according to a second embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Some embodiments of the present invention are described in details below. However, in addition to the descriptions given below, the present invention can be applicable to other embodiments, and the scope of the present invention is not limited by such, rather by the scope of the claims. Moreover, for better understanding and clarity of the description, some components in the drawings may not necessary be drawn to scale, in which some may be exaggerated relative to others, and irrelevant parts are omitted. 
     Sensing Information 
     In the present invention, sensing information can be provided by a touch sensitive device for representing 1-D, 2-D or multi-dimensional statuses on the touch sensitive device. The sensing information can be obtained by one or more sensors and converted into a plurality of continuous signal values by one or more Analog-to-Digital converters to represent among or change in amount of detected charges, current, voltage, capacitance, impedance or other electrical characteristics. Sensing information can be obtained or transmitted alternately, sequentially or in parallel, and can be compounded into one or more signals. These are obvious to those having ordinary skill in the art. 
     One having ordinary skill in the art may also recognize that sensing information described in the present invention includes, but not limited to, a signal of a sensor, a result of the signal of the sensors subtracted by a baseline (e.g. a signal when untouched or initial signals), a digitally converted value of said signal or said result of signal subtracted by baseline or said value converted in any other ways. In other words, sensing information can be in the form of a signal status, a status that is converted from any electrical signal or can be converted into electrical signal recorded in a storage medium (e.g. a register, a memory, a magnetic disk, an optical disk), including but not limited to analog or digital information. 
     Sensing information can be provided by two 1-D sensing information on different axes. The two 1-D sensing information can be used to represent the sensing information on a first axis (e.g. vertical axis) and a second axis (e.g. horizontal axis) on the touch sensitive device. They are used for position detection on the first and second axes, respectively, i.e. providing 1-D positions on the first and second axes or further constructing a 2-D position. In addition, the two 1-D sensing information can also be used for triangulation based on the distances between sensors to detect a 2-D position on the touch sensitive device. 
     Sensing information can be 2-D sensing information that consists of a plurality of 1-D sensing information on the same axis. The 2-D sensing information can represent signal distribution on a 2-D plane. For example, a plurality of 1-D sensing information on the vertical axis and a plurality of 1-D sensing information on the horizontal axis can represent a signal matrix, such that position detection can be achieved by watershed algorithm or other image processing methods. 
     In an example of the present invention, the sensing area on the touch sensitive device includes an overlapping range of a first 2-D detecting range detected by at least one first sensor and a second 2-D detecting range detected by at least one second sensor. One with ordinary skill in the art may also recognize that the sensing area can be an overlapping range of three or more 2-D detecting ranges. 
     For example, the detecting range of a single sensor can be a 2-D detecting range. A sensor (e.g. CCD or CMOS sensor) with camera-based optical detection or a piezoelectric sensor with surface acoustic wave detection obtains 1-D sensing information in the 2-D detecting range. The 1-D sensing information can be comprised of information sensed at a plurality of continuous time points, which correspond to different angles, positions or ranges. In addition, the 1-D sensing information can be generated according to images obtained (e.g. by CCD-CMOS sensor) within a time interval. 
     Furthermore, for example, the 2-D sensing range can consist of detecting ranges of a plurality of sensors. For example, the detecting range of each infrared photoreceptor, capacitive or resistive conductive bar or strip, or inductive U-shape coil is a fan or stripe shaped detecting range towards one axis. The detecting ranges of a plurality of sensors arranged on the same axis on a line segment (straight or curved) can form a 2-D detecting range of that axis, which can be a square or fan-shaped planar or arc detecting range, for example. 
     In a preferred example of the present invention, the sensing area on the touch sensitive device includes a 2-D range detected by a plurality of sensors on the first and second axes. For example, through self-capacitive detection, a driving signal is provided to a plurality of first sensors, and capacitive-coupling signals or changes in said signal in a 2-D detecting range of these first sensors are sensed to obtain first 1-D sensing information. Furthermore, a driving signal is provided to a plurality of second sensors, and capacitive-coupling signals or changes in said signal in a 2-D detecting range of these second sensors are sensed to obtain second 1-D sensing information. 
     In another example of the present invention, the sensing area on the touch sensitive device involves a plurality of sensors detecting a plurality of 1-D sensing information in a 2-D sensing range to construct 2-D sensing information. For example, when a signal source sequentially applies a driving signal to sensors on a first axis, signal(s) of at least one of sensors in a second axis is sequentially detected or on a plurality of sensors (partially or all) are simultaneously detected to obtain 2-D sensing information on the axis, wherein the sensors are adjacent or not adjacent but neighboring sensors on the second axis. For example, in mutual-capacitive detection or analog matrix resistive detection, a plurality of sensors constitute a plurality of sensing areas for detecting sensing information at each respective area. For example, a plurality of first sensors (e.g. a plurality of first conductive lines) and a plurality of second sensors (e.g. a plurality of second conductive lines) intersect with each other to from a plurality of overlapping regions. When a driving signal is sequentially provided to each of the first sensors, corresponding to the first sensor being driven by the driving signal, signal(s) or changes in signal(s) on at least one of the second sensors on the second axis is sequentially detected or on a plurality of the second sensors (partially or all) on the second axis are simultaneously detected to obtain 1-D sensing information corresponding to that first sensor. By collecting 1-D sensing information corresponding to each of the first sensors together, 2-D sensing information can be constructed. In an example of the present invention, 2-D sensing information can be regarded as an image. 
     One with ordinary skill in the art can appreciate that the present invention can be applied to touch sensitive display, for example, a display attached with aforementioned resistive, capacitive, surface acoustic wave, or other touch detection device (or referred to as touch sensitive device). Thus, sensing information obtained by the touch sensitive display or device can be regarded as touch sensitive information. 
     In an example of the present invention, a touch sensitive device may use continuous signals from different time points, that is, composite signal continuously detected by one sensor or simultaneously by a plurality of sensors. For example, the touch sensitive device may be inductive and continuously scan coils thereon to emit electromagnetic waves. Meanwhile, sensing information is detected by one or more sensors on an electromagnetic pen and continuously compounded to form a signal. This signal is then converted into a plurality of continuous signal values by an ADC. Alternatively, electromagnetic waves are emitted by an electromagnetic pen or electromagnetic waves from an inductive touch sensitive device are reflected, and sensing information is obtained by a plurality of sensors (coils) on the touch sensitive device. 
     Touch Related Sensing Information 
     When an external object (e.g. a finger) touches or approaches a touch sensitive device, electrical characteristic or changes will be generated by sensing information at an area corresponding to the touch or proximity of the object. The larger the electrical characteristic or changes, the closer it is to the center (e.g. centroid, center of gravity of center of geometry) of the external object. Continuous sensing information can be regarded as constituted by a plurality of continuous values whether it is digital or analog. The center of the external object may correspond between one or two values. In the present invention, a plurality of continuous values can be spatially or temporally continuous. 
     A first type of 1-D sensing information provided by the present invention is in the form of a plurality of continuous signal values, which can be signal values detected by a plurality of sensors in a time interval, by a single sensor in a continuous time interval or by a single sensor in a single time interval at different detecting locations. In the process of representing sensing information as signal values, signals from respective sensors, time intervals or locations are sequentially converted into signal values, or part or all of sensing information is obtained, thereafter, respective signal values are then analyzed. When an external object touches or draws near to a sensing device, continuous signal values of 1-D sensing information can be those as shown in  FIG. 1B . Position touched by the external object corresponds to the peak  14  of the sensing information, wherein peak  14  may reside between two signal values. As described earlier, the present invention does not limit the form of sensing information. Signal values can be another form of the signals of the sensors. For brevity of the description, the present invention below is described in the context of implementations of the signal values. One with ordinary skill in the art may appreciate the implementations of signals from the implementations of signal values. 
     A second type of 1-D sensing information provided by the present invention is in the form of a plurality of continuous differences, compared to the signal values above, each difference is the difference of a pair of signal values, and the sensing information represented by a plurality of differences can be regarded as differential sensing information. In the present invention, differential sensing information can be obtained directly during sensing, for example, simultaneously or continuously obtaining a plurality of signals, each difference being generated based on a differential signal corresponding to a pair of sensor, time intervals, or locations. The differential sensing information can be generated based on the original sensing information including a plurality of signal values generated previously. As described earlier, the present invention does not limit the form of sensing information. Differences can be another form of the differential signals. For brevity of the description, the present invention below is described in the context of implementations of the differences. One with ordinary skill in the art may appreciate the implementations of differential signals from the implementations of differences. 
     In an example of the present invention, a difference can be the difference between a pair of adjacent or not adjacent signal values, for example, the difference between a signal value and its immediately preceding signal value, or between a signal value and its following signal value. In another example of the present invention, the difference can be the difference between non-adjacent signal values. When an external object touches or draws close to the touch sensitive device, continuous differences of 1-D sensing information can be those shown in  FIG. 1C , wherein the position of the external object corresponds to zero-crossing  15  of the sensing information. Zero-crossing  15  may reside between two signal values. In an example of the present invention, on the touch sensitive device, the location of each difference is the middle of the two corresponding signal values. 
     A third type of 1-D sensing information provided by the present invention is in the form of a plurality of continuous dual differences, compared to the signal values and differences above, each dual difference can be the sum or difference of the difference for a first pair of signal values and the difference for a second pair of signal values, that is, the sum or difference of the differences of two pairs of signal values. For example, two pairs of signal values include a first signal value, a second signal value, a third signal value, and a fourth signal value. The dual difference for these four signals is (second signal value−first signal value)+(third signal value−fourth signal value), (second signal value−first signal value)−(fourth signal value−third signal value), (first signal value−second signal value)+(fourth signal value−third signal value) or (first signal value−second signal value)−(third signal value−fourth signal value). In addition, sensing information represented by continuous dual differences can be regarded as dual-differential sensing information. In the present invention, a dual difference is not limited to being provided after signal values or differences, but can also be provided through the sum or difference after subtraction of two pairs of signals upon sensing information being provided, providing dual differential signal similar or equivalent to the sum or difference of the differences between two pair of signal values. As described earlier, the present invention does not limit the form of sensing information. Dual differences can be another form of the dual differential signals. For brevity of the description, the present invention below is described in the context of implementations of the dual differences. One with ordinary skill in the art may appreciate the implementations of dual differential signals from the implementations of dual differences. 
     In an example of the present invention, when the external object touches or approaches the touch sensitive device, two pairs of signal values are constituted by three adjacent or non-adjacent signal values. In an example of the present invention, the differences between the prior two signal values and the latter two signal values are a first difference and a second difference, respectively, and the dual difference is the difference between the first difference and the second difference, wherein the first difference and the second difference both can be the results of the preceding signal value minus the following signal value or the following signal value minus the preceding signal value. In another example of the present invention, the differences between the first two signal values and the last two signal values are a first difference and a second difference, respectively, and the dual difference is the sum of the first difference and the second difference, wherein one of the first difference and the second difference is the result of the preceding signal value minus the following signal value, whereas the other one of the first difference and the second difference is the result of the following signal value minus the preceding signal value. For example, two pairs of signal values include a first signal, a second signal, and a third signal. The dual difference for these three signal values is (second signal value−first signal value)+(second signal value−third signal value), (second signal value−first signal value)−(third signal value−second signal value), (first signal value−second signal value)+(third signal value−second signal value), or (first signal value−second signal value)−(second signal value−third signal value). When two pairs of signal values are constituted by three adjacent signal values, and an external object touches or approaches the touch sensitive device, the continuous dual differences of 1-D sensing information can be those shown in  FIG. 1D , wherein the position of the external object corresponds to middle peak  16  of the sensing information. Middle peak  16  may reside between two signal values. When two pairs of signal values are constituted by three non-adjacent signal values, and an external object touches or approaches the touch sensitive device, the continuous dual differences of 1-D sensing information can be those shown in  FIG. 1E , wherein the position of the external object corresponds to middle peak  17  of the sensing information. Middle peak  17  may reside between two signal values. 
     In the present invention, sensing information corresponding to respective sensor, time interval or position can be signals detected by the sensors. When the signals are analog, it can be converted into digital signal values by an ADC. Thus, the above difference can also be the value of the difference between a pair of signals, for example, value converted from a pair of signals subtracted via a differential amplifier. Similarly, the above dual difference can also be the value converted from two pairs of signals subtracted via a differential amplifier and then added (or subtracted) together. One with ordinary skill in the art can appreciate that the difference and dual difference described by the present invention not only include being generated by signals or signal values, but also include temporary states of records (electrical, magnetic or optical records), signals or signal values during hardware or software implementations. 
     In other words, sensing information can be signals, differential signals (e.g. difference between a pair of signals), dual differential signals (e.g. sum or difference of two pairs of signals) on or between the sensors, and signal values, differences, dual differences (analog-to-digital converted signal values, differences or dual differences) can be another form. Signals and signal values, differential signals and differences, and dual differential signals and dual differences are sensing information represented at different stages. In addition, for brevity of the description, touch related sensing information mentioned herein broadly refers to sensing information corresponding to touch or proximity of an external object, such as original touch related sensing information, differential touch related sensing information and dual-differential touch related sensing information. 
     One with ordinary skill in the art can appreciate that in the case of differences or dual differences, zero-crossing is between at least one positive value and at least one negative value that is between a pair of positive and negative values. The difference or dual difference that corresponds to the touch or proximity of the external object may be an alternating continuous combination of at least one positive value and at least one negative value, wherein at least one zero value is interposed between the at least one positive value and at least one negative value. In most cases, the difference or dual difference that corresponds to the touch or proximity of the external object is an alternating continuous combination of multiple positive values and multiple negative values, wherein zero-crossings between positive and negative values may be at least a zero value or between two values. 
     In contrast, touch related signal values include a plurality of continuous non-zero values, or an independent non-zero value not adjacent to other non-zero values. In some cases, an independent non-zero value not adjacent to other non-zero values may be generated by noise, which should be identified and neglected by thresholding or other types of mechanisms. 
     Since noise could generate zero-crossing similar to the touch or proximity of an external object when large, thus in an example of the present invention, values that fall within a zero-value range will be treated as zero values. Difference or dual difference corresponding to the touch or proximity of an external object is an alternating continuous combination of multiple values above a positive threshold and multiple values below a negative threshold, wherein a zero-crossing between a value above the positive threshold and a value below a negative threshold may be at least one zero value or between two values. 
     In summary of the above, differential touch related sensing information and dual-differential touch related sensing information are alternating continuous combinations of at least one positive value and at least one negative value including a zero-crossing, wherein the zero-crossing can be at least one zero value or between the positive and negative values. In other words, a plurality of continuous zero values between positive and negative values in the differential touch related sensing information and dual-differential touch related sensing information are treated as zero-crossings, or one of which is treated as a zero-crossing. 
     In an example of the present invention, touch related sensing information is set to begin with at least a positive or negative value, and from there an alternating continuous combination of at least one positive value and at least one negative value including a zero-crossing is searched, wherein the zero-crossing may be at least one zero value or between positive and negative values. In differential touch related sensing information, alternating combinations of at least one positive value and at least one negative value occur symmetrically, and in dual-differential touch related sensing information, alternating combinations of at least one positive value and at least one negative value do not occur symmetrically. In an example of the present invention, touch related sensing information is continuous non-zero values, e.g. a plurality of continuous non-zero signal values. 
     The at least one positive value above can be regarded as a positive-value set including at least one positive value. Similarly, the at least one negative value above can be regarded as a negative-value set including at least one negative value. Thus, the above alternating combination can be a combination of two sets: a positive-value set and a negative-value set, or a combination of three or more set with alternating positive-value and negative-value sets. In an example of the present invention, at least one zero value may exist between zero, one, or multiple positive-value and negative-value sets. 
     System Framework 
     In order to more clearly illustrate how sensing information of the present invention is generated, the present invention uses a capacitive touch sensitive device as an example, and one with ordinary skill in the art can readily recognize other applications such as in resistive, infrared, surface acoustic wave, or optical touch sensitive devices. 
     Referring to  FIG. 1F , the present invention provides a position detecting device  100 . As shown, the device includes a sensing device  120  and a driving/detecting unit  130 . Sensing device  120  has a sensing layer. In an example of the present invention, the sensing layer can include a first sensing layer  120 A and a second sensing layer  120 B. First and second sensing layers  120 A and  120 B each has a plurality of sensors  140 , wherein first sensors  140 A of first sensing layer  120 A cross upon second sensors  140 B of second sensing layer  120 B. In another example of the present invention, first and second sensors  140 A and  140 B are disposed in a co-planar sensing layer. Driving/detecting unit  130  produces sensing information based on signals of sensors  140 . In the case of self-capacitive detection, for example, sensors  140  driven are sensed. In the case of mutual-capacitive detection, some of sensors  140  not directly driven by driving/detecting unit  130  are sensed. In addition, sensing device  120  can be disposed on a display  110 . An optional shielding layer (not shown) can be interposed between sensing device  120  and display  110 . 
     The position detecting device  100  of the present invention can be applied to a computing system as shown in  FIG. 1G , which includes a controller  160  and a host  170 . The controller includes driving/detecting unit  130  to operatively couple sensing device  120  (not shown). In addition, controller  160  can include a processor  161  for controlling driving/detecting unit  130  in generating sensing information. Sensing information can be stored in a memory  162  and accessible by processor  161 . Moreover, host  170  constitutes the main body of the computing system, mainly includes a central processing unit  171 , a storage unit  173  that can be accessed by central processing unit  171 , and display  110  for displaying results of operations. 
     In another example of the present invention, there is a transmission interface between controller  160  and host  170 . The controlling unit transmits data to the host via the transmission interface. One with ordinary skill in the art can appreciate that the transmission interface may include, but not limited to, UART, USB, I 2 C, Bluetooth, Wi-Fi wireless or wired transmission interfaces. In an example of the present invention, data transmitted can be position (e.g. coordinates), identification results (e.g. gesture codes), command, sensing information or other information provided by controller  160 . 
     In an example of the present invention, sensing information can be initial sensing information generated under the control of processor  161 , and position analysis is carried out by host  170 , such as position analysis, gesture identification, command identification etc. In another example of the present invention, sensing information can be analyzed by processor  161  first before forwarding determined position, gesture or command etc. to host  170 . The present invention does not limit to this example, and one with ordinary skill in the art can readily recognize other interactions between controller  160  and host  170 . 
     Referring to  FIG. 2A , in an example of the present invention, driving/detecting unit  130  may include a driving unit  130 A and a detecting unit  130 B. The plurality of sensors  140  of sensing device  120  are operatively coupled to driving/detecting unit  130  via a plurality of wires. In the example of  FIG. 2A , driving unit  130 A and detecting unit  130 B are operatively coupled to sensors  140 A via wires W 1  and to sensors  140 B via wires W 2 . 
     For example, in self-capacitive detection, all sensors  140 A are sequentially or simultaneously driven or some of sensors  140 A are driven simultaneously in batch by driving unit  130 A via wires W 1  in a first time period. Sensing information of a first axis (1-D sensing information) is generated via wires W 1  by detecting unit  130  based on signals of sensors  140 A. Similarly, all sensors  140 B are sequentially or simultaneously driven or some of sensors  140 A are driven simultaneously in batch by driving unit  130 A via wires W 2  in a second time period. Sensing information of a second axis (1-D sensing information) is generated via wires W 2  by detecting unit  130  based on signals of sensors  140 B. 
     For example, in mutual-capacitive detection, sensors  140 B are driven by driving unit  130  via wires W 2  in a first time period, and when each sensor  140 B is respectively driven, 1-D sensing information corresponding to a first axis of the driven sensors is generated by detecting unit  130 B based on signals of sensors  140 A via wires W 1 . These 1-D sensing information on the first axis construct 2-D sensing information (or an image) on the first axis. Similarly, sensors  140 A are driven by driving unit  130  via wires W 1  in a second time period, and when each sensor  140 A is respectively driven, 1-D sensing information corresponding to a second axis of the driven sensors is generated by detecting unit  130 B based on signals of sensors  140 B via wires W 2 . These 1-D sensing information on the second axis construct 2-D sensing information (or an image) on the second axis. In addition, driving unit  130 A and detecting unit  130 B can be synchronized via lines  132  by providing signals. The signals on lines  132  can be provided by said processor  160 . 
     Referring to  FIG. 2B , sensor device  120  can also generate 2-D sensing information on only a single axis. In this example, sensors  140 B are driven by wires W 2 , and when each sensor  140 B is respectively driven, 1-D sensing information of the driven sensor is generated by detecting unit  130 B based on the signals of sensors  140 A via wires W 1 . These 1-D sensing information constitute 2-D sensing information (or an image). 
     In other words, position detecting device  100  of the present invention is capable of producing 1-D sensing information in 2 axes or 2-D sensing information in 2 axes, producing both 1-D and 2-D sensing information in 2 axes, or producing 2-D sensing information in a single axis. The present invention may include but not limited to said capacitive position detecting device, one with ordinary skill in the art can appreciate other applications, such as in resistive, capacitive, surface acoustic wave, or other touch sensitive device. 
     Referring to  FIG. 3A , detecting unit  130 B is operatively coupled to the sensing device via wires (e.g. W 1 ). The operative coupling can be achieved by a switching circuit  310 , which can be one or more electrical elements such as multiplexers and/or switches. One with ordinary skill in the art can recognize other use of switching circuits. Signals of sensors  140  can be detected by a detecting circuit  320 . When signal output by detecting circuit  320  is analog, it is then passed through ADC circuit  330  to generate sensing information SI. Sensing information SI can be analog or digital. In a preferred example of the present invention, sensing information is digital, but the present invention is not limited to the above example. One with ordinary skill in the art can appreciate that detecting circuit  320  and ADC circuit  330  can be integrated in one or more circuits. 
     Detecting circuit  320  can be comprised of one or more detectors, each receiving a signal from at least one sensor  140  and generating an output. The detectors can be detectors  340 ,  350  and  360  shown in  FIGS. 3B to 3D . 
     In an example of the present invention, the detection of the signals of sensors  140  can be achieved by an integrator. One with ordinary skill in the art can appreciate other circuits that measure electrical characteristics (e.g. voltage, current, capacitance, induction etc.), such as an ADC, can be applied to the present invention. An integrator can be implemented by an amplifier Cint, which includes an input (e.g. as shown by integrator  322  of  FIG. 3B ) or a pair of input (e.g. as shown by integrator  324  of  FIGS. 3C and 3D ) and an output. Output signal can be used by ADC circuit  330  to generate values of sensing information SI, each of these values can be controlled by a reset signal, such as a reset signal Sreset shown in  FIGS. 3B to 3D . 
     In another example of the present invention, signals of sensors  140  are AC signals that vary with a pair of half cycles. Thus, the detection of the signals of sensors  140  also changes with different half cycles. For example, signals of sensors  140  are detected in the prior half cycle, and inverse signals of sensors  140  are detected in the latter half  1 ′ cycle, or vice versa. Therefore, the detection of the signals of sensors  140  can be controlled by a synchronizing signal Ssync, as shown in  FIGS. 3B to 3C . Synchronizing signal Ssync and the signals of sensors  140  are in sync or having the same cycle. For example, synchronizing signal Ssync is used to control one or more switches (e.g. switching circuits  321 ,  323 ,  325 ) to switch between base points P 1  and P 2 , so as to detect the signals of sensor  140  in the prior half cycle, and to detect the inverse signals of sensor  140  in the latter half cycle. In  FIG. 3B , the inverse signals are provided by an inverter Cinv. 
     In yet another example of the present invention, the detection of the signals of sensors  140  is performed in at least a predetermined time interval (or phase) in at least a cycle. Detection can be done in at least an interval in the first half cycle and at least an interval in the second half cycle; or in at least an interval in only the first or second half cycle. In a preferred example of the present invention, at least a preferred time interval in a cycle is scanned as the detection interval, wherein noise interference in this detection interval is smaller than in other intervals. Scanning of the detection interval can be determined by the detection of the signal of at least one sensor in each interval in at least a cycle. Upon determining a detection interval, detection of the signals of sensors is performed only in that detection interval, and this can be controlled by a signal, such as an enable signal Senable in  FIGS. 3B to 3D . 
     The present invention generates the values of sensing information SI based on the signal of at least one sensor  140 . In an example of the present invention, sensing information SI consists of a plurality of signal values. As shown in  FIG. 3B , an input  311  is operatively coupled to a sensor  140  for detecting a signal and a signal value of sensing information SI is generated through ADC circuit  330 . In another example of the present invention, sensing information SI consists of a plurality of differences. As shown in  FIG. 3C , a pair of inputs  312  and  313  are operatively coupled to a sensor  140  for detecting a differential signal and a difference (or single difference) of sensing information SI is generated through ADC circuit  330 . In yet another example of the present invention, sensing information SI consists of a plurality of dual differences. As shown in  FIG. 3D , three inputs  314 ,  315  and  316  are operatively coupled to a sensor  140  for detecting a dual differential signal and a dual difference of sensing information SI is generated through ADC circuit  330 . A dual differential signal is generated from the difference between a pair of differential signals; each differential signal is generated based on signals of a pair of sensors. In other words, a dual differential signal is generated based on signals of a first pair of sensors and a second pair of sensors, wherein the first pair of sensors are the first two sensors in the three sensors, and the second pair of sensors are the latter two sensors in the three sensors; these three sensors can be adjacent or not adjacent. 
     In a preferred example of the present invention, detecting circuit  320  includes a plurality of detectors, which simultaneously generate all or some values of sensing information SI. As shown in  FIGS. 3E to 3J , detecting circuit  320  can comprise of a detector  340 ,  350  or  360 . The output of the detector is then converted into values of sensing information SI by ADC circuit  330 . 
     ADC circuit  330  includes at least one ADC. Each ADC may output values of sensing information SI based on an output of only one detector, as shown in  FIGS. 3E ,  3 G and  3 I. Alternatively, an ADC may output values of sensing information SI based on outputs of several detectors in turn, as shown in  FIGS. 3F ,  3 H and  3 J. Values of sensing information SI can be generated in parallel or in series. In a preferred example of the present invention, values of sensing information SI are generated in series, which can be achieved by a switching circuit  370 , for example, by outputting values of sensing information SI from a plurality of ADCs in turn, as shown in  FIGS. 3E ,  3 G, and  3 I, or by providing outputs of a plurality of integrators to a single ADC in turn to generate values of sensing information SI, as shown in  FIGS. 3F ,  3 H and  3 J. 
     Accordingly, in an example of the present invention, sensing information SI having a plurality of signal values are generated based on signals of a plurality of sensors, wherein each signal value is generated based on a signal from a sensor, as shown in  FIGS. 3B ,  3 E and  3 F. In another example of the present invention, sensing information SI having a plurality of differences are generated based on signals of a plurality of sensors, wherein each difference is generated based on signals from a pair of sensors, as shown in  FIGS. 3C ,  3 G and  3 H. In yet another example of the present invention, sensing information SI having a plurality of dual differences are generated based on signals of a plurality of sensors, wherein each dual difference is generated based on signals from three sensors, as shown in  FIGS. 3D ,  3 I and  3 J. 
     In  FIGS. 3E to 3J , wires connecting the detectors may include but not limited to wires W 1  and wires W 2 . Connection between an integrator and a wire can be direct or indirect through a switching circuit, as shown in  FIG. 3A . In an example of the present invention, values of sensing information are generated by multiple detections by at least a detector of detecting circuit  320 . Detecting circuit  320  selects some of the sensors for detection by using switching circuit  310 . In addition, only selected sensors are driven by driving unit  130 A, for example, in self-capacitive detection. Moreover, only selected sensors and some sensors adjacent to the selected sensors are driven by driving unit  130 A. 
     In a first example of the present invention, the sensing information can be obtained by a dual-differential circuit, which includes: a first-stage differential circuit, a second-stage differential circuit and a measuring circuit, as shown in  FIG. 3D ,  3 I or  3 J. 
     The first-stage differential circuit includes a pair or a plurality of first subtractors (e.g. differential amplifiers in switching circuits  325 ). Each of first subtractors generates a first-stage differential signal according to a pair of sensors in these sensors. 
     In addition, the second-stage differential circuit includes a pair or a plurality of first subtractors (e.g. integrators in integrating circuits  324 ). Each of first subtractors generates a second-stage differential signal according to a pair of first-stage differential signals in these first-stage differential signals. 
     Further, the measuring circuit may be an ADC circuit as shown  FIG. 3A , a combination of integrator  324  and an ADC circuit as shown in  FIG. 3D , or a combination of a plurality of integrator  324 , ADC circuits and a switching circuit  370  as shown in  FIG. 3I . Moreover, the measuring circuit measures these second-stage differential signal at one or a plurality of time points to generate the sensing information. As shown in  FIG. 3D  or  FIG. 3J , these second-stage differential signals are measured at a plurality of time points, or as shown in  FIG. 3I , these second-stage differential signals are measured at a single time point. 
     In  FIGS. 3D ,  3 I and  3 J of the present invention, differential integrators  324  are used for simultaneous subtraction and measurement of signals, wherein the subtraction of signals can further include generating a digital value using an ADC circuit. The drawings and descriptions given above are merely examples of the present invention; the present invention is not limited to these. One with ordinary skill in the art can recognize that signal subtraction and measurement can be performed by different circuits, for example, first by a subtractor then an integrator, which will not be described further in details. 
     In said dual-differential circuit, each value of the sensing information is generated by one of these second-stage differential signals, and each of the second-stage differential signals is generated by a first differential signal and a second differential signal of a pair of first-stage differential signals, wherein the first differential signal is generated based on a signals of a first sensor and a second sensor of these sensors, and the second differential signal is generated based on a signals of the second sensor and a third sensor of these sensors. In other words, each value of the sensing information corresponds to signals of three sensors in these sensors. 
     In a second example of the present invention, the sensing information can be obtained by a differential circuit, which includes: one or a plurality of subtractors and a measuring circuit, as shown in  FIG. 3C ,  3 G or  3 H. In these subtractors, each subtractor generates a differential signal according to signals of a pair of sensors. The measuring circuit measures these differential signals to generate a differential sensing information, wherein each value of the sensing information is the difference of a pair of values of the differential sensing information. 
     Further, the measuring circuit may measure these differential signals at one or a plurality of time points to generate the sensing information. As shown in  FIG. 3C  or  FIG. 3H , these differential signals are measured at a plurality of time points, or as shown in  FIG. 3G , these differential signals are measured at a single time point. 
     In  FIG. 3C ,  3 G or  3 H of the present invention, the subtractors and a portion of the measuring circuit can be implemented by integrator  324 . The drawings and descriptions given above are merely examples of the present invention; the present invention is not limited to these. One with ordinary skill in the art can recognize that signal subtraction and measurement can be performed by different circuits, for example, first by a subtractor then an integrator, which will not be described further in details. 
     In addition, each value of the sensing information is generated by the difference of a first difference and a second difference of the differential signals, wherein the first difference is generated based on a signals of a first sensor and a second sensor of these sensors, and the second difference is generated based on a signals of the second sensor and a third sensor of these sensors. In other words, each value of the sensing information corresponds to signals of three sensors in these sensors. 
     In a third example of the present invention, the sensing information can be obtained by a measuring circuit, as shown in  FIG. 3B ,  3 E or  3 F. The measuring circuit measures signals of these sensors to generate an initial sensing information. The sensing information is generated according to the initial sensing information, wherein each value of the sensing information is generated from three values of the initial sensing information. 
     Further, the measuring circuit may measure these signals at one or a plurality of time points to generate the initial sensing information. As shown in  FIG. 3B  or  FIG. 3F , these signals are measured at a plurality of time points, or as shown in  FIG. 3E , these signals are measured at a single time point. 
     Each value of the sensing information is the difference or sum of the first difference and a second difference, wherein the first difference is the difference between two prior values of three values of the initial sensing information, and the second difference is the difference between two latter values of the three values of the initial sensing information. In other words, the three values of the initial sensing information are a first value, a second value and a third value. Each value of the sensing information is (second value−first value)−(third value−second value), (first value−second value)−(second value−third value), (second value−first value)+(second value−third value), or (first value−second value)+(third value−second value). Each value of the initial sensing information is generated according to signals of one of these sensors, that is, each value of the initial sensing information corresponds to signals of three sensors of these sensors. 
     In an example of the present invention, each touch related sensing information of the sensing information has two zero-crossings, and a position touched or approached by an external object is determined by each touch related sensing information. In another example of the present invention, the touch related sensing information is at the beginning or end portion of the sensing information, an external object only approaches or touches the edges of the active region of the touch-detection device. In this case, there will not be two zero-crossings, and exception handling is required. 
     Moreover, said time points may include but not limited to via one or more clocks, or portions of one or more clocks. 
     Furthermore, the obtaining and generation of said sensing information can be implemented by controller  160 . Said dual-differential circuit, differential circuit and measuring circuit can also be implemented by the controller  160 . 
     In the present invention, sensors can consist of a plurality of conductive sheets and wires, such as a set of rhombic or square conductive sheets connected together by wires. Structurally, conductive sheets of first sensors  140 A and second sensors  140 B may be arranged in different or same planes. For example, an insulating or piezoresistive layer can be interposed between first and second sensing layers  120 A and  120 B, wherein the piezoresistive layer is made from anisotropic conductive gel. Moreover, for example, conductive sheets of first sensors  140 A and second sensors  140 B are substantially arranged in the same plane, with the wires of first sensors  140 A bridging over the wires of second sensors  140 B. In addition, pads can be disposed between the wires of first sensors  140 A and second sensors  140 B. These pads can be made of insulating or piezoresistive materials. 
     Thus, in an example of the present invention, each sensor is responsible for a sensing range. There are a plurality of sensors, including a plurality of first sensors and a plurality of second sensors. The sensing ranges of these first sensors are parallel to each other, while the sensing ranges of these second sensors are parallel to each other. The parallel sensing ranges of the first and second sensors intersect to form an intersecting matrix. For example, the first and second sensors are two lines of infrared receivers arranged horizontally and vertically for sensing horizontal scanning ranges and vertical scanning ranges, respectively. The horizontal and vertical scanning ranges form an intersecting matrix. The horizontal and vertical scanning ranges are implemented by several lines of intersecting capacitive or resistive sensors. 
     Conversion of Sensing Information 
     The signal values, differences and dual differences of the sensing information can be converted into one another. In a first conversion method provided by the present invention, continuous signal values are converted into continuous differences; each difference being the difference between a pair of adjacent or non-adjacent signal values. 
     In a second conversion method provided by the present invention, continuous signal values are converted into continuous dual differences; each dual difference being the sum or difference between two pairs of signal values. 
     In a third conversion method provided by the present invention, continuous differences are converted into continuous signal values; each difference is added to all the preceding or following differences to obtain a corresponding signal value, thereby constructing continuous signal values. 
     In a fourth conversion method provided by the present invention, continuous differences are converted into continuous dual differences; each dual difference is the sum or difference of a pair of adjacent or non-adjacent differences. 
     In a fifth conversion method provided by the present invention, continuous dual differences are converted into continuous differences; each dual difference is added to all the preceding or following dual differences to obtain a corresponding difference, thereby constructing continuous differences. 
     In a sixth conversion method provided by the present invention, continuous dual differences are converted into continuous signal values. In an example of the present invention, each dual difference is added to all the preceding dual differences to obtain a corresponding difference, thereby constructing continuous differences, and thereafter each difference subtracts all the following differences to generate a corresponding signal value, thereby constructing continuous signal values. In another example of the present invention, each dual difference subtracts all the preceding dual differences to obtain a corresponding difference, thereby constructing continuous differences, and thereafter each difference is added to all the following differences to generate a corresponding signal value, thereby constructing continuous signal values. 
     Adding all the preceding or following differences or dual differences to generate a corresponding signal value or difference is performed by forward or backward accumulation. 
     These conversion methods may include but not limited to the conversion of 1-D sensing information, one with ordinary skill in the art can appreciate that the above conversion methods can be applied to 2-D sensing information or 3-D (or even more dimensional) sensing information. In addition, one with ordinary skill in the art can appreciate that the above conversion methods can be performed by said controller  160  or host  170 . 
     Accordingly, in an example of the present invention, a first form of sensing information (e.g. 1-D or 2-D sensing information) detected is converted into sensing information for position analysis. In another example of the present invention, a first form of sensing information is converted into a second form of sensing information, and then the second form of sensing information is converted into sensing information for position analysis, for example, continuous dual difference is converted to continuous signal values. 
     One-Dimension Position Analysis 
     A first type of position analysis provided by the present invention involves analyzing the position of a zero-crossing based on a plurality of differences in sensing information as the corresponding position of an external object. One with ordinary skill in the art can recognize that position analysis may include but not limited to determination of the touch or proximity of an object, that is, determination of a corresponding position of an external object may include but not limited to the touch or proximity of the object. 
     In an example of the present invention, a pair of neighboring differences including a positive and a negative value is searched, that is, a pair of positive and negative values at both sides of a zero-crossing, and then the position of the zero-crossing in this pair of neighboring differences is then determined, for example, a slope is determined based on this pair of adjacent differences to infer the position of the zero-crossing. In addition, order of the positive and negative values can be used in conjunction for determining the position of the zero-crossing. Said pair of neighboring differences can be directly adjacent to each other, or not adjacent and with at least one zero value between them. In addition, a pair of neighboring differences with a predetermined order of arrangement can be searched for, for example, a pair of neighboring differences with a positive value appearing first and followed by a negative value is searched for. 
     In another example of the present invention, a threshold is used for determining the starting position of the search. From there, a pair of neighboring differences including a positive and a negative value is searched for, and then the position of a zero-crossing is determined based on the found pair of neighboring differences. One with ordinary skill in the art can appreciate that in the case that sensing information is represented by differences, when sensing information corresponding to the touch or proximity of an external object is above a positive threshold or below a negative threshold, the searching using these threshold values may include but not limited to the determination of the touch or proximity of the external object. In other words, whenever sensing information is above a positive threshold or below a negative threshold, it can be determined that there is a zero-crossing in the sensing information that corresponds to a touch or proximity of an external object. 
     For example, a threshold generates binary values corresponding to positive differences. For example, a difference smaller than a threshold (e.g. positive threshold) is represented by 0 or false, and a difference larger than the threshold is represented by 1 or true, and the position of a 1 or true in adjacent differences 10 is regarded as the starting position for a backward search of a zero-crossing. Similarly, a difference larger than a threshold (e.g. negative threshold) is represented by 0 or false, and a difference smaller than the threshold is represented by 1 or true, and the position of a 1 or true in adjacent differences 01 is regarded as the starting position for a forward search of a zero-crossing. 
     For example, Table 1 and  FIG. 4B  are examples of using threshold for determining touch or proximity of an external object. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                   
                   
                 First Binary 
                 Second Binary 
               
               
                   
                   
                 Signal 
                   
                 Difference 
                 Difference 
               
               
                   
                 Index 
                 Value 
                 Difference 
                 (T1 = 4) 
                 (T2 = −4) 
               
               
                   
                   
               
             
            
               
                   
                  1 
                  0 
                   0 
                 0 
                 0 
               
               
                   
                  2 
                  0 
                   0 
                 0 
                 0 
               
               
                   
                  3 
                  0 
                   3 
                 0 
                 3 
               
               
                   
                  4 
                  3 
                   7 
                 1 
                 0 
               
               
                   
                  5 
                 10 
                 −7 
                 0 
                 1 
               
               
                   
                  6 
                  3 
                 −3 
                 0 
                 0 
               
               
                   
                  7 
                  0 
                   0 
                 0 
                 0 
               
               
                   
                  8 
                  0 
                   0 
                 0 
                 0 
               
               
                   
                  9 
                  0 
                   2 
                 0 
                 0 
               
               
                   
                 10 
                  2 
                   5 
                 1 
                 0 
               
               
                   
                 11 
                  7 
                   0 
                 0 
                 0 
               
               
                   
                 12 
                  7 
                 −5 
                 0 
                 1 
               
               
                   
                 13 
                  2 
                 −2 
                 0 
                 0 
               
               
                   
                 14 
                  0 
                   0 
                 0 
                 0 
               
               
                   
                 15 
                  0 
                   0 
                 0 
                 0 
               
               
                   
                   
               
            
           
         
       
     
     This example includes signal values or difference of 15 sensors and determination results using a positive threshold T 1  (e.g. 4) and a negative threshold T 2  (e.g. −4). In the determination results using the positive threshold, the starting positions are the 4th and 10th differences, that is, the position of a 1 in adjacent differences 10. In the diagram with vertical-stripe bar, it is found that there are two instances of touch or proximity of external objects. Similarly, in the determination results using the negative threshold, the starting positions are the 5th and 12th differences, that is, the position of a 1 in adjacent differences 01. In the diagram with horizontal-stripe bar, it is found that there are two instances of touch or proximity of external objects. One with skill the art can appreciate that the number of starting position corresponds to the number of instances of touch or proximity of external objects. The present invention does not limit to only two instances of touch or proximity of external objects, but there can be more. 
     In another example of the present invention, an interval for a zero-crossing is determined using a first threshold and a second threshold, which may include but not limited to touch or proximity of an external object, and then the position of the zero-crossing is searched within this interval. For example, a first threshold produces binary values of positive differences, for example, a difference smaller than the first threshold is represented by 0 or false, and a difference larger than the first threshold is represented by 1 or true, and the position of a 1 in adjacent differences 10 is regarded as the starting position. In addition, a second threshold produces binary values of negative differences, for example, a difference larger than the second threshold is represented by 0 or false, and a difference smaller than the second threshold is represented by 1 or true, and the position of a 1 in adjacent differences 01 is regarded as the end position. Moreover, the starting and end positions are paired to form intervals for searching zero-crossings. In an example of the present invention, a slope is used to determine the zero-crossing between a starting position (e.g. position of a 1 in 10) and an end position (e.g. position of a 1 in 01). One with ordinary skill in the art can appreciate that the starting and end positions are interchangeable. One with ordinary skill in the art can appreciate that touch related sensing information can be determined by regarding the location of 1 in 01 as the starting position and the location of 1 in 10 as the end position. 
     Take again the example shown in  FIG. 4A  and Table 1, after pairing, a first search interval is between the 4th and 5th differences, and a second search interval is between the 10th and 12th differences. 
     One with ordinary skill in the art can appreciate that positive and negative thresholdings can be performed simultaneously (or in parallel). Interval pairing can be carried out by pairing a determined starting position with an end position that determined immediately afterwards. 
     In an example of the present invention, thresholds can be generated by sensing information. For example, a threshold value can be determined by multiplying a maximum of the absolute values of all differences by a ratio (e.g. a ratio smaller than one, such as 0.9), or a positive threshold value can be determined by multiplying a maximum of all positive differences by a ratio, or a negative threshold value can be determined by multiplying a minimum of all negative differences by a ratio. In other words, a threshold value can be static or dynamic. Thus, when the absolute value of a threshold is relatively large, it is possible that external object is determined when using the positive thresholding but not in the negative thresholding, or vice versa. A larger threshold value is favorable for noise or ghost points filtering, while a smaller threshold value is favorable for avoiding miss of real touch or for determining approaching of external objects. 
     From the above, it is clear that, corresponding to the same touch or approaching of an object, regardless of a backward search from a starting position identified using a positive threshold value or a forward search from a starting position identified using a negative threshold value, the same zero-crossing will be searched. Thus, in an example of the present invention, search for a zero-crossing starts from starting positions identified using positive and negative threshold values, and the number of external touch or approaching is determined based on the number of zero-crossings found, and then the positions of the zero-crossings are determined. When the values at both sides of a zero-crossing that corresponds to an external touch or approaching are first positive and then negative, the search for zero-crossing is backward from the starting position when using positive thresholding, whereas the search for zero-crossing is forward from the starting position when using negative thresholding, and vice versa. In addition, an external touch or approaching may not always exhibit starting positions in both positive and negative thresholdings. 
     A second type of position analysis provided by the present invention involves analyzing the position of centroid (position of center of weight or weighted average position) based on a plurality of signal values or dual differences in sensing information as the corresponding position of an external object. 
     In an example of the present invention, a threshold value is used to determine the centroid position of signal values or dual differences, as shown in  FIGS. 4B and 4D . A threshold can generate binary values corresponding to signal values or dual differences. For example, a signal value or dual difference smaller than a threshold is represented by 0 or false, and a signal value or dual difference larger than the threshold is represented by 1 or true. In this example, a signal value or dual difference represented by 1 or true is used in determining centroid position. One with ordinary skill in the art can appreciate other ways for determining a centroid position of signal values or dual differences using a threshold. For example, a signal value or dual difference represented by 1 or true, as well as a plurality of signal values or dual differences at either side thereof, are used in determining centroid position. As another example, in a continuous series of adjacent signal value or dual difference represented by 1 or true, a number (i) of and a number (j) of signal values or dual differences before and after a signal value or dual difference that is at the center of the series are taken to determine the centroid position. 
     In another example of the present invention, continuous signal values or dual differences are converted into continuous differences to identify the center signal value or dual difference that corresponds to a zero-crossing, and i and j signal values or dual differences before and after the center signal value or dual difference are used for determining the centroid position. 
     In another example of the present invention, a zero-crossing is determined by continuous differences, and the continuous differences are converted into continuous signal values or dual differences, and then the center signal value or dual difference that corresponds to the zero-crossing is identified, thereafter, i and j signal values or dual differences before and after the center signal value or dual difference are used for determining the centroid position. 
     Assuming that using i and j signal values respectively before and after the nth signal value as a centroid calculation range, the centroid position can be determined based on each signal value C k  and its position in the centroid calculation range as follows: 
     
       
         
           
             
               C 
               centroid 
             
             = 
             
               
                 
                   ∑ 
                   
                     k 
                     = 
                     
                       n 
                       - 
                       i 
                     
                   
                   
                     n 
                     + 
                     j 
                   
                 
                 ⁢ 
                 
                   
                     X 
                     k 
                   
                   ⁢ 
                   
                     C 
                     k 
                   
                 
               
               
                 
                   ∑ 
                   
                     k 
                     = 
                     
                       n 
                       - 
                       i 
                     
                   
                   
                     n 
                     + 
                     j 
                   
                 
                 ⁢ 
                 
                   C 
                   k 
                 
               
             
           
         
       
     
     wherein X k  can be a 1-D coordinate (e.g. X or Y coordinate) or 2-D coordinates (e.g. (X, Y)). 
     Assuming the difference between the k−1th signal value and the kth signal value is D k , and the kth dual difference is DD k =D k−1 −D k =(C k −C k−1 )−(C k+1 −C k )=2C k −C k−1 +C k+1 , and assuming using i and j signal values respectively before and after the nth dual difference DD n  as a centroid calculation range, the centroid position can be determined based on each dual difference DD k  in the centroid calculation range as follows: 
     
       
         
           
             
               DD 
               centroid 
             
             = 
             
               
                 
                   ∑ 
                   
                     k 
                     = 
                     
                       n 
                       - 
                       i 
                     
                   
                   
                     n 
                     + 
                     j 
                   
                 
                 ⁢ 
                 
                   
                     X 
                     k 
                   
                   ⁢ 
                   
                     DD 
                     k 
                   
                 
               
               
                 
                   ∑ 
                   
                     k 
                     = 
                     
                       n 
                       - 
                       i 
                     
                   
                   
                     n 
                     + 
                     j 
                   
                 
                 ⁢ 
                 
                   DD 
                   k 
                 
               
             
           
         
       
     
     wherein X k  can be a 1-D coordinate (e.g. X or Y coordinate) or 2-D coordinates (e.g. (X, Y)). One with ordinary skill in the art can similarly appreciate the calculation for centroid position when the kth dual difference is DD k =(C k −C k−2 )−(C k+2 −C k )=2C k −C k−2  C k+2 . This will not be described further. 
     In another example of the present invention, signal values or dual differences used for determining centroid position is obtained by first subtracting a base value. For example, this base value can be the average of all signal values or dual differences, the average of a plurality of signal values or dual differences at either sides of the signal values or dual differences used for centroid position determination, or the average of a plurality of signal values or dual differences not used for centroid position determination that are adjacent to either sides of the signal values or dual differences used for centroid position determination. One with ordinary skill in the art can recognize other ways of determining the base value. For example, the base value can be determined based on a first ratio of at least one signal value or dual difference at one side and a second ratio of at least one signal value or dual difference at the other side. 
     Taken the average of the ith signal value C n-i  and the jth signal value I n+j  respectively before and after the nth signal value as base value 
                 C     base   ⁡     (     i   ,   j     )         ⁡     (       C     base   ⁡     (     i   ,   j     )         =         C     n   -   i       +     C     n   +   j         2       )       ,         
and using i and j signal values respectively before and after the nth signal value as a centroid calculation range, the centroid position can be determined based on each signal value C k  minus the base value C base(i,j)  in the centroid calculation range as follows:
 
     
       
         
           
             
               C 
               
                 base 
                 ⁡ 
                 
                   ( 
                   
                     i 
                     , 
                     j 
                   
                   ) 
                 
               
             
             = 
             
               
                 
                   C 
                   
                     n 
                     - 
                     i 
                   
                 
                 + 
                 
                   C 
                   
                     n 
                     + 
                     j 
                   
                 
               
               2 
             
           
         
       
       
         
           
             
               
                 C 
                 k 
               
               - 
               
                 C 
                 
                   base 
                   ⁡ 
                   
                     ( 
                     
                       i 
                       , 
                       j 
                     
                     ) 
                   
                 
               
             
             = 
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       C 
                       k 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       - 
                       i 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       + 
                       j 
                     
                   
                 
                 2 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         C 
                         k 
                       
                       - 
                       
                         C 
                         
                           n 
                           - 
                           i 
                         
                       
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         C 
                         k 
                       
                       - 
                       
                         C 
                         
                           n 
                           + 
                           j 
                         
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
       
         
           
             
               C 
               cnetroid 
             
             = 
             
               
                 
                   
                     ∑ 
                     
                       k 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     
                       X 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             2 
                             ⁢ 
                             
                               C 
                               k 
                             
                           
                           - 
                           
                             C 
                             
                               n 
                               - 
                               i 
                             
                           
                           - 
                           
                             C 
                             
                               n 
                               + 
                               j 
                             
                           
                         
                         2 
                       
                       ) 
                     
                   
                 
                 
                   
                     ∑ 
                     
                       k 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           C 
                           k 
                         
                       
                       - 
                       
                         C 
                         
                           n 
                           - 
                           i 
                         
                       
                       - 
                       
                         C 
                         
                           n 
                           + 
                           j 
                         
                       
                     
                     2 
                   
                 
               
               = 
               
                 
                   
                     ∑ 
                     
                       k 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     
                       X 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           2 
                           ⁢ 
                           
                             C 
                             k 
                           
                         
                         - 
                         
                           C 
                           
                             n 
                             - 
                             i 
                           
                         
                         - 
                         
                           C 
                           
                             n 
                             + 
                             j 
                           
                         
                       
                       ) 
                     
                   
                 
                 
                   
                     ∑ 
                     
                       k 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         
                           C 
                           k 
                         
                       
                       - 
                       
                         C 
                         
                           n 
                           - 
                           i 
                         
                       
                       - 
                       
                         C 
                         
                           n 
                           + 
                           j 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     wherein X k  can be a 1-D coordinate (e.g. X or Y coordinate) or 2-D coordinates (e.g. (X, Y)). 
     A third type of position analysis provided by the present invention involves analyzing the position of centroid (position of center of weight or weighted average position) based on a plurality of differences in sensing information as the corresponding position of an external object. 
     Assuming the difference between the k−1th signal value C k−1  and the kth signal value C k  is D k . 
     
       
         
           
             
               ( 
               
                 
                   C 
                   k 
                 
                 - 
                 
                   C 
                   
                     n 
                     - 
                     i 
                   
                 
               
               ) 
             
             = 
             
               
                 
                   D 
                   
                     n 
                     - 
                     
                       ( 
                       
                         i 
                         - 
                         1 
                       
                       ) 
                     
                   
                 
                 + 
                 
                   D 
                   
                     n 
                     - 
                     
                       ( 
                       
                         i 
                         - 
                         2 
                       
                       ) 
                     
                   
                 
                 + 
                 … 
                 + 
                 
                   
                     D 
                     k 
                   
                   ⁢ 
                   
                     
 
                   
                   ( 
                   
                     
                       C 
                       k 
                     
                     - 
                     
                       C 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 - 
                 
                   ( 
                   
                     
                       D 
                       
                         k 
                         + 
                         1 
                       
                     
                     + 
                     
                       D 
                       
                         k 
                         + 
                         2 
                       
                     
                     + 
                     … 
                     + 
                     
                       D 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 C 
                 k 
               
               - 
               
                 C 
                 
                   base 
                   ⁡ 
                   
                     ( 
                     
                       i 
                       , 
                       j 
                     
                     ) 
                   
                 
               
             
             = 
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       C 
                       k 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       - 
                       i 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       + 
                       j 
                     
                   
                 
                 2 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         D 
                         
                           n 
                           - 
                           
                             ( 
                             
                               i 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                       + 
                       
                         D 
                         
                           n 
                           - 
                           
                             ( 
                             
                               i 
                               - 
                               2 
                             
                             ) 
                           
                         
                       
                       + 
                       … 
                       + 
                       
                         D 
                         k 
                       
                     
                     ) 
                   
                   - 
                   
                     ( 
                     
                       
                         D 
                         
                           k 
                           + 
                           1 
                         
                       
                       + 
                       
                         D 
                         
                           k 
                           + 
                           2 
                         
                       
                       + 
                       … 
                       + 
                       
                         D 
                         
                           n 
                           + 
                           j 
                         
                       
                     
                     ) 
                   
                 
                 2 
               
             
           
         
       
       
         
           
             
               
                 C 
                 k 
               
               - 
               
                 C 
                 
                   base 
                   ⁡ 
                   
                     ( 
                     
                       i 
                       , 
                       j 
                     
                     ) 
                   
                 
               
             
             = 
             
               
                 
                   
                     ∑ 
                     
                       s 
                       = 
                       
                         n 
                         - 
                         
                           ( 
                           
                             i 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                     k 
                   
                   ⁢ 
                   
                     D 
                     s 
                   
                 
                 - 
                 
                   
                     ∑ 
                     
                       s 
                       = 
                       
                         k 
                         + 
                         1 
                       
                     
                     
                       n 
                       + 
                       j 
                     
                   
                   ⁢ 
                   
                     D 
                     s 
                   
                 
               
               2 
             
           
         
       
       
         
           
             
               C 
               cnetroid 
             
             = 
             
               
                 
                   
                     ∑ 
                     
                       s 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     
                       X 
                       s 
                     
                     ( 
                     
                       
                         
                           
                             ∑ 
                             
                               s 
                               = 
                               
                                 n 
                                 - 
                                 
                                   ( 
                                   
                                     i 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             k 
                           
                           ⁢ 
                           
                             D 
                             s 
                           
                         
                         - 
                         
                           
                             ∑ 
                             
                               s 
                               = 
                               
                                 k 
                                 + 
                                 1 
                               
                             
                             
                               n 
                               + 
                               j 
                             
                           
                           ⁢ 
                           
                             D 
                             s 
                           
                         
                       
                       2 
                     
                     ) 
                   
                 
                 
                   
                     ∑ 
                     
                       s 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     
                       
                         
                           ∑ 
                           
                             s 
                             = 
                             
                               n 
                               - 
                               
                                 ( 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           k 
                         
                         ⁢ 
                         
                           D 
                           s 
                         
                       
                       - 
                       
                         
                           ∑ 
                           
                             s 
                             = 
                             
                               k 
                               + 
                               1 
                             
                           
                           
                             n 
                             + 
                             j 
                           
                         
                         ⁢ 
                         
                           D 
                           s 
                         
                       
                     
                     2 
                   
                 
               
               = 
               
                 
                   
                     ∑ 
                     
                       s 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     
                       X 
                       k 
                     
                     ( 
                     
                       
                         
                           ∑ 
                           
                             s 
                             = 
                             
                               n 
                               - 
                               
                                 ( 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           k 
                         
                         ⁢ 
                         
                           D 
                           s 
                         
                       
                       - 
                       
                         
                           ∑ 
                           
                             s 
                             = 
                             
                               k 
                               + 
                               1 
                             
                           
                           
                             n 
                             + 
                             j 
                           
                         
                         ⁢ 
                         
                           D 
                           s 
                         
                       
                     
                     ) 
                   
                 
                 
                   
                     ∑ 
                     
                       s 
                       = 
                       
                         n 
                         - 
                         i 
                       
                     
                     
                       
                         n 
                         - 
                         i 
                       
                       ≤ 
                       k 
                       ≤ 
                       
                         n 
                         + 
                         j 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           ∑ 
                           
                             s 
                             = 
                             
                               n 
                               - 
                               
                                 ( 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           k 
                         
                         ⁢ 
                         
                           D 
                           s 
                         
                       
                       - 
                       
                         
                           ∑ 
                           
                             s 
                             = 
                             
                               k 
                               + 
                               1 
                             
                           
                           
                             n 
                             + 
                             j 
                           
                         
                         ⁢ 
                         
                           D 
                           s 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     Accordingly, the centroid position C centroid  can be calculated based on the differences between the signal values, wherein the differences in the centroid calculation range are D n-(i-1) , D n-(i-2) , . . . , D k , D k+1 , . . . D n+j , D n+(j+1) . In other words, the centroid position C centroid  can be calculated based on the differences in the centroid calculation range. 
     As an example, assuming 1 signal value before and after the nth signal value are taken for determining the centroid position, differences in the centroid calculation range can be used to calculate it. This is proven as follows: 
     
       
         
           
             
               D 
               
                 n 
                 - 
                 1 
               
             
             = 
             
               
                 C 
                 
                   n 
                   - 
                   1 
                 
               
               - 
               
                 C 
                 
                   n 
                   - 
                   2 
                 
               
             
           
         
       
       
         
           
             
               D 
               n 
             
             = 
             
               
                 C 
                 n 
               
               - 
               
                 C 
                 
                   n 
                   - 
                   1 
                 
               
             
           
         
       
       
         
           
             
               D 
               
                 n 
                 + 
                 1 
               
             
             = 
             
               
                 C 
                 
                   n 
                   + 
                   1 
                 
               
               - 
               
                 C 
                 n 
               
             
           
         
       
       
         
           
             
               D 
               
                 n 
                 + 
                 2 
               
             
             = 
             
               
                 C 
                 
                   n 
                   + 
                   2 
                 
               
               - 
               
                 C 
                 
                   n 
                   + 
                   1 
                 
               
             
           
         
       
       
         
           
             
               C 
               
                 base 
                 ⁡ 
                 
                   ( 
                   
                     2 
                     , 
                     2 
                   
                   ) 
                 
               
             
             = 
             
               
                 
                   C 
                   
                     n 
                     - 
                     2 
                   
                 
                 + 
                 
                   C 
                   
                     n 
                     + 
                     2 
                   
                 
               
               2 
             
           
         
       
       
         
           
             
               
                 C 
                 
                   n 
                   - 
                   1 
                 
               
               - 
               
                 C 
                 
                   base 
                   ⁡ 
                   
                     ( 
                     
                       2 
                       , 
                       2 
                     
                     ) 
                   
                 
               
             
             = 
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       C 
                       
                         n 
                         - 
                         1 
                       
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       - 
                       2 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       + 
                       2 
                     
                   
                 
                 2 
               
               = 
               
                 
                   
                     D 
                     
                       n 
                       - 
                       1 
                     
                   
                   - 
                   
                     D 
                     n 
                   
                   - 
                   
                     D 
                     
                       n 
                       + 
                       1 
                     
                   
                   - 
                   
                     D 
                     
                       n 
                       + 
                       2 
                     
                   
                 
                 2 
               
             
           
         
       
       
         
           
             
               
                 C 
                 n 
               
               - 
               
                 C 
                 
                   base 
                   ⁡ 
                   
                     ( 
                     
                       2 
                       , 
                       2 
                     
                     ) 
                   
                 
               
             
             = 
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       C 
                       n 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       - 
                       2 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       + 
                       2 
                     
                   
                 
                 2 
               
               = 
               
                 
                   
                     D 
                     
                       n 
                       - 
                       1 
                     
                   
                   + 
                   
                     D 
                     n 
                   
                   - 
                   
                     D 
                     
                       n 
                       + 
                       1 
                     
                   
                   - 
                   
                     D 
                     
                       n 
                       + 
                       2 
                     
                   
                 
                 2 
               
             
           
         
       
       
         
           
             
               
                 C 
                 
                   n 
                   + 
                   1 
                 
               
               - 
               
                 C 
                 
                   base 
                   ⁡ 
                   
                     ( 
                     
                       2 
                       , 
                       2 
                     
                     ) 
                   
                 
               
             
             = 
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       C 
                       
                         n 
                         + 
                         1 
                       
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       - 
                       2 
                     
                   
                   - 
                   
                     C 
                     
                       n 
                       + 
                       2 
                     
                   
                 
                 2 
               
               = 
               
                 
                   
                     D 
                     
                       n 
                       - 
                       1 
                     
                   
                   + 
                   
                     D 
                     n 
                   
                   + 
                   
                     D 
                     
                       n 
                       + 
                       1 
                     
                   
                   - 
                   
                     D 
                     
                       n 
                       + 
                       2 
                     
                   
                 
                 2 
               
             
           
         
       
       
         
           
             
               C 
               centroid 
             
             = 
             
               
                 
                   
                     
                       
                         
                           X 
                           
                             n 
                             - 
                             1 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               C 
                               
                                 n 
                                 - 
                                 1 
                               
                             
                             - 
                             
                               C 
                               
                                 base 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           X 
                           n 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               C 
                               n 
                             
                             - 
                             
                               C 
                               
                                 base 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                     
                   
                 
                 
                   
                     
                       
                         X 
                         
                           n 
                           + 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             C 
                             
                               n 
                               + 
                               1 
                             
                           
                           - 
                           
                             C 
                             
                               base 
                               ⁡ 
                               
                                 ( 
                                 
                                   2 
                                   , 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     
                       C 
                       
                         n 
                         - 
                         1 
                       
                     
                     - 
                     
                       C 
                       
                         base 
                         ⁡ 
                         
                           ( 
                           
                             2 
                             , 
                             2 
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
                 + 
                 
                   ( 
                   
                     
                       C 
                       n 
                     
                     - 
                     
                       C 
                       
                         base 
                         ⁡ 
                         
                           ( 
                           
                             2 
                             , 
                             2 
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
                 + 
                 
                   ( 
                   
                     
                       C 
                       
                         n 
                         + 
                         1 
                       
                     
                     - 
                     
                       C 
                       
                         base 
                         ⁡ 
                         
                           ( 
                           
                             2 
                             , 
                             2 
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               C 
               centroid 
             
             = 
             
               
                 ( 
                 
                   
                     
                       X 
                       
                         n 
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           D 
                           
                             n 
                             - 
                             1 
                           
                         
                         - 
                         
                           D 
                           n 
                         
                         - 
                         
                           D 
                           
                             n 
                             + 
                             1 
                           
                         
                         - 
                         
                           D 
                           
                             n 
                             + 
                             2 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       X 
                       n 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           D 
                           
                             n 
                             - 
                             1 
                           
                         
                         + 
                         
                           D 
                           n 
                         
                         - 
                         
                           D 
                           
                             n 
                             + 
                             1 
                           
                         
                         - 
                         
                           D 
                           
                             n 
                             + 
                             2 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       X 
                       
                         n 
                         + 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           D 
                           
                             n 
                             - 
                             1 
                           
                         
                         + 
                         
                           D 
                           n 
                         
                         + 
                         
                           D 
                           
                             n 
                             + 
                             1 
                           
                         
                         - 
                         
                           D 
                           
                             n 
                             + 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
                 ) 
               
               / 
               
                 ( 
                 
                   
                     ( 
                     
                       
                         D 
                         
                           n 
                           - 
                           1 
                         
                       
                       - 
                       
                         D 
                         n 
                       
                       - 
                       
                         D 
                         
                           n 
                           + 
                           1 
                         
                       
                       - 
                       
                         D 
                         
                           n 
                           + 
                           2 
                         
                       
                     
                     ) 
                   
                   + 
                   
                     ( 
                     
                       
                         D 
                         
                           n 
                           - 
                           1 
                         
                       
                       + 
                       
                         D 
                         n 
                       
                       - 
                       
                         D 
                         
                           n 
                           + 
                           1 
                         
                       
                       - 
                       
                         D 
                         
                           n 
                           + 
                           2 
                         
                       
                     
                     ) 
                   
                   + 
                   
                     ( 
                     
                       
                         D 
                         
                           n 
                           - 
                           1 
                         
                       
                       + 
                       
                         D 
                         n 
                       
                       + 
                       
                         D 
                         
                           n 
                           + 
                           1 
                         
                       
                       - 
                       
                         D 
                         
                           n 
                           + 
                           2 
                         
                       
                     
                     ) 
                   
                 
                 ) 
               
             
           
         
       
     
     One with ordinary skill in the art can recognize that taking i and j signal values, differences or dual differences respectively before and after the nth signal value as the centroid calculation range can be applied to determine the signal value, difference or dual difference on the centroid position. 
     From the above description, it can be seen that the present invention performs position detection by analyzing sensing information that may not only include originally obtained signal values, differences, or dual differences, but also signal values, differences, or dual differences converted from originally obtained sensing information. By analyzing 1-D or 2-D sensing information on two difference axes (e.g. X and Y axes) that corresponds to the same object, that is, by performing 1-D or 2-D position analysis on two different axes, the positions (or coordinates) of the object on these two axes can be obtained, thereby a 2-D position (or 2-D coordinates) can be constructed. 
     One with ordinary skill in the art can appreciate that operations of the above 1-D position analysis can be performed by said controller  160  or host  170 . 
     Two-Dimension Position Analysis 
     2-D sensing information can be comprised of a plurality of 1-D sensing information, wherein each 1-D sensing information includes sensing information that corresponds to a plurality of first 1-D positions, and each 1-D sensing information corresponds to a second 1-D position. Thus, 2-D position analysis can at least include 1-D position analysis on a plurality of 1-D touch sensitive information, that is, 2-D position analysis can at least include a plurality of 1-D position analysis. 
     In addition, in a first example of the present invention, a first 1-D centroid position of any external object on each first dimensional sensing information is a 2-D position (e.g. 2-D coordinates (first 1-D centroid position, second 1-D position of the first dimensional sensing information)), and can be used to calculate a 2-D centroid position of the object (or center of geometry), wherein the weight of each 1-D centroid position can be a signal value or dual difference of the external object on the corresponding first dimensional sensing information (e.g. one or average or interpolation of two signal values or dual differences closest to the 1-D centroid position on the first dimensional sensing information), or sum of signal values or dual differences of the external object on the corresponding first dimensional sensing information. 
     Thus, 2-D position analysis can perform 1-D position analysis on each first dimensional sensing information, and analyze a 2-D centroid position of each external object based on at least one 2-D position that corresponds to each external object. 
     In addition, in a second example of the present invention, 2-D position analysis may include performing 1-D position analysis on a plurality of 1-D sensing information on a first axis (or a first dimension), respectively, and based on at least one 1-D position corresponding to each external object on the first axis, analyzing a first 1-D centroid position of each external object on the first axis. Similarly, 2-D position analysis may further include performing 1-D position analysis on a plurality of 1-D sensing information on a second axis (or a second dimension), respectively, and based on at least one 1-D position corresponding to each external object on the second axis, analyzing a second 1-D centroid position of each external object on the second axis. By pairing the first 1-D centroid position on the first axis with the second 1-D centroid position on the second axis for each external object, a 2-D position for each external object can be analyzed. 
     In other words, 2-D position analysis may include performing 1-D position analysis on 2-D sensing information on two different axes (e.g. 2-D sensing information on the first axis and 2-D sensing information on the second axis) to obtain a 2-D position for each external object. 
     In addition, in a third example of the present invention, 2-D position analysis may include analyzing 1-D centroid position corresponding to each external object from a plurality of 1-D sensing information on a first axis, and based on a 2-D position corresponding to each 1-D sensing information, determining a 2-D position of each 1-D centroid position that corresponds to each external object on the first axis. 2-D position analysis may further include analyzing 1-D centroid position corresponding to each external object from a plurality of 1-D sensing information on a second axis, and based on a 2-D position corresponding to each 1-D sensing information, determining a 2-D position of each 1-D centroid position that corresponds to each external object on the second axis. 2-D position analysis may further include analyzing a 2-D centroid position based on the 2-D positions of all 1-D centroid positions on the first and second axes that correspond to each external object. 
     One with ordinary skill in the art can appreciate that 2-D sensing information can determine the position of each external object by image processing, for example, using watershed or other image processing techniques. As another example, watershed algorithm can be used to analyze the position of each watershed, and then the centroid position is calculated using sensing information near each watershed position to obtain a more accurate position. 
     In a fourth example of the present invention, a plurality of 1-D sensing information originally obtained can be represented by signal values or dual differences, which construct an image (or matrix) formed from 2-D sensing information. Watershed algorithm or other image processing techniques can be used for position analysis. Alternatively, a “connected component” algorithm can be used, which analyzes connected portions in an image to determine an image of each external object, and further determines the position or the type of the object, such as a finger, a palm or a pen. 
     In a fifth example of the present invention, a plurality of 1-D sensing information originally obtained can be represented by differences, which are then converted into signal values or dual differences, which in turn construct an image (or matrix) formed from 2-D sensing information. Watershed algorithm or other image processing techniques can be used for position analysis. 
     In a sixth example of the present invention, a plurality of 1-D sensing information originally obtained can be represented by differences. By performing position analysis on each 1-D sensing information, the position of each zero-crossing, as well as the signal value or dual difference on the position of each zero-crossing can be determined, thereby constructing an image (or matrix) formed from 2-D sensing information. Watershed algorithm or other image processing techniques can be used for position analysis. 
     The dual difference of a zero-crossing point can be generated by two directly adjacent differences, for example, a zero-crossing is between the k−1th difference and the kth difference, and the dual difference at this zero-crossing point is DD k =D k−1 −D k . The signal value of a zero-crossing point can be generated after converting all differences representing the 1-D sensing information into signal values, or generated based on a plurality of differences closest to the zero-crossing. For example, zero-crossing is closest to the nth signal value, and the average of ith signal value C n-1 , and the jth signal value I n+j  before and after the nth signal value is taken as the base value 
                 C     base   ⁡     (     i   ,   j     )         ⁡     (       C     base   ⁡     (     i   ,   j     )         =         C     n   -   i       +     C     n   +   j         2       )       ,         and   ⁢           ⁢     C   n       -     C     base   ⁡     (     i   ,   j     )           =         2   ⁢     C   n       -     C     n   -   i       -     C     n   +   j         2             
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     In other words, between the n−(i−1)th difference to the (n+j)th difference, the signal value at zero-crossing can be determined. 
     In a seventh example of the present invention, a plurality of 1-D sensing information originally obtained can be represented by signal values and dual differences and are then converted to differences. By performing analysis on each 1-D sensing information, the position of each zero-crossing is determined. In conjunction with the signal value or dual difference on each zero-crossing position, an image (or matrix) formed by 2-D sensing information can be constructed. Watershed algorithm or other image processing techniques can be used for position analysis. 
     In an eighth example of the present invention, when or in the process of obtaining 2-D sensing information on the first axis, 1-D sensing information on the second axis is also obtained. After performing position analysis on the position of the 2-D sensing information on the first axis, the 1-D position or 2-D position of each external object on the first axis can be obtained. In addition, after performing position analysis on the position of the 2-D sensing information on the second axis, the 1-D position of each external object on the second axis can be obtained. The 1-D position on the second axis can be paired up with the 1-D position on the first axis to form a 2-D position, or can be used to replace or correct the position on the second axis in the 2-D position on the first axis. 
     One with ordinary skill in the art can appreciate that the operations of the above 2-D position analysis can be performed by said controller  160  or host  170 . In addition, in an example of the present invention, the 1-D distance or 2-D distance between each 1-D centroid position corresponding to the same touch or approach and at least one other 1-D centroid position corresponding to the same touch or approach is within a threshold. In another example of the present invention, the weight of each 1-D centroid position corresponding to the same touch or approach is greater than a threshold. 
     In the following description, a touch related sensing information can be a touch related sensing information or one of multiple touch related sensing information in a sensing information. Operations related to touch related sensing information can be applied not only to specific touch related sensing information but also to all touch related sensing information of the present invention. 
     In addition, for convenient description, in numerous diagrams and descriptions of the present invention, explanations are given in terms of positive values. One with ordinary skill in the art can appreciate that same principles are applicable to sensing information after having swapped its positive and negative values with each other. The 2-D sensing information proposed by the present invention can be partial sensing information with inner lower values within outer high values, as shown by a basin  510  in  FIGS. 5A and 5B . In an example of the present invention that includes a plurality of dual differences as 2-D sensing information, when an external object touches a large area, in the corresponding touch related sensing information, locations closer to the center of the area will exhibit depressions (smaller values) relative to surrounding higher locations (larger values). In another example of the present invention that includes a plurality of differences as 2-D sensing information in which all negative values are converted to positive values, when the area touched by an external object is larger than a certain degree, in the corresponding touch related sensing information, locations closer to the middle of the area will exhibit depressions (smaller values) relative to surrounding higher locations (larger values). 
     If they are viewed as topographic relief, partial sensing information with lower inner values within higher external values may be regarded as a valley or basin area in the 2-D sensing information, including higher and lower places surrounding a valley or basin. For example, it can be a valley surrounded by one or more mountains, e.g. a basin surrounded by mountains or canyon, or a mountain or a plateau with a depressed top. Sensing information with inner lower values within outer high values can be one or more openings, e.g. a canyon open at both ends. In 2-D sensing information that includes a plurality of dual differences, touch related sensing information may also include a trench surrounding a valley. 
     In contrast, partial sensing information with inner higher values within outer low values may be a hill or a plateau with one or more peaks. Each peak is a partial sensing information with inner higher values within outer low values, wherein the peak are higher locations (larger values) relative to other surrounding lower locations (small values), as illustrated by basins  510  shown in  FIGS. 5A and 5B . In an example of the present invention, a hill with several peaks corresponds to neighboring partial sensing information inner lower values within outer high values. 
     For example, in 2-D sensing information that includes a plurality of signal values, touch related sensing information that contains partial sensing information with inner higher values within outer low values can be a hill (smaller range) or a plateau (larger range). Similarly, 2-D sensing information that includes a plurality of dual differences or differences in which all negative values have been converted into positive values can also include a hill or a plateau. 
     In an example of the present invention, partial sensing information with inner lower values within outer high values and partial sensing information with inner higher values within outer low values are touch related sensing information. In another example of the present invention, a plateau is regarded as a larger hill, and a basin is regarded as a valley without or fewer openings. In yet another example of the present invention, touch related sensing information that is not a valley or a basin is a hill, or that is not a hill is a valley or a basin. 
     In addition, When 2-D sensing information includes a plurality of differences in which all negative values are converted into positive values, two adjacent sensing information with inner higher values within outer low values are regarded as at the same touch related sensing information. 
     In the following descriptions, a basin is used to represent partial sensing information with inner lower values within outer high values, and a hill is used to represent partial sensing information with inner higher values within outer low values for the sake of convenience, and the present invention is not limited to these aspects. One with ordinary skill in the art can appreciate other aspects of partial sensing information with inner lower values within outer high values and partial sensing information with inner higher values within outer low values. 
     In a first embodiment of the present invention, a method for converting sensing information according to the best mode of the present invention is provided, as shown in  FIG. 6 . First, as shown in step  610 , a first sensing information is obtained. Then, in step  620 , each first touch related sensing information of the first sensing information is detected. Thereafter, in step  630 , at least one of the first touch related sensing information of the first sensing information is replaced by a second touch related sensing information to generated a second sensing information. In other words, a second sensing information is generated according to the first sensing information. The second sensing information is generated by replacing each of some or all of the first touch related sensing information of the first sensing information with a second touch related sensing information. 
     In an example of the present invention, touch related sensing information and non-touch related sensing information in the sensing information are determined, and some or all of the touch related sensing information are converted to generate new sensing information, wherein the sensing information can be 1-D sensing information or 2-D sensing information. Non-touch related sensing information can be represented by zero values, and all the values in a zero-value range can be regarded as zero values. Conversely, touch related sensing information includes at least one non-zero value, but not all non-zero values are touch related sensing information, some may be caused by noises. In addition, touch related sensing information may also include at least one zero value, e.g. at least one zero value at a zero-crossing point. 
     In an example of the present invention, accumulation conversion is performed on each first touch related sensing information to be replaced at least once to generate a corresponding second touch related sensing information, wherein the accumulation conversion includes converting each value of first touch related sensing information to be replaced to an accumulation of said value with all the values preceding or following said value. For example, a first touch related sensing information including a plurality of dual differences is converted into a second touch related sensing information including a plurality of differences, or a first touch related sensing information including a plurality of differences is converted into a second touch related sensing information including a plurality of signal values. 
     As another example, a first touch related sensing information including a plurality of dual differences is converted into a second touch related sensing information including a plurality of signal values. Accumulation conversion is performed on each first touch related sensing information to be replaced twice to generate a second touch related sensing information. One of the two accumulation conversions includes converting each value of the first touch related sensing information to be replaced to an accumulation of the value with all the values preceding said value. The other one of the two accumulation conversions includes converting each value of the first touch related sensing information to be replaced to an accumulation of the value with all the values following said value. As mentioned before, accumulation can be incrementing or decrementing. 
     In another example of the present invention, each value of each second sensing information is the difference between a pair of replaced first sensing information. For example, a first touch related sensing information including a plurality of signal values is converted into a second touch related sensing information including a plurality of differences, or a first touch related sensing information including a plurality of differences is converted into a second touch related sensing information including a plurality of dual differences. 
     In yet another example of the present invention, each value of each second sensing information is the difference or sum of a first difference and a second difference of the replaced first sensing information, wherein the first difference is the difference between the prior two values among three values of the replaced first sensing information, and the second difference is the difference between the latter two values among three values of the replaced first sensing information. In addition, these three values can be adjacent or not adjacent to one another. For example, a first touch related sensing information including a plurality of signal values is converted into a second touch related sensing information including a plurality of dual differences. 
     In addition, the first sensing information can be a 2-D sensing information. The first touch related sensing information can be detected by image segmentation, for example, touch related sensing information with inner lower values within outer high values or touch related sensing information with inner higher values within outer low values. The first sensing information can be constituted by one or more 1-D sensing information, each 1-D sensing information can be converted by the methods described earlier to constitute a second sensing information. 
     As described earlier, corresponding to a larger touch range, there may be a plurality of continuous zero values within the first touch related sensing information, for example in places closer to the centroid position or geometric centre, thereby constituting a valley or basin. Accordingly, only those sensing information with inner lower values within outer high values are converted. For example, only the first touch related sensing information that corresponds to basin  510  shown in  FIG. 5A  is converted into a second touch related sensing information with a single peak, such as a second touch related sensing information including a plurality of signal values. In addition, first touch related sensing information with two peaks can be converted, such as a two-peak hill  522  shown in  FIG. 5B . 
     Accordingly, second sensing information may include at least one first touch related sensing information and at least one second touch related sensing information, constituting 1-D sensing information or 2-D sensing information including a plurality of quasi signal values. In an example of the present invention, each touch related sensing information in the second sensing information are all single peaked, wherein the touch related sensing information in the second sensing information may simultaneously include first touch related sensing information and second touch related sensing information. 
     In an example of the present invention, the first sensing information may be generated according to a plurality of differences. All the negative values of these differences are converted into positive values. Replaced first sensing information are portions that make up valleys or basins or two-peak hills. Hills with a single peak can remain intact without replacement. 
     Steps  610  to  630  can be performed by controller  160  or host  170 . The first sensing information can be provided based on signals of a plurality of sensors by the controller  160 . Thereafter, relevant operations described in steps  610  to  630  are then performed by host  170 . Alternatively, the first sensing information can be provided based on signals of a plurality of sensors and relevant operations described in steps  610  to  630  are then performed by the controller  160 . 
     In a second embodiment of the present invention, a method for converting sensing information is provided, as shown in  FIG. 7 . First, as shown in step  710 , a dual-differential sensing information is obtained. The dual-differential sensing information can be a 1-D dual-differential sensing information or 2-D dual-differential sensing information, for example, a 2-D dual-differential sensing information including a plurality of 1-D dual-differential sensing information, or a 1-D dual-differential sensing information including a plurality of dual differences. 
     Next, in step  720 , each touch related sensing information having two peaks at a pair of zero-crossings in each dual-differential sensing information is detected. In the dual-differential sensing information, there may be dual differences (e.g. zero values) that are not touch related, touch related sensing information having a single peak at a pair of zero crossings, and touch related sensing information having two peaks at a pair of zero-crossings. 
     Thereafter, in step  730 , the dual-differential sensing information is converted into sensing information of quasi all signal values, including: converting each touch related sensing information having two peaks at a pair of zero-crossings into signal values. In an example of the present invention, partial conversion of sensing information is performed only at places where touch related sensing information having two peaks at a pair of zero-crossings exists. In other words, after conversion, the sensing information may include dual differences (e.g. zero values) that are not touch related, touch related sensing information having a single peak at a pair of zero crossings, and converted signal values. Since the sensing information after said operation approximates sensing information that are all signal values, in the present invention, it is called a sensing information with quasi all signal values. 
     In addition, said converting of dual-differential sensing information into sensing information with quasi all signal values may further include converting all negative values into zero values so as to remove all negative values at the peripheral of each touch related sensing information. In doing so, when the sensing information is two dimensional, said operation will generate a 2-D sensing information with quasi all signal values, which can be applied to conventional touch-detection method or device for 2-D sensing information with all normal signal values. In an example of the present invention, a method or device for analyzing touches in sensing information that includes a plurality of signal values is provided to analyzing said sensing information with quasi all signal values. For example, when the sensing information with quasi all signal values is a 2-D sensing information, image segmentation methods such as watershed algorithm or connected component algorithm can be used for touch detection. As another example, when the sensing information with quasi all signal values is a 1-D sensing information, a touch location can be determined according to some or all of each touch related sensing information. For example, a threshold is used to identify an area close to the peak in a touch related sensing information, and the location of the peak is further determined, or the centroid position or geometric center is calculated based on some or all of the touch related sensing information. 
     In step  720 , each zero-crossing is identified and paired up. For example, a zero-crossing is between a pair of positive and negative values. According to the sequence of the positive and negative values, a zero-crossing may be one between a negative value followed by a positive value or between a positive value followed by a negative value. Accordingly, the two adjacent zero-crossings can be paired up. For example, each paired zero-crossings may be a preceding zero crossing between a negative value followed by a positive value paired with a following zero crossing between a positive value followed by a negative value, and vice versa. In an example of the present invention, pairing of zero-crossings can be performed at the same time as the searching for zero-crossing. In another example of the present invention, pairing of zero-crossings can be performed after the searching for zero-crossing is completed. 
     By doing so, the number of peaks between each pair of zero-crossings can be determined. As a result, each touch related sensing information having two peaks in a pair of zero-crossings can be determined, and each touch related sensing information having two peaks in a pair of zero-crossings can be further converted into signal values. 
     In an example of the present invention, only touch related sensing information having two peaks in a pair of zero-crossings is converted into signal values, thereby converting 2-D dual-differential sensing information into 2-D sensing information with quasi all signal values. 
     In an example of the present invention, first, a differential sensing information can be obtained. This differential sensing information includes a plurality of differences. Then, the differential sensing information is converted into the dual-differential sensing information, wherein each value of the dual-differential sensing information is the difference or sum of a pair of differences. Thus, the process of converting touch related sensing information having two peaks in a pair of zero-crossings can be achieved by converting a corresponding portion in the differential sensing information into signal values. As a result, accumulation calculation only needs to be performed once, thus achieving better performance. As mentioned earlier, each said signal value corresponds to a signal in one of a plurality of sensors, and each difference corresponds to the signal difference between a pair of sensors in a plurality of sensors. In the present invention, the magnitude of a signal value, a difference and a dual difference corresponds to corresponding portions in signals of the plurality of sensors, respectively. That is, changes in corresponding signals will be reflected in changes in the signal value, the difference and the dual difference. 
     For example, first, a sensing information including a plurality of signal values can be obtained, and the sensing information is converted into a dual-differential sensing information, wherein each value of the dual-differential sensing information is generated based on three signal values. The sensing information is generated based on signals of a plurality of sensors. When the peak of a touch related sensing information in the sensing information becomes larger, the peak of the corresponding touch related sensing information in the dual-differential sensing information also becomes larger. In addition, conversion of each touch related sensing information having two peaks in a pair of zero-crossings into signal values is done by replacing each touch related sensing information having two peaks in a pair of zero-crossings with the corresponding portion in the sensing information. In other words, no accumulation calculation is required. 
     Steps  710  to  730  can be performed by controller  160  or host  170 . For example, a dual-differential sensing information can be provided based on signals of a plurality of sensors by the controller  160 . Thereafter, relevant operations described in steps  710  to  730  are then performed by host  170 . Alternatively, a dual-differential sensing information can be provided based on signals of a plurality of sensors and relevant operations described in steps  710  to  730  are then performed by the controller  160 . In addition, the dual-differential sensing information can be converted from sensing information with quasi all signal values or differential sensing information, relevant operations of which may also be performed by controller  160  or host  170 . 
     The above embodiments are only used to illustrate the principles of the present invention, and they should not be construed as to limit the present invention in any way. The above embodiments can be modified by those with ordinary skill in the art without departing from the scope of the present invention as defined in the following appended claims.