Patent Publication Number: US-8976916-B2

Title: Apparatus and method for receiving dual band RF signals simultaneously

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a U.S. continuation application filed under 37 USC 1.53(b) claiming priority benefit of U.S. Ser. No. 13/242,820 filed in the United States on Sep. 23, 2011, which claims earlier priority benefit, under 35 U.S.C §119, of Korean Patent Application Nos. 10-2010-0092913 filed Sep. 24, 2010, and 10-2011-0022055 filed Mar. 11, 2011, the entirety of which is incorporated by reference herein. 
    
    
     BACKGROUND 
     Exemplary embodiments relate to a radio-frequency (RF) signal receiver used for a wireless communication, and more particularly, relate to a dual band receiver capable of making direct frequency down-conversion and receiving simultaneously two signals transmitted via different frequency bands. 
     In addition to a small-sized RF communication system, a need for a next-generation RF communication receiver with the flexibility, adaptability, and cognitivity is being increased. Such a need may be satisfied by placing an Analog-to-Digital Converter (ADC) to be closer to an antenna and making frequency conversion and demodulation using a Digital Signal Processor (DSP). A next-generation RF communication receiver satisfying such a condition may be a band pass sampling receiver. The band pass sampling receiver may provide excellent functionality in relation to reconfiguration and multi-band/multi-mode receiving. 
     A typical band pass sampling receiver may receive an analog RF signal via an antenna and the received signal is bandpass-filtered through an analog bandpass filter. The bandpass-filtered analog signal may be amplified via a Low Noise Amplifier (LNA) and converted into a digital baseband signal via an Analog-Digital Converter ADC. Since the bandpass sampling receiver does not require an analog device such as a mixer and a local oscillator, it may provide a flexible, low cost, and small wireless communication receiver. However, the typical band pass sampling receiver may receive a single RF signal. Further, the typical bandpass sampling receiver may down-convert a received analog RF signal into a baseband signal of a digital format only when a carrier frequency is integer times of a sample rate in receiving a single RF signal. 
     To simultaneously receive two signals at any frequency band using a general band pass sampling receiver, a sampling rate must be determined such that interference between two signals is not generated at a baseband after digital conversion. However, it is very difficult to determine a sampling rate such that interference between two signals is not generated. Further, a solution of the sampling rate making interference between two signals not generated can&#39;t be often obtained. Accordingly, there is limited to simultaneously receive two RF signals at any frequency band using the general band pass sampling receiver. 
     There may increase a need for a dual band (or, multi-band) receiver which receives simultaneously at least two or more different frequency band signals or at least two or more different communications standards signals, via a single receiver. Further, a communication technique such as a cognitive radio communications system may require a function of receiving any frequency band signal and at the same time, scanning whether a signal exists at another frequency band. However, a general dual band receiver may have a receiver circuit or chip every mode, frequency band, or channel. Accordingly, a receiver may become complicated and expensive. As a result, there is required a receiver which supports a dual band and a dual mode using a single receiver circuit. 
     SUMMARY 
     One aspect of embodiments of the inventive concept is directed to provide a dual band receiver which comprises an analog-to-digital converter configured to convert a dual band analog RF signal into a dual baseband digital signal; and a first signal extractor configured to generate a first path signal and a second path signal from the dual baseband signal and to extract a first baseband signal using a relative sample delay difference between the first and second path signals, wherein the dual baseband signal includes the first baseband signal and a second baseband signal, the first path signal is a signal obtained by sample delay of the dual baseband signal and then down sampling of a resultant signal, and the second path signal is a signal obtained by down sampling of the dual baseband signal without sample delay. 
     In this embodiment, the dual band receiver further comprises a second signal extractor configured to extract the second baseband signal by subtracting the first baseband signal extracted by the first signal extractor from a sample delay result of the second path signal. 
     In this embodiment, the second signal extractor comprises a second delay configured to delay the second path signal generated from the first signal extractor; and a subtractor configured to extract the second baseband signal by subtracting the first baseband signal extracted by the first baseband extractor from a sample delay result from the second delay. 
     In this embodiment, the first signal extractor comprises a first delay configured to delay the dual baseband digital signal converted by the analog-to-digital converter; a first down sampler configured to generate the first path signal by down-sampling a delay result of the first delay; a second down sampler configured to generate the second path signal by down-sampling the dual baseband digital signal converted by the analog-to-digital converter; a first digital filter configured to filter the first path signal; a second digital filter configured to filter the second path signal; and an adder configured to output the first baseband signal by adding a filtering result of the first digital filter and a filtering result of the second digital filter. 
     In this embodiment, the adder is replaced with a subtractor, which outputs the first baseband signal by subtracting a filtering result of the second digital filter from a filtering result of the first digital filter. 
     In this embodiment, a relative time delay difference due to the relative sample delay difference between the first and second path signals is determined according to a sample rate of the analog-to-digital converter, a delay value of the first delay, and down sampling rates of the first and second down samplers. 
     In this embodiment, each of digital filter coefficients of the first and second digital filters is determined by at least one of a carrier frequency of each of first and second analog RF signals, a frequency band location index of each of the first and second analog RF signals, a sampling rate of the analog-to-digital converter, a sample delay value of the first delay, a down sampling rate of each of the first and second down samplers, and a sign determined according to inversion of a spectrum of each of the first and second baseband signals. 
     In this embodiment, each of digital filter coefficients of the first and second digital filters is re-calculated when at least one of a carrier frequency of each of first and second analog RF signals, a frequency band location index of each of the first and second analog RF signals, a sampling rate of the analog-to-digital converter, a sample delay value of the first delay, a down sampling rate of each of the first and second down samplers, and a sign determined according to inversion of a spectrum of each of the first and second baseband signals is changed, and the first and second digital filters are reconfigured based upon the re-calculated digital filter coefficient. 
     In this embodiment, each of the first and second digital filters is determined to satisfy one of equations: S(f)=S A   δ (f)+S B   δ (f)=R 1− (f)+R 1+ (f), S(f)=S A   δ (f)+S B   δ (f)=R 2− (f)+R 2+ (f), S(f)=S A   δ (f)−S B   δ (f)=R 1− (f)+R 1+ (f), and S(f)=S A   δ (f)−S B   δ (f)=R 2− (f)+R 2+ (f), and S(f), S A   δ (f), S B   δ (f), R 1− (f), R 1+ (f), R 2− (f), and R 2+ (f) correspond to a spectrum of the output signal of the adder, a spectrum of the output signal of the first digital filter, a spectrum of the output signal of the second digital filter, a negative frequency spectrum of the first baseband signal, a positive frequency spectrum of the first baseband signal, a negative frequency spectrum of the second baseband signal, and a positive frequency spectrum of the second baseband signal, respectively. 
     In this embodiment, an operating speed of each of the first and second digital filters is determined by a sampling rate of the analog-to-digital converter and a down sampling rate of each of the first and second down samplers. 
     In this embodiment, the first and second down samplers are replaced with first and second decimators which configured to down convert a sampling rate by decimating the first and second path signals, each of the first and second decimators including a pre-filter and a down sampler. 
     In this embodiment, the second digital filter is replaced with a sample delay and a gain adjustment logic. 
     Another aspect of embodiments of the inventive concept is directed to provide a dual band signal receiving method of a dual band receiver which comprises converting a dual band analog RF signal into a dual baseband digital signal using a single analog-to-digital converter; generating a first path signal and a second path signal from the dual baseband signal; and extracting a first baseband signal using a relative sample delay difference between the first and second path signals, wherein the dual baseband signal includes the first baseband signal and a second baseband signal, the first path signal is a signal obtained by sample-delaying the dual baseband signal and then down sampling a resultant signal, and the second path signal is a signal obtained by down-sampling the dual baseband signal without sample delay. 
     In this embodiment, the dual band signal receiving method further comprises sample-delaying the second path signal while the first baseband signal is extracted; and extracting the second baseband signal by subtracting the first baseband signal from a sample delay result of the second path signal. 
     In this embodiment, extracting a first baseband signal comprises sample-delaying the dual baseband digital signal converted by the analog-to-digital converter; generating the first path signal by down-sampling the sample delay result; generating the second path signal by down-sampling the dual baseband digital signal converted by the analog-to-digital converter; filtering the first path signal using a first digital filter; filtering the second path signal using a second digital filter; and extracting the first baseband signal by adding a filtering result of the first digital filter and a filtering result of the second digital filter 
     In this embodiment, each of digital filter coefficients of the first and second digital filters is determined by at least one of a carrier frequency of each of first and second analog RF signals, a frequency band location index of each of the first and second analog RF signals, a sampling rate of the analog-to-digital converter, a sample delay value of the first delay, a down sampling rate for generating the first and second path signals, and a sign determined according to inversion of a spectrum of each of the first and second baseband signals. 
     In this embodiment, each of digital filter coefficients of the first and second digital filters is re-calculated when at least one of a carrier frequency of each of first and second analog RF signals, a frequency band location index of each of the first and second analog RF signals, a sampling rate of the analog-to-digital converter, a sample delay value of the first delay, a down sampling rate for generating the first and second path signals, and a sign determined according to inversion of a spectrum of each of the first and second baseband signals is changed, and the first and second digital filters are reconfigured based upon the re-calculated digital filter coefficient. 
     In this embodiment, each of the first and second digital filters is determined to satisfy one of equations: S(f)=S A   δ (f)+S B   δ (f)=R 1− (f)+R 1+ (f), S(f)=S A   δ (f)+S B   δ (f)=R 2− (f)+R 2+ (f), S(f)=S A   δ (f)−S B   δ (f)=R 1− (f)+R 1+ (f), and S(f)=S A   δ (f)−S B   δ (f)=R 2− (f)+R 2+ (f), and S(f), S A   δ (f), S B   δ (f), R 1− (f), R 1+ (f), R 2− (f), and R 2+ (f) correspond to a spectrum of the output signal of the adder, a spectrum of the output signal of the first digital filter, a spectrum of the output signal of the second digital filter, a negative frequency spectrum of the first baseband signal, a positive frequency spectrum of the first baseband signal, a negative frequency spectrum of the second baseband signal, and a positive frequency spectrum of the second baseband signal, respectively. 
     In this embodiment, an operating speed of each of the first and second digital filters is determined by a sampling rate of the analog-to-digital converter and the down sampling rate. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The above and other objects and features will become apparent from the following description with reference to the following figures, wherein like reference numerals refer to like parts throughout the various figures unless otherwise specified, and wherein 
         FIG. 1  is a diagram illustrating a dual band receiver according to an exemplary embodiment of the inventive concept. 
         FIG. 2  is a diagram illustrating analog spectrums of two signals at any frequency band. 
         FIG. 3  is a diagram illustrating a dual band receiver according to another exemplary embodiment of the inventive concept. 
         FIG. 4  is a diagram illustrating a dual band signal extracting unit according to an exemplary embodiment of the inventive concept. 
         FIG. 5  is a diagram illustrating a spectrum of a first path signal output from a first down sampler illustrated in  FIG. 4 . 
         FIG. 6  is a diagram illustrating a spectrum of a second path signal output from a second down sampler illustrated in  FIG. 4 . 
         FIGS. 7 to 9  are diagrams illustrating a spectrum of a second path signal output from a second down sampler illustrated in  FIG. 4 . 
         FIG. 10  is a diagram illustrating a spectrum of a first baseband signal output from an adder illustrated in  FIG. 4 . 
         FIG. 11  is a diagram illustrating a spectrum of a first baseband signal output from a subtractor illustrated in  FIG. 4 . 
         FIG. 12  is a diagram illustrating first and second digital up/down converters  81  and  82  according to an exemplary embodiment of the inventive concept. 
         FIG. 13  is a diagram illustrating a first signal extractor and a dual band signal extracting unit according to another exemplary embodiment of the inventive concept. 
         FIGS. 14 and 15  are diagrams illustrating a first signal extractor and a dual band signal extracting unit according to other exemplary embodiments of the inventive concept. 
         FIGS. 16 and 17  are diagrams illustrating a first signal extractor and a dual band signal extracting unit according to still other exemplary embodiments of the inventive concept. 
         FIG. 18  is a flowchart illustrating a dual baseband signal extracting method of a dual band receiver according to an exemplary embodiment of the inventive concept. 
         FIG. 19  is a flowchart illustrating a reconfiguring method of a digital filter of a dual band receiver according to an exemplary embodiment of the inventive concept. 
     
    
    
     DETAILED DESCRIPTION 
     The inventive concept is described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the inventive concept are shown. This inventive concept may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the inventive concept to those skilled in the art. In the drawings, the size and relative sizes of layers and regions may be exaggerated for clarity. Like numbers refer to like elements throughout. 
     It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the inventive concept. 
     Spatially relative terms, such as “beneath”, “below”, “lower”, “under”, “above”, “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” or “under” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary terms “below” and “under” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. In addition, it will also be understood that when a layer is referred to as being “between” two layers, it can be the only layer between the two layers, or one or more intervening layers may also be present. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the inventive concept. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     It will be understood that when an element or layer is referred to as being “on”, “connected to”, “coupled to”, or “adjacent to” another element or layer, it can be directly on, connected, coupled, or adjacent to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to”, “directly coupled to”, or “immediately adjacent to” another element or layer, there are no intervening elements or layers present. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this inventive concept belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and/or the present specification and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
       FIG. 1  is a diagram illustrating a dual band receiver according to an exemplary embodiment of the inventive concept. A dual band receiver may be formed of a band pass sampling receiver. 
     Referring to  FIG. 1 , a dual band receiver  100 _ 1  may include an antenna  10 , first and second band pass filters  21  and  22 , an adder  30 , an Analog-Digital Converter (ADC)  50 , a dual band signal extracting unit  60 , first and second digital up/down converters  81  and  82 , and a Digital Signal Processor (DSP)  90 . 
     The antenna  10  may receive an analog RF signal which is transmitted in wireless. The input analog RF signal to the antenna  10  may include at least two or more frequency bands signals. The first and second band pass filters  21  and  22  may be formed of a wideband band pass filter which filters a wideband signal. The first band pass filter  21  may be designed such that a pass band is limited to a first bandwidth B1. The first band pass filter  21  may generate a first analog RF signal AR 1  having the first bandwidth B1 and a first carrier frequency fc1. The second band pass filter  22  may be designed such that a pass band is limited to a second bandwidth B2. The second band pass filter  22  may generate a second analog RF signal AR 2  having the second bandwidth B2 and a second carrier frequency f c2 . In an embodiment, pass bands and pass bandwidths B1 and B2 of the first and second band pass filters  21  and  22  may have a fixed value or may be adjusted to another value. To this end, the first and second band pass filters  21  and  22  may be formed of a tunable band pass filter. 
     The adder  30  may add a filtering result of the first band pass filter  21  and a filtering result of the second band pass filter  22  to generate a dual band analog RF signal AR12. 
       FIG. 2  is a diagram illustrating analog spectrums of two signals at any frequency band. 
     Referring to  FIG. 2 , it is assumed that a first analog RF signal AR 1  has a first carrier frequency f c1  and a first signal bandwidth B1. Further, it is assumed that a second analog RF signal AR 2  has a second carrier frequency f c2  and a second signal bandwidth B2. In  FIG. 2 , R AR1+ (f) may indicate a positive frequency spectrum of the first analog RF signal AR 1 , and R AR1− (f) may indicate a negative frequency spectrum of the first analog RF signal AR 1 . R AR2+ (f) may indicate a positive frequency spectrum of the second analog RF signal AR 2 , and R AR2− (f) may indicate a negative frequency spectrum of the second analog RF signal AR 2 . 
     Returning to  FIG. 1 , the ADC  50  may convert the dual band analog RF signal AR 12  provided from the adder  30  into a dual baseband digital signal DR 12 . For example, the dual band analog RF signal AR 12  provided via the adder  30  may be converted to the dual baseband digital signal DR 12  having a sampling rate of f S  via the ADC  50 . The dual baseband digital signal DR 12  converted via the ADC  50  may correspond to a sum of a first baseband signal DR 1  having a first bandwidth B1 and a second baseband signal DR 2  having a second bandwidth B2. 
     The dual band signal extracting unit  60  may extract the first baseband signal DR 1  and the second baseband signal DR 2  from the dual baseband digital signal DR 12  output from the ADC  50 . To this end, the dual band signal extracting unit  60  may include a first signal extractor  61  and a second signal extractor  62 . The first signal extractor  61  may generate a first path signal DR A  and a second path signal DR B  from the dual baseband digital signal DR 12 . The first path signal DR A  may be a signal obtained by down-sampling the sample-delayed signal DR 12     —   D of the dual baseband digital signal DR 12 , and the second path signal DR B  may be a signal obtained by down sampling the dual baseband digital signal DR 12  without sampling delay. 
     The first signal extractor  61  may be configured to exactly extract a wanted baseband signal (e.g., the first baseband signal DR 1 ) by removing aliasing between the first and second baseband signals DR 1  and DR 2  using a relative phase difference due to a relative sampling delay difference between the first and second path signals DR A  and DR B . 
     The second signal extractor  62  may be configured to extract a second baseband signal DR 2  using the first baseband signal DR 1  extracted by the first signal extractor  61  and the second path signal DR B . 
     With the dual band signal extracting unit  60  of the inventive concept, although interference between the first and second baseband signals DR 1  and DR 2  is generated at a baseband due to the aliasing, it is possible to extract the first and second baseband signals DR 1  and DR 2  perfectly and simultaneously. Thus, a dual band and a dual-mode signal receiving may be supported using a single receiver circuit. In particular, since a receiver circuit of the inventive concept uses a single ADC, it is possible to implement a simple and high-integrity receiver. Accordingly, a cost may be lowered, and power consumption may be reduced. 
     With the above-described configuration, the dual band receiver of the inventive concept may receive at least two or more signals having any frequency band and signal bandwidth using a single receiver circuit. Further, in a communication system such as a cognitive radio communication system, it is possible to provide a function of receiving any frequency band signal and at the same time, scanning whether a signal exists at another frequency band. 
     The dual band signal extracting unit  60  may be configured to selectively extract either one of the first and second baseband signals DR 1  and DR 2  from the dual baseband signal DR 12  output from the ADC  50 . In this case, an actual signal extracting operation may be performed only by the first signal extractor  61 . 
     The first and second baseband signals DR 1  and DR 2  extracted from the dual band signal extracting unit  60  may be provided to the first and second digital up/down converters  81  and  82  such that digital frequency up/down conversion is made. A conversion result of the first and second baseband signals DR 1  and DR 2  may be provided to the DSP  90  such that baseband signal processing (e.g., demodulation) is made. 
       FIG. 3  is a diagram illustrating a dual band receiver according to another exemplary embodiment of the inventive concept. 
     Referring to  FIG. 3 , a dual band receiver  100 _ 2  may further include a track and holder  40  in addition to components of a dual band receiver  100 _ 1  illustrated in  FIG. 1 . The remaining components of the dual band receiver  100 _ 2  other than the track and holder  40  may be substantially identical to those in  FIG. 1 , and description thereof is thus omitted. 
     The track and holder  40  called a sample-and-holder may function as an input-sampling circuit. Although not illustrated in  FIG. 3 , the track and holder  40  may be formed of an analog switch and a sampling switch. If the sampling switch is closed, the track and holder  40  may operate at a track mode for tracking an input signal. If the sampling switch is open, the track and holder  40  may operate at a hold mode, in which the track and holder  40  keeps a last instantaneous value of the input using the sampling capacitor. With operations of the track and hold modes executed by the track and holder  40 , an analog-digital conversion bandwidth to be processed by an ADC  50  may be increased. 
     With the dual band receivers  100 _ 1  and  100 _ 2  described in relation to  FIGS. 1 and 3 , the dual band receivers  100 _ 1  and  100 _ 2  may make direct down conversion of a dual band analog RF signal, located at any band, into a baseband using a single ADC  50 . Although interference due to aliasing is generated at a baseband, it is possible to remove the aliasing via a dual band signal extracting unit  60 . Accordingly, at least two or more analog RF signals at any frequency band can be received at the same time. This may mean that at least two or more frequency band signals are received using a single receiver circuit or chip including the single ADC  50  without independently implementing a receiver circuit or chip every frequency band or channel. As a result, since a dual band and a dual mode are supported using a single receiver circuit, it is possible to simplifying a receiver circuit and to lower a fabrication cost thereof. 
     The dual band signal extracting unit  60  illustrated in  FIGS. 1 and 3  is not limited to this disclosure. For example, the dual band signal extracting unit  60  can be modified or changed variously, which will be more fully described with reference to embodiments to be described later. Further, a first signal extractor can be modified or changed variously. 
       FIG. 4  is a diagram illustrating a dual band signal extracting unit according to an exemplary embodiment of the inventive concept. 
     Referring to  FIG. 4 , a dual band signal extracting unit  60 _ 1  may include a first signal extractor  61 _ 1  and a second signal extractor  62 . 
     The first signal extractor  61 _ 1  may generate a first path signal DR A  through sample delay and down sampling and a second path signal DR B  through only down sampling without sample delay, using a dual baseband digital signal DR 12  output from an ADC  50 . Herein, the first path signal DR A  may be a signal obtained by forcing sample delay and down sampling to the dual baseband digital signal DR 12 . The second path signal DR B  may be a signal obtained by forcing down sampling to the dual baseband digital signal DR 12 . 
     The first signal extractor  61 _ 1  may extract a first baseband signal DR 1  via first and second digital filters  615  and  616  and an adder  619 . The first and second digital filters  615  and  616  may be designed depending upon a relative phase difference due to a relative sample delay difference between the first and second path signals DR A  and DR B . The second signal extractor  62  may receive the second path signal DR B  from the first signal extractor  61 _ 1 , and may extract a second baseband signal DR 2  by subtracting the first baseband signal DR 1 , being an output signal of the first signal extractor  61 _ 1 , from a signal obtained by sample-delaying the second path signal DR B  from the first signal extractor  61 _ 1 . 
     The first and second signal extractors  61 _ 1  and  62  will be more fully described below. 
     The first signal extracting unit  61 _ 1  may include a first delay  610 , first and second down samplers  611  and  612 , first and second digital filters  615  and  616 , and an adder  619 . 
     The first delay  610  may delay by D-sample a dual baseband digital signal DR 12  output from an ADC  50 . Herein, a sample delay value D may have an integer value larger than 0 and smaller than a down sample rate N. A signal delayed via the first delay  610  may be down-sampled such that a sample rate becomes 1/N via the first down sampler  611 . The first path signal DR A  being an output signal of the first down sampler  611  may be provided to the first digital filter  615 . 
     The dual baseband digital signal DR 12  output from the ADC  50  may be provided to the second down sampler  612  without sample delay to generate the second path signal DR B . The dual baseband digital signal DR 12  output from the ADC  50  may be down-sampled such that a sample rate becomes 1/N via the second down sampler  612 . The second path signal DR B  output from the second down sampler  612  may be provided to the second digital filter  616  and the second signal extractor  62 . Sample rates f S  of signals output from the first and second down samplers  611  and  612  may be f S /N. With the above-described configuration of the inventive concept, a relative sample delay difference of D/N may exist between the first and second path signals DR A  and DR B  output from the first and second down samplers  611  and  612 . 
       FIG. 5  is a diagram illustrating a spectrum of a first path signal output from a first down sampler illustrated in  FIG. 4 .  FIG. 6  is a diagram illustrating a spectrum of a second path signal output from a second down sampler illustrated in  FIG. 4 .  FIGS. 7 to 9  are diagrams illustrating a spectrum of a first path signal output from a first down sampler illustrated in  FIG. 4 . 
     Spectrums illustrated in  FIGS. 5 to 9  may correspond to a spectrum within a first Nyquist zone. Referring to  FIGS. 5 to 9 , it is understood that the aliasing between first and second baseband signals DR 1  and DR 2 , constituting a first path signal DR A , and first and second baseband signals DR 1  and is generated at a baseband. That is, the first and second baseband signals DR 1  and DR 2  may cause mutual interference at a baseband. Nevertheless, a dual band receiver  100 _ 1 / 100 _ 2  of the inventive concept may remove the aliasing between the first and second baseband signals DR 1  and DR 2  to exactly extract the first and second baseband signals DR 1  and DR 2 , respectively. There will be described a configuration for extracting the first and second baseband signals DR 1  and DR 2  when the aliasing is generated between first and second baseband signals DR 1  and DR 2 . Signal characteristics of the first and second path signals DR A  and DR B  of the inventive concept are as follows. 
     As described above, the first path signal DR A  may be a signal obtained by D-sample delaying an output signal of an ADC  50  and then down sampling it. On the other hand, the second path signal DR B  may be a signal obtained by down sampling an output signal of the ADC  50  without sample delay. As a result, the first path signal DR A  may be a signal obtained by delaying the second path signal DR B  by D/f s (=D/Nf s ′). Thus a spectrum of the first path signal DR A  may be identical to one of the second path signal DR B  except for the effect of a group delay due to a relative time delay difference between the first and the second path signals DR A  and DR B . 
     The effect of the group delay due to a time delay of the first baseband signal DR 1  included in the first path signal DR A  may be expressed by: 
               ⅇ       jθ     1   -       ⁡     (   f   )         =       ⅇ       j2π   ⁢           ⁢     s   1     ⁢     n   1     ⁢   D     N       ⁢     ⅇ     -       j2π   ⁢           ⁢     D   f         Nf   s   l                   
on a spectrum component shifted from a negative frequency band and
 
               ⅇ       jθ     1   +       ⁡     (   f   )         =       ⅇ     -       j2π   ⁢           ⁢     s   1     ⁢     n   1     ⁢   D     N         ⁢     ⅇ     -       j2π   ⁢           ⁢     D   f         Nf   s   l                   
on a spectrum component shifted from a positive frequency band.
 
     The effect of the group delay due to a time delay of the second baseband signal DR 2  included in the second path signal DR B  may be expressed by: 
               ⅇ       jθ     2   -       ⁡     (   f   )         =       ⅇ       j2π   ⁢           ⁢     s   2     ⁢     n   2     ⁢   D     N       ⁢     ⅇ     -       j2π   ⁢           ⁢     D   f         N   ⁢           ⁢     f   s   ′                     
on a spectrum component shifted from a negative frequency band and
 
               ⅇ       jθ     2   +       ⁡     (   f   )         =       ⅇ     -       j2π   ⁢           ⁢     s   2     ⁢     n   2     ⁢   D     N         ⁢     ⅇ     -       j2π   ⁢           ⁢     D   f         N   ⁢           ⁢     f   s   ′                     
on a spectrum component shifted from a positive frequency band. Herein, s 1  and s 2  may indicate signs determined according to whether spectrums of the first and second baseband signals DR 1  and DR 2  are inverted. s 1  and s 2  may have a sign of −1 when a spectrum is inverted and a sign of +1 when no spectrum is inverted. Accordingly, (s 1 , s 2 ) may be one of four cases, that is, (+1, +1), (+1, −1), (−1, +1), and (−1, −1), which correspond to spectrums illustrated in  FIGS. 5 ,  7 ,  8 , and  9 , respectively.
 
     For example, in  FIG. 5 , there is illustrated the case that spectrums of the first and second baseband signals DR 1  and DR 2  are not inverted, that is, (s 1 , s 2 )=(+1, +1). In  FIG. 7 , there is illustrated the case that a spectrum of the first baseband signal DR 1  is not inverted and a spectrum of the second baseband signal DR 2  is inverted, that is, (s 1 , s 2 )=(+1, −1). In  FIG. 8 , there is illustrated the case that a spectrum of the first baseband signal DR 1  is inverted and a spectrum of the second baseband signal DR 2  is not inverted, that is, (s 1 , s 2 )=(−1, +1). In  FIG. 9 , there is illustrated the case that spectrums of the first and second baseband signals DR 1  and DR 2  are inverted, that is, (s 1 , s 2 )=(−1, −1). 
     Herein, spectrum inversion may mean that a spectrum component shifted from a positive frequency is located at a negative frequency at a baseband and a spectrum component shifted from a negative frequency is located at a positive frequency at a baseband. n 1  and n 2  may be frequency band location indexes of first and second analog RF signals AR 1  and AR 2 , and may have an integer value. The n 1  and n 2  may be determined as follows by a sampling rate f S  (=f S /N) at outputs of first and second down samplers  611  and  612  and signal carrier frequencies f c1  and f c2 . 
     
       
         
           
             
               
                 
                   
                     n 
                     1 
                   
                   = 
                   
                     round 
                     [ 
                     
                       
                         f 
                         
                           c 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         
                           f 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           s 
                         
                         N 
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     n 
                     2 
                   
                   = 
                   
                     round 
                     [ 
                     
                       
                         f 
                         
                           c 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       
                         
                           f 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           s 
                         
                         N 
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In equations, round may indicate a round. 
     The first and second baseband signals DR 1  and DR 2  may be separated by designing first and second digital filters  615  and  616  using a relationship between the first path signal DR A  and the second path signal DR B  and affection of a relative sample delay between the first and second baseband signals DR 1  and DR 2  included in the first path signal DR A . In an embodiment, the first and second digital filters  615  and  616  may be formed of a Finite Impulse Response (FIR) filter. 
     With the inventive concept, the first or second baseband signal DR 1  or DR 2  may be extracted from an added signal of the first and second baseband signal DR 1  and DR 2 , using the first and second digital filters  615  and  616  and an adder  619 . If a dual band receiver of the inventive concept selectively receives one baseband signal (e.g., the first baseband signal DR 1 ), another baseband signal (e.g., the second baseband signal DR 2 ) being not extracted may be removed because it is recognized to be an interference signal. 
     The first and second digital filters  615  and  616  may be designed according to the following manner. 
     A frequency response of the first digital filter  615  may be expressed by H A (f), and a frequency response of the second digital filter  616  may be expressed by H B (f). 
     Referring to  FIGS. 5 to 9 , a spectrum of the first path signal DR A  and a spectrum of the second path signal DR B  within a first Nyquist zone at outputs of the first and second down samplers  611  and  612  may be expressed by the following equations. 
                     R   A   δ     =       f   s     ⁢     ′   ⁡     [               R     1   -       ⁡     (   f   )       ⁢     ⅇ         j2πs   1     ⁢     n   1     ⁢   D     N       ⁢     ⅇ       -       j2πD   f       Nf   s   ′         +                       R     1   +       ⁡     (   f   )       ⁢     ⅇ     -         j2πs   1     ⁢     n   1     ⁢   D     N         ⁢     ⅇ       -       j2πD   f       Nf   s   ′         +                       R     2   -       ⁡     (   f   )       ⁢     ⅇ         j2πs   2     ⁢     n   2     ⁢   D     N       ⁢     ⅇ       -       j2πD   f       Nf   s   ′         +                       R     2   +       ⁡     (   f   )       ⁢     ⅇ     -         j2πs   2     ⁢     n   2     ⁢   D     N         ⁢     ⅇ     -       j2πD   f       Nf   s   ′                   ]                 (   3   )                 R   N   δ   =f   s   ′{R   1− ( f )+ R   1+ ( f )+ R   2− ( f )+ R   2− ( f )}  (4)
 
     Herein, R 1− (f) and R 1+ (f) may indicate negative and positive frequency components of the first baseband signal DR 1  on a first signal path, and R 2− (f) and R 2+ (f) may indicate negative and positive frequency components of the second baseband signal DR 2  on the second signal path. 
     The negative frequency spectrum components of R 1− (f) and R 2− (f) and the positive frequency spectrum components of R 1+ (f) and R 2+ (f) of the first and second baseband signals DR 1  and DR 2  on the second signal path may be a baseband replica spectrum that a negative frequency and a positive frequency spectrum component of first and second analog RF signals is frequency shifted. 
     A spectrum of the first path signal DR A  passing through the first digital filter  615  and a spectrum of the second path signal DR B  passing through the second digital filter  616  may be expressed by the following equations respectively. 
                       S   A   δ     ⁡     (   f   )       =         f   s       ′   ⁢   H     A       ⁡     (   f   )       ⁡     [               R     1   -       ⁡     (   f   )       ⁢     ⅇ       j2π   ⁢           ⁢     s   1     ⁢     n   1     ⁢   D     N       ⁢     ⅇ       -       j2π   ⁢           ⁢     D   f         Nf   s   ′         +                       R     1   +       ⁡     (   f   )       ⁢     ⅇ     -       j2π   ⁢           ⁢     s   1     ⁢     n   1     ⁢   D     N         ⁢     ⅇ       -       j2π   ⁢           ⁢     D   f         Nf   s   ′         +                       R     2   -       ⁡     (   f   )       ⁢     ⅇ       j2π   ⁢           ⁢     s   2     ⁢     n   2     ⁢   D     N       ⁢     ⅇ       -       j2π   ⁢           ⁢     D   f         Nf   s   ′         +                       R     2   +       ⁡     (   f   )       ⁢     ⅇ     -       j2π   ⁢           ⁢     s   2     ⁢     n   2     ⁢   D     N         ⁢     ⅇ     -       j2π   ⁢           ⁢     D   f         Nf   s   ′                   ]               (   5   )                 S   B   δ ( f )= f   s   ′H   B ( f ){ R   1− ( f )+ R   1+ ( f )+ R   2− ( f )+ R   2− ( f )}  (6)
 
     A filtering result of the first path signal DR A  passing through the first digital filter  615  and a filtering result of the second path signal DR B  passing through the second digital filter  616  may be added via the adder  619 . 
     A spectrum of an output signal of the adder  619  illustrated in  FIG. 4  may be expressed by the following equation.
 
 S ( f )= S   A   δ ( f )+ S   B   δ ( f )  (7)
 
     In order to obtain the first baseband signal DR 1  by removing the second baseband signal DR 2  via the first signal extractor  61 _ 1 , the first and second digital filters  615  and  616  may be designed to satisfy the following equation.
 
 S ( f )= S   A   δ ( f )+ S   B   δ ( f )= R   1− ( f )+ R   1+ ( f )  (8)
 
     In relation to the equation 8, H A (f) corresponding to a frequency response of the first digital filter  615  may be expressed by the following equations 9-1 to 9-3, and H B (f) corresponding to a frequency response of the second digital filter  616  may be expressed by the following equations 10-1 to 10-3. 
     
       
         
           
             
               
                 
                   
                     
                       
                         H 
                         A 
                       
                       ⁡ 
                       
                         ( 
                         
                           f 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       { 
                       
                         
                           ( 
                           
                             
                               - 
                               
                                 ⅇ 
                                 
                                   - 
                                   
                                     
                                       j 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         s 
                                         2 
                                       
                                       ⁢ 
                                       
                                         n 
                                         2 
                                       
                                       ⁢ 
                                       D 
                                     
                                     N 
                                   
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 
                                   j 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     D 
                                     f 
                                   
                                 
                                 
                                   Nf 
                                   s 
                                   ′ 
                                 
                               
                             
                           
                           ) 
                         
                         / 
                         
                           
                             f 
                             s 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             
                               1 
                               - 
                               
                                 ⅇ 
                                 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       π 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             
                                               s 
                                               1 
                                             
                                             ⁢ 
                                             
                                               n 
                                               1 
                                             
                                           
                                           - 
                                           
                                             
                                               s 
                                               2 
                                             
                                             ⁢ 
                                             
                                               n 
                                               2 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     D 
                                   
                                   N 
                                 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       - 
                       
                         f 
                         s 
                         ′ 
                       
                     
                     &lt; 
                     f 
                     &lt; 
                     0 
                   
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         H 
                         A 
                       
                       ⁡ 
                       
                         ( 
                         
                           f 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       { 
                       
                         
                           ( 
                           
                             
                               - 
                               
                                 ⅇ 
                                 
                                   - 
                                   
                                     
                                       j 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       π 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         s 
                                         2 
                                       
                                       ⁢ 
                                       
                                         n 
                                         2 
                                       
                                       ⁢ 
                                       D 
                                     
                                     N 
                                   
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 
                                   j 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     D 
                                     f 
                                   
                                 
                                 
                                   Nf 
                                   s 
                                   ′ 
                                 
                               
                             
                           
                           ) 
                         
                         / 
                         
                           
                             f 
                             s 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             
                               1 
                               - 
                               
                                 ⅇ 
                                 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       π 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             
                                               s 
                                               1 
                                             
                                             ⁢ 
                                             
                                               n 
                                               1 
                                             
                                           
                                           - 
                                           
                                             
                                               s 
                                               2 
                                             
                                             ⁢ 
                                             
                                               n 
                                               2 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     D 
                                   
                                   N 
                                 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     0 
                     &lt; 
                     f 
                     &lt; 
                     
                       
                         f 
                         s 
                         ′ 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         
                           H 
                           A 
                         
                         ⁡ 
                         
                           ( 
                           
                             f 
                             ′ 
                           
                           ) 
                         
                       
                       = 
                       0 
                     
                     , 
                     otherwise 
                   
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         
                           H 
                           B 
                         
                         ⁡ 
                         
                           ( 
                           
                             f 
                             ′ 
                           
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           1 
                           / 
                           
                             
                               f 
                               s 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   ⅇ 
                                   
                                     
                                       
                                         j2π 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               
                                                 s 
                                                 1 
                                               
                                               ⁢ 
                                               
                                                 n 
                                                 1 
                                               
                                             
                                             - 
                                             
                                               
                                                 s 
                                                 2 
                                               
                                               ⁢ 
                                               
                                                 n 
                                                 2 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                       ⁢ 
                                       D 
                                     
                                     N 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     , 
                     
                       
                         - 
                         
                           
                             f 
                             s 
                             ′ 
                           
                           2 
                         
                       
                       &lt; 
                       f 
                       &lt; 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         
                           H 
                           B 
                         
                         ⁡ 
                         
                           ( 
                           
                             f 
                             ′ 
                           
                           ) 
                         
                       
                       = 
                       
                         { 
                         
                           1 
                           / 
                           
                             
                               f 
                               s 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   ⅇ 
                                   
                                     
                                       
                                         j2π 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               
                                                 s 
                                                 1 
                                               
                                               ⁢ 
                                               
                                                 n 
                                                 1 
                                               
                                             
                                             - 
                                             
                                               
                                                 s 
                                                 2 
                                               
                                               ⁢ 
                                               
                                                 n 
                                                 2 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                       ⁢ 
                                       D 
                                     
                                     N 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     , 
                     
                       0 
                       &lt; 
                       f 
                       &lt; 
                       
                         
                           f 
                           s 
                           1 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         
                           H 
                           B 
                         
                         ⁡ 
                         
                           ( 
                           
                             f 
                             ′ 
                           
                           ) 
                         
                       
                       = 
                       0 
                     
                     , 
                     otherwise 
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     An impulse response h A (t) of the first digital filter  615  expressed by the following equation 11 may be obtained by inverse Fourier transforming the above equation 9-1, 9-2, or 9-3 corresponding to a frequency response of the first digital filter  615 , and an impulse response h B (t) of the second digital filter  616  expressed by the following equation 12 may be obtained by inverse Fourier transforming the above equation 10-1, 10-2, or 10-3 corresponding to a frequency response of the second digital filter  616 .
 
 h   A ( t )= A/B   (11)
 
     Herein, A may be expressed by 
                 -     sin   ⁡     (     2   ⁢   π   ⁢           ⁢     s   1     ⁢     n   1     ⁢     D   N       )         +     sin   ⁡     (     2   ⁢   π   ⁢           ⁢     s   2     ⁢     n   2     ⁢     D   N       )       +     sin   ⁡     [       2   ⁢   π   ⁢           ⁢     s   1     ⁢     n   1     ⁢     D   N       +     π   ⁡     (       D   N     +       f   s   ′     ⁢   t       )         ]       -     sin   ⁡     [       2   ⁢   π   ⁢           ⁢     s   2     ⁢     n   2     ⁢     D   N       +     π   ⁡     (       D   N     +       f   s   ′     ⁢   t       )         ]         ,         
and B may be expressed by
 
             2   ⁢       π   ⁡     [     1   -       cos   ⁡     [     2   ⁢     π   ⁡     (         s   1     ⁢     n   1       -       s   2     ⁢     n   2         )       ⁢     D   N       ]       ⁡     [       D   N     +       f   s   ′     ⁢   t       ]         ]       .             h   B ( t )= A/B   (12)
 
     Herein, A may be expressed by 
                 sin   ⁡     (     π   ⁢           ⁢     f   s   ′     ⁢   t     )       +     sin   ⁡     (     2   ⁢     π   ⁡     (         s   1     ⁢     n   1       -       s   2     ⁢     n   2         )       ⁢     D   N       )       -     sin   ⁡     [       π   ⁢           ⁢     f   s   ′     ⁢   t     +     2   ⁢     π   ⁡     (         s   1     ⁢     n   1       -       s   2     ⁢     n   2         )       ⁢     D   N         ]         ,         
and B may be expressed by:
 
     
       
         
           
             2 
             ⁢ 
             
               π 
               ⁡ 
               
                 [ 
                 
                   1 
                   - 
                   
                     cos 
                     ⁡ 
                     
                       [ 
                       
                         2 
                         ⁢ 
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   s 
                                   1 
                                 
                                 ⁢ 
                                 
                                   n 
                                   1 
                                 
                               
                               - 
                               
                                 
                                   s 
                                   2 
                                 
                                 ⁢ 
                                 
                                   n 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           D 
                           N 
                         
                       
                       ] 
                     
                   
                 
                 ] 
               
             
             ⁢ 
             
               f 
               s 
               ′ 
             
             ⁢ 
             
               t 
               . 
             
           
         
       
     
     The impulse response h A (t) of the first digital filter  615  and the impulse response h B (t) of the second digital filter  616  may be implemented by a digital filter having a operating speed of f s ′ (=f s /N). A coefficient of a digital filter may be re-calculated according to RF frequency bands of two signals, and the digital filter may be reconfigured using the re-calculated filter coefficient. As a result, dual band signals at any frequency band may be received at the same time. Further, as understood from the above equations 11 and 12, a condition of 
                 (         s   1     ⁢     n   1       -       s   2     ⁢     n   2         )     ⁢     D   N       ≠   m         
(m being an integer) must be satisfied. To this end, values of f s , D, and N may be changed to satisfy the condition of
 
                 (         s   1     ⁢     n   1       -       s   2     ⁢     n   2         )     ⁢     D   N       ≠     m   .           
Reconfiguration of a digital filter of the inventive concept may be more fully described in relation to  FIG. 19 .
 
     In a case wherein a condition of 
                 (         s   1     ⁢     n   1       -       s   2     ⁢     n   2         )     ⁢     D   N       =     k   2           
(k being a positive integer) is satisfied, the equation 9-1 to 9-3 and 10-1 to 10-3 may be rewritten by the following equations.
 
     
       
         
           
             
               
                 
                   
                     
                       
                         H 
                         A 
                       
                       ⁡ 
                       
                         ( 
                         
                           f 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       { 
                       
                         
                           - 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅇ 
                           
                             - 
                             
                               
                                 j2π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                                 ⁢ 
                                 
                                   n 
                                   2 
                                 
                                 ⁢ 
                                 D 
                               
                               N 
                             
                           
                         
                         ⁢ 
                         
                           
                             ⅇ 
                             
                               
                                 j2π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   D 
                                   f 
                                 
                               
                               
                                 Nf 
                                 s 
                                 ′ 
                               
                             
                           
                           / 
                           
                             f 
                             s 
                             ′ 
                           
                         
                       
                       } 
                     
                   
                   , 
                   
                     
                       - 
                       
                         
                           f 
                           s 
                           ′ 
                         
                         2 
                       
                     
                     &lt; 
                     f 
                     &lt; 
                     0 
                   
                 
               
               
                 
                   ( 
                   
                     13 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         H 
                         A 
                       
                       ⁡ 
                       
                         ( 
                         
                           f 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       { 
                       
                         
                           - 
                           C 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅇ 
                           
                             - 
                             
                               
                                 j2π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                                 ⁢ 
                                 
                                   n 
                                   2 
                                 
                                 ⁢ 
                                 D 
                               
                               N 
                             
                           
                         
                         ⁢ 
                         
                           
                             ⅇ 
                             
                               
                                 j2π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   D 
                                   f 
                                 
                               
                               
                                 Nf 
                                 s 
                                 ′ 
                               
                             
                           
                           / 
                           
                             f 
                             s 
                             ′ 
                           
                         
                       
                       } 
                     
                   
                   , 
                   
                     0 
                     &lt; 
                     f 
                     &lt; 
                     
                       
                         f 
                         s 
                         ′ 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     13 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         H 
                         A 
                       
                       ⁡ 
                       
                         ( 
                         
                           f 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     0 
                   
                   , 
                   otherwise 
                 
               
               
                 
                   ( 
                   
                     13 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         H 
                         B 
                       
                       ⁡ 
                       
                         ( 
                         
                           f 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       C 
                       / 
                       
                         f 
                         s 
                         ′ 
                       
                     
                   
                   , 
                   
                     
                       - 
                       
                         
                           f 
                           s 
                           ′ 
                         
                         2 
                       
                     
                     &lt; 
                     f 
                     &lt; 
                     
                       
                         f 
                         s 
                         ′ 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Herein, C=1/√{square root over (2{1−cos(2π(s 1 n 1 −s 2 n 2 )D/N})}=½. 
     An impulse response h A (t) of the first digital filter  615  expressed by the following equation 16 may be obtained by inverse Fourier transforming the above equation 13-1, 13-2, or 13-3 corresponding to a frequency response of the first digital filter  615 , and an impulse response h B (t) of the second digital filter  616  expressed by the following equation 16 may be obtained by inverse Fourier transforming the above equation 14 corresponding to a frequency response of the second digital filter  616 . 
     
       
         
           
             
               
                 
                   
                     
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     Herein, C=1/(√(2{1−cos  (2π   (s   ↓ 1n ↓ 1−s   ↓ 2n ↓ 2)D/N} )=½). 
     Since an operating speed of the second digital filter  616  expressed by the equation 16 is f s ′, an impulse response h B (t) of the second digital filter  616  may have a constant C when t=0 and a value of 0 when t≠0. Accordingly, the second digital filter  616  may be replaced with a sample delay and a gain adjustment logic providing a gain of C (refer to FIGS. 14 to 17). Herein, a sample delay operation of the sample delay may be performed to compensate a delay time from a time where a first down sampler  611  outputs a down sampling result to a time where the first digital filter  615  outputs a filtering result signal. 
     A technique of designing the first and second digital filters  615  and  616  is described using an example that the first signal extract  61 _ 1  removes a second baseband signal DR 2  to obtain the first baseband signal DR 1 . 
     However, the first signal extract  61 _ 1  can remove the first baseband signal DR 1  to extract the second baseband signal DR 2 . In this case, the first and second digital filters  615  and  616  may be designed to satisfy the following equation 17.
 
 S ( f )= S   A   δ ( f )+ S   B   δ ( f )= R   2− ( f )+ R   2+ ( f )  (17)
 
     A digital filter designing method, in which the first signal extractor  61 _ 1  removes the first baseband signal DR 1  to extract the second baseband signal DR 2 , may be identical to that, in which the first signal extractor  61 _ 1  removes the second baseband signal DR 2  to extract the first baseband signal DR 1 , expressed by the equations 9 to 16, and description thereof is thus omitted. 
     Accordingly, if the first and second digital filters  615  and  616  are designed to satisfy the above equation 17, the first signal extractor  61 _ 1  may extract the second baseband signal DR 2 , and the second signal extractor  62  may extract the first baseband signal DR 1 . 
       FIG. 10  is a diagram illustrating a spectrum of a first baseband signal output from an adder illustrated in  FIG. 4 .  FIG. 11  is a diagram illustrating a spectrum of a first baseband signal output from a subtractor illustrated in  FIG. 4 . 
     Referring to  FIGS. 4 and 10 , a second baseband signal DR 2  may be removed from an output of a first signal extractor  61 _ 1  by adding a filtering result of a first path signal DR A  passing through a first digital filter  615  and a filtering result of a second path signal DR B  passing through a second digital filter  616  via an adder  619 . Accordingly, the first baseband signal DR 1  may remain as an output signal of the first signal extractor  61 _ 1 . 
     Referring to  FIGS. 4 and 11 , a second signal extractor  62  may be configured to include a second delay  620  and a subtractor  629 . 
     The second delay  620  may receive a second path signal DR B  from a second down sampler  612  of the first signal extractor  61 _ 1  to delay it by Q sample. A sample delay operation of the second delay  620  may be made to compensate a delay time from a time when the first down sampler  611  (or, a second down sampler  612 ) outputs a down sampling result to a time when the adder  619  outputs the first baseband signal DR 1 . That is, a sample delay value Q of the second delay  629  may be determined according to a time taken to extract the first baseband signal DR 1  from the first path signal DR A  (or, the second path signal DR B ). 
     An output signal of the second delay  620  may be a signal obtained by Q sample delaying the second path signal DR B  being an output signal of the second down sampler. The second path signal DR B  may include the first baseband signal DR 1  and the second baseband signal DR 2 . Accordingly, the subtractor  629  may acquire the second baseband signal DR 2  by subtracting the first baseband signal DR 1  extracted by the first signal extractor  61 _ 1  from the delayed signal DR B     —   D of the second path signal DR B . 
     An embodiment of the above-described dual band receiver may be related to the case that the first signal extractor  61 _ 1  uses the adder  619  to extract the first or second baseband signal DR 1  or DR 2 . In another embodiment, the adder  619  can be replaced with a subtractor to extract the first or second baseband signal DR 1  or DR 2  using the first signal extractor  61 _ 1 . In this case, in order to extract the first or second baseband signal DR 1  or DR 2  using the first signal extractor  61 _ 1 , the first and second digital filters  615  and  616  may be designed to satisfy the following equations 18 and 19.
 
 S ( f )= S   A   δ ( f )− S   B   δ ( f )= R   1− ( f )+ R   1+ ( f )  (18)
 
 S ( f )= S   A   δ ( f )− S   B   δ ( f )= R   2− ( f )+ R   2+ ( f )  (19)
 
     Herein, the equation 18 may correspond to the case that the first signal extractor  61 _ 1  removes the second baseband signal DR 2  to extract the first baseband signal DR 1 . The equation 19 may correspond to the case that the first signal extractor  61 _ 1  removes the first baseband signal DR 1  to extract the second baseband signal DR 2 . 
     The above-described design method of the first and second digital filters  615  and  616  according this embodiment may be identical to that expressed by the equations 3 to 16, and description thereof is thus omitted. 
       FIG. 12  is a diagram illustrating first and second digital up/down converters  81  and  82  according to an exemplary embodiment of the inventive concept. 
     Referring to  FIGS. 1 and 12 , a first baseband signal DR 1  extracted by a first signal extractor  61 _ 1  may be provided as an input signal of a first digital up/down converter  81 , and the first digital up/down converter  81  may convert the first baseband signal DR 1  into a first complex signal. 
     A second baseband signal DR 2  extracted by a second signal extractor  62  may be provided as an input signal of a second digital up/down converter  82 , and the second digital up/down converter  82  may convert the second baseband signal DR 2  into a second complex signal. 
     Referring to  FIG. 12 , the first and second digital up/down converters  81  and  82  may be configured to perform a digital up/down conversion operation and a low pass filtering operation, respectively. 
     The digital up/down conversion operation on a first baseband signal s 1 (t) may be expressed by the following equation 20, and may be followed by the low pass filtering operation. And the digital up/down conversion operation on a second baseband signal s 2 (t) may be expressed by the following equation 21, and may be followed by the low pass filtering operation.
 
 r   1 ( t )= s   1 ( t )cos(2 πs   1   f   if     1     t )− js   1 ( t )sin(2 πs   1   f   if     1     t )  (20)
 
 r   2 ( t )= s   2 ( t )cos(2 πs   2   f   if     2     t )− js   2 ( t )sin(2 πs   2   f   if     2     t )  (21)
 
     Herein, s 1  and s 2  may indicate signs determined according to whether spectrums of the first and second baseband signals DR 1  and DR 2  are inverted. f if     1    and f if     2    may be expressed by the following equations 22 and 23, respectively.
 
 f   if     1     =f   c1   −n   1   f   s ′  (22)
 
 f   if     2     =f   c2   −n   2   f   s ′  (22)
 
     With the digital up/down conversion operations of the first and second digital up/down converters  81  and  82  expressed by the equations 20 and 21, the first and second baseband signals DR 1  and DR 2  may be converted into the first and second complex signals, respectively. Image components of the first and second complex signals may be removed by digital low pass filtering, respectively, and resultant signals may be provided to a digital signal processor  90 . 
     The above-described dual band signal extracting unit  60 _ 1  is not limited to this disclosure. In particular, a first signal extractor  61 _ 1  extracting a first baseband signal DR 1  may be modified or changed variously. Various embodiments of the dual band signal extracting unit  60 _ 1  and the first signal extractor  61 _ 1  will be more fully described below. 
       FIG. 13  is a diagram illustrating a first signal extractor and a dual band signal extracting unit according to another exemplary embodiment of the inventive concept. 
     Referring to  FIG. 13 , a first down sampler  611  in  FIG. 4  may be replaced with a first decimator  613 , and a second down sampler  612  in  FIG. 4  may be replaced with a second decimator  614 . The first and second decimators  613  and  614  may be formed of a pre-digital filter and a down sampler, and may adjust a sample rate of an output signal so as to become 1/N to an input signal (N being an integer of 2 or more). Pre-filtering and down sampling operations of the first and second decimators  613  and  614  may correspond to down sampling operations of the first and second down samplers  611  and  612 . 
     In  FIG. 13 , the remaining elements of the first signal extractor  61 _ 2  other than the first and second decimators  613  and  614  may be identical to those in  FIG. 4 . The remaining elements of the dual band signal extracting unit  60 _ 2  other than the first and second decimators  613  and  614  may be identical to those in  FIG. 4 , and description thereof is thus omitted. 
       FIGS. 14 and 15  are diagrams illustrating a first signal extractor and a dual band signal extracting unit according to other exemplary embodiments of the inventive concept. 
     Referring to  FIGS. 14 and 15 , a second digital filter  616  in  FIG. 4  can be replaced with a third delay and gain adjustment logic  618  providing a predetermined gain. The third delay  617  may be configured to delay a second path signal DR B  by Y sample. A sample delay operation of the third delay  617  may be made to compensate a delay time from a time when a first down sampler  611  outputs a down sampling result to a time when a first digital filter  615  outputs a filtering result signal. In this case, a time taken when the first digital filter  615  outputs a filtering result signal may correspond to a time taken at a filtering operation of the first digital filter  615 . Accordingly, a sample delay value Y of the third delay  617  may be determined according to a time taken at a filtering operation of the first digital filter  615  of a first signal extractor  61 _ 1 . For example, in a case where the first digital filter  615  of the first signal extractor  61 _ 1  is implemented by a FIR filter having a length of L, a FIR filtering operation may cause a time delay by 
               [     L   2     ]     ,         
so that a sample delay value is determined to become
 
               [     L   2     ]     .         
Herein, └X┘ may mean the largest integer of an integer less than X. The gain adjustment logic  618  may provide a gain of C to a sample delay result DR B     —   D of the third delay  617 . An output signal MR B     —   D of the gain adjustment logic  618  may be provided to an adder  619 . A second baseband signal component R 2− (f) and R 2+ (f) may be removed from an output of the first signal extractor  61 _ 3  by adding a filtering result S A  of the first digital filter  615  and the output signal MR B     —   D of the gain adjustment logic  618  using the adder  619 , and a first baseband signal component R 1− (f) and R 1+ (f) may remain as an output signal of the first signal extractor  61 _ 3 .
 
     Interconnection of the third delay  617  and the gain adjustment logic  618  is not limited to a specific shape, and can be changed to be exchanged mutually as illustrated in  FIGS. 14 and 15 . 
     In a case where the first signal extractor  61 _ 3 / 61 _ 4  has the third delay  617  and the gain adjustment logic  618  instead of a second digital filter  616 , a circuit structure may become more simple. This may mean that a size and a fabrication cost of a receiver are reduced. 
     In  FIGS. 14 and 15 , the remaining elements of the first signal extractor  61 _ 3 / 61 _ 4  other than the third delay  617  and the gain adjustment logic  618  may be identical to that  61 _ 1  in  FIG. 4 . Therefore, the remaining elements of a dual band signal extracting unit  60 _ 3 / 60 _ 4  other than the third delay  617  and the gain adjustment logic  618  may be identical to those in  FIG. 4 , and description thereof is thus omitted. 
       FIGS. 16 and 17  are diagrams illustrating a first signal extractor and a dual band signal extracting unit according to still other exemplary embodiments of the inventive concept. 
     Referring to  FIGS. 16 and 17 , a first down sampler  611  in  FIG. 4  may be replaced with a first decimator  613 , and a second down sampler  612  in  FIG. 4  may be replaced with a second decimator  614 . The first and second decimators  613  and  614  may be formed of a pre-digital filter and a down sampler, and may adjust a sample rate of an output signal so as to become 1/N to an input signal (N being an integer of 2 or more). Pre-filtering and down sampling operations of the first and second decimators  613  and  614  may correspond to down sampling operations of the first and second down samplers  611  and  612 . 
     A second digital filter  616  in  FIG. 4  may be replaced with a third delay  617  and gain adjustment logic  618  providing a gain corresponding to a constant C. 
     Interconnection of the third delay  617  and the gain adjustment logic  618  is not limited to a specific shape, and can be changed to be exchanged mutually as illustrated in  FIGS. 16 and 17 . 
     In  FIGS. 16 and 17 , the remaining elements of a first signal extractor  61 _ 5 / 61 _ 6  other than the third delay  617  and the gain adjustment logic  618  may be identical to that  61 _ 1  in  FIG. 4 . Therefore, the remaining elements of a dual band signal extracting unit  60 _ 5 / 60 _ 6  other than the third delay  617  and the gain adjustment logic  618  may be identical to those in  FIG. 4 , and description thereof is thus omitted. 
       FIG. 18  is a flowchart illustrating a dual baseband signal extracting method of a dual band receiver according to an exemplary embodiment of the inventive concept. A dual baseband signal extracting method illustrated in  FIG. 18  may be applied to dual band signal extracting units  60  and  60 _ 1  to  60 _ 6  and dual band receivers  100 ,  100 _ 1 , and  100 _ 2  including the same. 
     Referring to  FIG. 18 , a dual band receiver  100 / 100 _ 1 / 100 _ 2  according to the inventive concept may receive an analog RF signal via an antenna  10 . The received analog RF signal may include at least two or more analog RF signals. A first band pass filter  21  may be designed such that a pass band is limited to a first bandwidth B1. The first band pass filter  21  may generate a first analog RF signal AR 1  having the first bandwidth B1 and a first carrier frequency f c1 , as a filtering result. A second band pass filter  22  may be designed such that a pass band is limited to a second bandwidth B2. The second band pass filter  22  may generate a second analog RF signal AR 2  having the second bandwidth B2 and a second carrier frequency f c2 , as a filtering result. Filtering results of the first and second band pass filters  21  and  22  may be added by an adder  30  such that a dual band analog RF signal AR 12  is generated. The above-described operations may be performed in step S 1000 . 
     In step S 1100 , the dual band analog RF signal AR 12  may be converted into a dual baseband digital signal DR 12  via an ADC  50 . 
     In step S 1200 , a first signal extractor  61 / 61 _ 1  to  61 _ 6  in a dual band signal extracting unit  60 / 60 _ 1  to  60 _ 6  may generate a first path signal DR A , being sample delayed, and a second path signal DR B , being not sample delayed, from the dual baseband digital signal DR 12 . In an embodiment, the first path signal DR A  may be generated by sample-delaying an output signal DR 12  of the ADC  50  via a first delay  610  and down-sampling it via a first down sampler  611 . The second path signal DR B  may be generated by down-sampling the output signal DR 12  of the ADC  50  without sample delay. Herein, the first and second down sampler  611  and  612  may perform down sampling operations such that a sample rate becomes 1/N, and a sample rate f S  of each of the first and second path signals DR A  and DR B  output from the first and second down samplers  611  and  612  may be f S /N. With the above description, a sample delay difference of D/N may exist between the first and second path signals DR A  and DR B  output from the first and second down samplers  611  and  612 . 
     In an embodiment, the first and second down samplers  611  and  612  can be replaced with first and second decimators  613  and  614  (refer to  FIGS. 13 ,  16 , and  17 ) such that a sample rate of an output signal is adjusted to become 1/N to an input signal via a pre-filtering and a down sampling operation. 
     The first path signal DR A  generated from the first down sampler  611  may be provided to a first digital filter  615 . The second path signal DR B  generated from the second down sampler  612  may be provided to a second digital filter  616  (or, a third delay  617 ) and a second delay  620  of a second signal extractor. 
     In step S 1300 , the first signal extractor  61 / 61 _ 1  to  61 _ 6  may extract a first baseband signal DR 1  using a phase difference (i.e., corresponding to a sample delay difference of D/N) generated from a relative sample delay between the first and second path signals DR A  and DR B . Extraction of the first baseband signal DR 1  may be made by a first digital filter  615 , a second digital filter  616  (or, a third delay  617  and gain adjustment logic  618 ), and an adder  619  of the first signal extractor  61 / 61 _ 1  to  61 _ 6 . The first and second digital filters  615  and  616  may be implemented by a Finite Impulse Response (FIR) filter. The second digital filter  616  can be replaced with the third delay  617  and the gain adjustment logic  618  (refer to  FIGS. 14 to 17 ). A second baseband signal component R 2− (f) and R 2+ (f) may be removed from an output of the first signal extractor  61 / 61 _ 1  to  61 _ 6  by adding a filtering result S A  of the first digital filter  615  and a filtering result S B  of the second digital filter  616  (in case of  FIGS. 14 to 17 , an output of the gain adjustment logic  618  instead of the filtering result S B  of the second digital filter  616 ) via the adder  619 . As a result, a first baseband signal component R 1− (f) and R 1+ (f) may remain as an output signal of the first signal extractor  61 _ 3 . 
     While the first baseband signal DR 1  is extracted in step S 1300 , in step S 1400 , the second signal extractor  62  may Q sample delay the second path signal DR B  via a second delay  620 . The Q sample delay operation of the second delay  620  may be performed to compensate a delay time from a time when a first down sampler  611  outputs the first and second path signals DR A  and DR B  and a time when the first adder  619  outputs the first baseband signal DR 1 . Herein, an output signal DR B     —   D of the second delay  620  may be a Q sample delayed version of the second path signal DR B . The output signal DR B     —   D of the second delay  620  may include the baseband signal component R 1− (f) and R 1+ (f) and the second baseband signal component R 2− (f) and R 2+ (f). 
     Accordingly, in step S 1500 , a second baseband signal DR 2  may be acquired by subtracting the first baseband signal DR 1  being an output signal of the first signal extractor  61 _ 3  from the output signal DR B     —   D of the second delay  620 . This may be made by a subtractor  629  included in the second signal extractor  62 . 
     The first baseband signal DR 1  extracted in step S 1300  and the second baseband signal DR 2  extracted in step S 1500  may be provided to first and second digital up/down converters  81  and  82 , respectively such that digital up/down conversion is made. This may be made in step S 1600 . In step S 1700 , digital up/down conversion results of the first baseband signal DR 1  and the second baseband signal DR 2  may be provided to a digital signal processor  90  such that baseband signal processing is made (e.g., demodulation). 
     With the dual baseband signal extracting method of a dual band receiver of the inventive concept, although the first and second baseband signals DR 1  and DR 2  are aliased at a baseband, such aliasing may be removed, and the first and second baseband signals DR 1  and DR 2  may be extracted perfectly. Accordingly, it is possible to simultaneously receive dual band signals with respect to all signals having any frequency band and a signal bandwidth using the dual band receiver according to the inventive concept. 
     A dual band and a dual mode may be supported using a single receiver circuit without including an independent receiver circuit every frequency band or communication mode. The excellent performance may be provided from various aspects such as a fabrication cost, power consumption, a receiver size, and an integration as compared with a general receiver where a receiver circuit is replaced according to a frequency band and a communication mode and an independent receiver circuit is implemented every band and communication mode to support a dual band and a dual mode. 
     The dual band receiver according to the inventive concept may receive at least two or more signals having any frequency band and signal bandwidth using a single receiver circuit. Further, in case of a communication manner such as a cognitive radio communication system, it is possible to provide a function of receiving any frequency band signal and at the same time scanning whether a signal exists at another frequency band. 
     The inventive concept is exemplarily described using such a case that first and second baseband signals are all extracted. However, the number of baseband signals received by the dual band receiver of the inventive concept can be changed. For example, the dual band receiver of the inventive concept may be configured to selectively extract at least one baseband signal from an input signal including at least two or more signals. In this case, first and second digital filters  615  and  616  and an adder  619  may provide a function of selectively extracting at least one baseband signal. 
       FIG. 19  is a flowchart illustrating a reconfiguring method of a digital filter of a dual band receiver according to an exemplary embodiment of the inventive concept. A reconfiguring method of a digital filter illustrated in  FIG. 19  may be applied to dual band signal extracting units  60  and  60 _ 1  to  60 _ 6  and dual band receivers  100 ,  100 _ 1 , and  100 _ 2  including the same. 
     The dual band receiver according to the inventive concept is not limited to a signal of a specific frequency band. That is, the dual band receiver according to the inventive concept may receive two RF signals at any frequency band. Functions of first and second digital filters  615  and  616  expressed by the equations 9 to 16 may be determined according to frequency bands (or, carrier frequencies) of two analog RF signals. Accordingly, the digital filters  615  and  616  may be flexibly reconfigured such that the dual band receiver according to the inventive concept may receive any frequency band signal. 
     Filter coefficients of the first and second digital filters  615  and  616  may be re-calculated when at least one of a sample rate of an ADC  50 , frequency band location indexes of first and second analog RF signals, a sample delay value of a first delay  610 , down sample rates of first and second down samplers  611  and  612 , and signs determined according to inversion of spectrums of first and second baseband signals DR 1  and DR 2  is changed. The digital filters  615  and  616  may be flexibly reconfigured according to the re-calculated digital filter coefficients of the first and second digital filters  615  and  616 . 
     Referring to  FIG. 19 , in step S 200 , filtering parameters, that is, the first and second carrier frequencies f c1  and f c2 , a sample rate f S , a sample delay value D of the first delay  610 , and down sample rates N of the first and second down samplers  611  and  612  may be established. 
     Herein, the first carrier frequency f c1  may indicate a carrier frequency of the first analog RF signal AR 1  constituting a dual band analog RF signal AR 12 . The second carrier frequency f c2  may indicate a carrier frequency of the second analog RF signal AR 2  constituting the dual band analog RF signal AR 12 . The sample rate f S  may mean a sample rate when the dual band analog RF signal AR 12  is converted to a dual baseband digital signal DR 12  via an ADC  50 . 
     A dual band signal extracting unit  60  may extract a first baseband signal DR 1  and a second baseband signal DR 2  from the ADC  50  output signal. The dual band signal extracting unit  60  may include a first signal extractor  61 , which extracts the first baseband signal DR 1  from the dual band analog RF signal AR 12 , and a second signal extractor  62  which extracts the second baseband signal DR 2  in response to the first baseband signal DR 1  extracted by the first signal extractor  61 . 
     The first signal extractor  61  may generate a first path signal DR A , being sample delayed, and a second path signal DR B , being not sample delayed, from the dual band analog RF signal AR 12  provided from the ADC  50 . 
     The first delay  610  may delay the dual base band signal DR 12  by D sample, to generate a delayed signal DR 12     —   D. The delayed signal DR 12     —   D may be down-sampled such that a sample rate becomes 1/N via the first down sampler  611 . As a result, the first path signal DR A  may be generated. The first path signal DR A  may be provided to the first digital filter  615 . Herein, N may be an integer more than 1, and a sample delay D may have an integer value larger than 0 and smaller than a down sample rate N. 
     The dual baseband signal DR 12 , which does not pass through the first delay  610 , may be down-sampled such that a sample rate becomes 1/N via the second down sampler  612 . As a result, the second path signal DR B  may be generated. The second path signal DR B  may be provided to the second signal extractor  62  and the second digital filter  616 . 
     Herein, a sample rate f S  of each of the first and second path signals DR A  and DR B  may be f S /N. With the above-described configuration, 
     a relative sample delay difference of D/N (i.e., a relative time delay difference of D/(Nf S ′) may exist between the first and second path signals DR A  and DR B  output from the first and second down samplers  611  and  612 . 
     In step S 2100 , parameters n 1 , n 2 , s 1 , and s 2  to be applied to the first and second digital filters  615  and  616  may be calculated. 
     Herein, n 1  and n 2  may be frequency band location indexes of first and second analog RF signals, and may have a integer value. The n 1  and n 2  may be calculated based upon the above equations 1 and 2. s 1  and s 2  may indicate signs determined whether spectrums of the first and second baseband signals are inverted. s 1  and s 2  may have a sign of −1 when a spectrum is inverted and a sign of +1 when no spectrum is inverted. Accordingly, (s 1 , s 2 ) may be one of four cases, that is, (+1, +1), (+1, −1), (−1, +1), and (−1, −1), which correspond to spectrums illustrated in  FIGS. 5 ,  7 ,  8 , and  9 , respectively. 
     After parameters are established and calculated, in step S 2200 , coefficients of the first and second digital filters  615  and  616  may be calculated using the calculated parameters. Coefficients of the first and second digital filters  615  and  616  may be calculated using filter functions expressed by the above equations 9 to 16. 
     After filter coefficients are calculated, in step S 2300 , the first and second digital filters  615  and  616  may be reconfigured using the calculated filter coefficients. 
     Coefficients of the first and second digital filters  615  and  616  may be re-calculated according to RF frequency bands of two signals, and the first and second digital filters  615  and  616  may be reconfigured using the re-calculated filter coefficients. As a result, frequency bands of signals simultaneously received by the dual band receiver of the inventive concept are not limited to a specific band, may be extended to a dual band signal at all frequency bands. 
     The dual band receiver according to the inventive concept may receive at least two or more signals having any frequency band and signal bandwidth using a single receiver circuit. Further, in case of a communication manner such as a cognitive radio communication system, it is possible to provide a function of receiving any frequency band signal and at the same time scanning whether a signal exists at another frequency band. 
     The above-disclosed subject matter is to be considered illustrative, and not restrictive, and the appended claims are intended to cover all such modifications, enhancements, and other embodiments, which fall within the true spirit and scope. Thus, to the maximum extent allowed by law, the scope is to be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be restricted or limited by the foregoing detailed description.