Patent Publication Number: US-7210627-B2

Title: Method and apparatus for authenticating a magnetic fingerprint signal using an adaptive analog to digital converter

Description:
RELATED APPLICATIONS 
   This application is a continuation-in-part of U.S. patent application Ser. No. 10/997,150, filed Nov. 24, 2004 now abandoned which is a continuation application of U.S. patent application Ser. No. 09/324,741, filed Jun. 3, 1999 now U.S. Pat. No. 6,899,269 which is a continuation-in-part of U.S. patent application Ser. No. 09/120,816, filed Jul. 22, 1998 now U.S. Pat. No. 6,098,881, all of which are hereby incorporated by reference as if set forth in full herein. 

   BACKGROUND OF THE INVENTION 
   The present invention relates generally to systems and processes involving the utilization of repeatable magnetic stripe characteristics to authenticate magnetic stripe-bearing documents. 
   Various forms of cards bearing a magnetic stripe (e.g., magstripe cards) have long been used for a variety of different purposes. Such cards are currently used in large numbers, for example in the forms of credit cards, debit cards, transportation/transit/airline tickets, I.D. cards and so on. Typically the magnetic strips/stripes (also referred to as the magstripes) of such cards carry recorded data relating to the use of the card, and in some instances relating to the assigned user or owner of the card. 
   Although magnetic stripe cards are widely and successfully used in commerce and industry, counterfeiting and modification of cards (along with other forms of documents) are common occurrences, resulting in great losses. Consequently, the ability to reliably verify the authenticity of documents generally, and specifically of magnetic stripe cards is important. 
   Over the years, there have been numerous proposals for verifying documents, including the authenticity of magnetic stripe cards. A substantial number of prior proposals have been based on a concept of using certain magnetic characteristics of the magnetic stripe to identify cards. In that regard, it has been determined that generally, the magnetic stripes of individual cards possess inherent, substantially unique, remanent magnetic characteristics that can be repeatedly sensed. These characteristics have been recognized as contributing a noise-like component to sensed signals that is present in repeated sensings. Thus, along with the signal component representing recorded data, the repeatable noise-like signal component also appears. Just as the magnetic characteristics of individual stripes are distinct, the repeatable noise-like signals are virtually unique among cards. Accordingly, it has been proposed to employ such magnetic characteristics and the resulting repeatable noise-like signals (referred to as the “remanent noise characteristic”) as a basis for authenticating individual magnetic stripe cards. U.S. Pat. Nos. 5,365,586, 5,428,683, 5,546,462, 5,587,654, 5,625,689, 5,740,244, 5,920,628, and 5,959,794 (the disclosures of all of which are incorporated herein by reference) issued to Indeck et al. chronicle the invention of the use of remanent noise characteristics to authenticate various magnetic media. In addition, U.S. Pat. No. 6,098,881 issued to Deland et al., the entire disclosure of which is incorporated herein by reference, discloses using “relatively flat” portions representative of the remanent noise characteristics of the stripe that are located between magnetic transitions to authenticate individual documents. 
   A major consideration relating to the extensive use of magnetic characteristics for card recognition involves the number of cards in a system. For example, a typical reader must readily accommodate many billions of individual cards operating in combination with millions of individual processing units. In extensive systems, effectiveness and low error rate becomes exceedingly important, particularly in the realms of financial and security transactions, as are involved with bank cards. 
   SUMMARY OF THE INVENTION 
   In general, the system of the present invention uses remanent noise characteristics to provide a magnetic characteristic verification technique that operates effectively and reliably in widespread commercial and industrial applications. 
   Embodiments of the invention select repeatable remanent noise characteristic signals for the magnetic medium (resulting from specific characteristic features of the magstripe) from defined areas of a digitally-recorded magnetic stripe. These remanent noise characteristic signals are also referred to as a magnetic fingerprint due to their repeatable and deterministic characteristics that are virtually unique for each magnetic stripe. The defined areas are located between magnetic data transitions. Such defined areas of the stripe may be magnetized to a level of saturation and would ideally produce relatively flat and stable remanent noise characteristic signals. The signal sensed includes a remanent noise signal component in combination with a recorded data signal component, where the magnitude of the recorded data signal component is much greater than the magnitude of the remanent noise signal component. Although the recorded data signal will be the same for authentic and forged cards, the remanent noise signal will be different for the authentic and forged cards. 
   One embodiment of the invention includes an over-sampled modulator and at least one channel in communication with an output of the over-sampled modulator. The at least one channel is configured to filter the output of the over-sampled modulator and the at least one channel is configured to vary the bandwidth of the filter applied to the output of the over-sampled modulator in response to variations in the bandwidth of the signal generated by the sensing unit. 
   A further embodiment also includes a plurality of delay lines between the over-sampled modulator and the at least one channel. Each of the delay lines is configured to provide a specific delay. 
   In another embodiment, the plurality of delay lines includes seven taps, where one of the delay line taps provides a zero delay and the other six delay line taps provide varying degrees of delay. 
   In a still further embodiment, each of the plurality of channels includes a delay line selector including a delay selection input, a sinc filter, a decimator including a decimated sampling rate selection input, a half-band filter configured such that the bandwidth of the half-band filter changes in response to changes in the decimator output rate, an up-sampler and a low pass filter. 
   In still another embodiment, the sinc filter and decimator includes an integrator, a decimator and a differencer. 
   In a yet further embodiment, the delay selection input is configured to receive a signal selective of a delay and the decimator sampling rate selection input is configured to receive a signal selective of a sampling rate. 
   Yet another embodiment, includes at least two channels, where signals from the selection inputs configure the delay, sampling rate and bandwidth of a first channel, signals from the selection inputs configure the delay, sampling rate and bandwidth of a second channel and signals from the selection inputs control the selection of the output of the first channel and the selection of the output of the second channel. 
   An embodiment of the method of the invention includes over-sampling the analog signal, applying a specific delay associated with a specific bandwidth and sampling rate, the specific bandwidth substantially matching the bandwidth of the analog signal, filtering the over-sampled signal to remove aliasing, decimating the over-sampled signal, filtering the over-sampled signal to reduce noise outside the signal bandwidth, up-sampling the signal and filtering the up-sampled signal to remove aliasing. 
   A further embodiment of the method of the invention also includes detecting a first peak, detecting a second peak and determining the bandwidth of a signal generated during the time between the detection of the first and second peaks. 
   Another embodiment of the method of the invention includes selecting a delay, sampling rate and bandwidth for a first channel, providing an input signal to the first channel, generating an output using the output of the first channel, selecting a delay, sampling rate and bandwidth for the second channel based on the determined bandwidth and generating an output using the output of the second channel. 
   A still further embodiment of the invention includes waiting for the output of the second channel to settle before generating an output using the output of the second channel. 
   A still further embodiment of the invention again includes a sensing unit configured to generate a signal indicative of the sensed magnetic field and an analog-to-digital converter (ADC) in communication with the sensing unit. The analog-to-digital converter includes an over-sampled modulator and at least one channel configured to filter the output of the over-sampled modulator. The at least one channel is configured to vary the bandwidth of the filter applied to the output of the over-sampled modulator in response to variations in the bandwidth of the signal generated by the sensing unit. In addition, a filter in communication with the ADC output and configured to attenuate the portion of the digitized output signal component indicative of the data stored on the magnetic medium, a data extraction unit, in communication with the ADC and the filter, configured to measure bit duration, swipe speed or peak location and an authentication extraction unit, in communication with the filter and the data extraction unit configured to extract a set of scaled samples representative of the remanent noise characteristic of the magnetic medium are also included. 
   Still another embodiment again also includes a plurality of delay lines between the over-sample modulator and the at least one channel. Each of the delay lines can be configured to provide a specific delay. In several embodiments, each of the plurality of delay lines includes seven delay line taps. One of the delay line taps can provide zero delay and the other six taps can provide varying degrees of delay. 
   In a further additional embodiment, each of the channels includes a delay line selector in communication with the data extraction unit, a sinc filter, a decimator in communication with the data extraction unit, a half-band filter in communication with the data extraction unit, an up-sampler and a low pass filter. 
   In another additional embodiment, the data extraction unit is configured to determine the bandwidth of the signal generated by the sensing unit. 
   In a still further additional embodiment, the data extraction unit is configured to determine the bandwidth of the signal generated by the sensing unit by determining the time between peaks in the output of the sensing unit. 
   In still another additional embodiment, the data extraction unit is configured to determine the time between peaks by detecting a first peak, detecting a second potential peak and waiting a predetermined period of time to verify that the second potential peak is actually a peak. 
   In a further additional embodiment again, the sinc filter and decimator of the analog-to-digital converter comprises an integrator, a decimator, and a differencer. 
   In another additional embodiment again, the data extraction unit is configured to determine the bandwidth of the output of the sensor unit. 
   In a still further additional embodiment again, the data extraction unit is configured to periodically provide information to one of the channels concerning the bandwidth of the output of the sensor system. 
   In still another additional embodiment again, the analog-to-digital converter also includes a channel selector in communication with the data extraction unit and configured to select the output of one of the channels as the output of the ADC. 
   In a yet further additional embodiment again, the channel selector is configured to select the output of a first channel as an output, the data extraction unit determines the bandwidth of the output of the sensor system, a second channel is configured using the determined bandwidth information and the channel selector is configured to select the output of the second channel as an output. 
   Yet another additional embodiment again includes a tapped delay line connected between the output of the over-sampled modulator and a delay line selector in each channel. The delay line selector is configured to select a delay line output as a channel input in response to the determined bandwidth information. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings, like reference characters generally refer to the same parts throughout the different drawings. 
       FIG. 1  illustrates an embodiment of a magstripe card reader system in accordance with aspects of the invention; 
       FIG. 2  is a graphic representation of a portion of a typical format of a track  200  of the magnetic stripe  155  as shown in  FIG. 1 ; 
       FIG. 3  is a grossly-enlarged pictorial of a magnetic data pattern showing a small portion of the stripe track of  FIG. 2 ; 
       FIGS. 4–6  illustrate a related set of various representations of a small portion of a track in  FIG. 2 ; 
       FIG. 7  illustrates a plot showing output signal level versus input signal level for a linear amplifier and a compressive amplifier of the present invention; 
       FIG. 8  is a plot illustrating an uncompressed signal generated by the sensing unit and a compressed signal generated by the compressive amplifier of the reader system of  FIG. 1 ; 
       FIG. 9  illustrates one exemplary architecture of a compressive amplifier constructed in accordance with aspects of the invention; 
       FIG. 10  illustrates another exemplary architecture of a compressive amplifier constructed in accordance with aspects of the invention; 
       FIG. 11A  illustrates an embodiment of an analog-to-digital converter (ADC) with multiple selectable bandwidths constructed in accordance with aspects of the invention; 
       FIG. 11B  illustrates a table listing various characteristics of delay lines provided by a tapped delay line of the ADC of  FIG. 11A ; 
       FIG. 11C  illustrates an embodiment of a sinc filter and decimator  115  in the ADC of  FIG. 11A ; 
       FIG. 12  illustrates a graphical representation of digitized signal produced by the ADC of  FIG. 11A ; 
       FIG. 13  is a signal flow diagram illustrating the processing flow for a filter constructed in accordance with aspects of the invention; 
       FIG. 14  depicts the frequency response of a plurality of filters of  FIG. 13  cascaded in accordance with aspects of the invention; 
       FIG. 15  illustrates plots comparing an unfiltered signal with a filtered signal filtered by the filter of  FIG. 13 ; 
       FIG. 16  illustrates an embodiment of the authentication extraction unit of  FIG. 1  in accordance with aspects of the invention; and 
       FIG. 17  is a correlation coefficient histogram comparing the distributions of correlations for authentic and forged cards. 
   

   DETAILED DESCRIPTION 
     FIG. 1  illustrates an embodiment of a magstripe card reader system in accordance with aspects of the invention. The magstripe card reader system  100  comprises a sensing unit  105 , a compressive amplifier  110 , a selectable ADC  115 , a controller  120 , a data extraction unit  125 , a filter  130 , an authentication extraction unit  135 , an encryption unit  145 , and a data combiner  140 . A transaction unit located outside of the reader system  100 , such as at a bank or its processor, receives the data produced by the reader system  100 . 
   In one embodiment, the sensing unit  105  reads the magnetic stripe  155  of a card  150 . The analog signal  160  produced by the sensing unit  105  includes a signal indicative of the card data and a remanent noise characteristic signal. As previously mentioned, the card data includes the account-related data that can be easily forged. On the other hand, the remanent noise characteristic is repeatable, deterministic, and virtually unique for a given magnetic medium that serves as an authenticity identifier for the magnetic medium. The remanent noise characteristic is very difficult to forge. The analog signal  160  generated by the compressive amplifier  110 , which preferentially amplifies the remanent noise characteristic signal component over the recorded data signal component. More specifically, the compressive amplifier  110  amplifies the remanent noise signal component with a greater gain than that with which it amplifies the recorded data signal component. The preferentially amplified analog signal  165  is then provided to the selectable ADC  115  for conversion and subsequent digital processing. 
   The selectable ADC  115  provides analog to digital conversion with variable bandwidths and sampling rates based on the swipe speed of the card  150  at the sensing unit  105 . To provide variable bandwidths and sampling rates, the selectable ADC  115  receives bandwidth and sampling rate select data from a controller  120 , which is in communication with the data extraction unit  125 . The digital signal produced by the selectable ADC  115  is provided to the data extraction unit  125  and the high pass filter  130 . 
   The data extraction unit  125  determines bit duration (which indicates swipe speed) and peak location, and provides these data to the controller  120 , the filter  130 , and the authentication extraction unit  135 . In some embodiments, the filter  130  is a mean-smoothing high pass filter with variable filter length based on the swipe speed. The filter  130  filters out the data signal to leave the relatively flat remanent noise-like characteristic signal from the portion of the signal that is the remanent noise characteristic. The filtered digital signal with the relatively flat area of remanent noise characteristic is received by the authentication extraction unit  135 . A selected group of samples are extracted and scaled by the authentication extraction unit, which then encrypts the samples using an encryption unit  145  using well known encryption schemes. In preparation for transmission to a transaction unit, the encrypted remanent noise characteristic samples are combined, using the data combiner  140 , with the card data from the data extraction unit  125 . 
   The encrypted samples and card data are provided to a transaction unit residing at an off-site secure location, such as a bank. The transaction unit compares the samples of the remanent noise characteristic (also referred to as the sensed magnetic fingerprint) with a reference magnetic fingerprint. Based on the result of the comparison, the transaction unit may approve the transaction contingent upon the magnetic fingerprint positively indicating that the card  150  is authentic. The reference comparison involves comparing a fingerprint taken from the authentic card with the magnetic fingerprint provided to the transaction unit for the purpose of authentication. The reference magnetic fingerprint can be obtained at the time that the card is issued or in the field. In some embodiments, the reference fingerprint associated with the card data, e.g., account number, is retrieved from a database storing a plurality of reference fingerprints associated with a plurality of cards. 
   Discussing the components of the reader system  100  of  FIG. 1  in more detail, the sensing unit  105  reads the magnetic medium of an object being offered for authentication. The sensing unit  105  includes any standard read head, such as an inductive magnetic transducer head. In some applications, only a limited size of data, e.g., 48 bytes of the remanent noise component, can be accommodated in the packets transmitted to the bank. Preferably, track  2  is a low density track with 75 bits per inch (bpi). In a preferred embodiment, a read head should have a small enough gap or a slit to capture adequate detail about the remanent noise component within the 48 byte size limitation. Thus, while a variety of read heads are suitable for use with the present invention, a preferred read head has a gap that is ½ mil or ½×10E-3 inches, such as Model 21052045 read head manufactured by MagTek, Inc. of Carson, Calif. 
   In one embodiment, the object being authenticated by the present invention is a magnetic data card  150  such as a credit card, ATM card or debit card. The present invention may also be used to authenticate any object having a magnetic medium such as a magstripe, or magnetic stripe  155 , upon which data is stored. Such objects include, but are not limited to, security badges/cards, floppy disks, cassette tapes (both VCR and audio tapes), and documents such as bank checks. 
   Data can be recorded in tracks on a magnetic stripe.  FIG. 2  illustrates a typical format of track two of an International Standards Organization (ISO) 7811 card, denoted as track  200  of the magnetic stripe  155  in  FIG. 1 . The low density track two (typically having 75 bpi) is preferred over high density tracks one and three (typically having 210 bpi). The track  200  includes a plurality of sections, such as LZ  205 , SS  210 , PAN  215 , ES  220 , LRC  225  and TZ  230 . Section LZ  205  stores a series of leading zeros (e.g., approximately twenty) designated as LZs. Section SS  210  carries a start sentinel SS indicating the beginning of card data and has 5 magnetic bits to represent special characters of standard banking or credit cards as defined by ISO. Section PAN  215  can carry 40 digits of data; each digit ranging from 0 to 9 and represented by a group of 5 magnetic bits. Section ES  220  carries the end sentinel ES character indicating the end of the card data also represented by a group of 5 magnetic bits. LRC  225  section carries longitudinal redundancy check, which comprises an error detection code providing a parity check on all the characters. TZ  230  section carries at least 20 trailing zeros. Along with the format of  FIG. 2 , a wide variety of formats may be employed in systems of the present invention. 
   In one implementation, wherein each character or number is represented by a group of 5 magnetic bits, the 4 least significant bits (LSBs) represent the number or character and the most significant bit (MSB) represents a parity check bit appended to the first 4 bits. 
     FIG. 3  is a grossly-enlarged pictorial of a magnetic data pattern showing a small portion of the stripe track of  FIG. 2 . The renasnent noise characteristic regions are separated by magnetic transitions (representing data). As illustrated in  FIG. 3 , individual magnetic transitions  30 – 39  define magnetized regions  30   a – 36   a  with remanent noise characteristics therebetween. In  FIG. 3 , the magnetic bits representing the recorded data are defined by the distance between the magnetic transitions. For example the transitions between  30  and  32 ,  32  and  34 ,  34  and  35 ,  35  and  37 ,  37  and  38 , and  38  and  39  are relatively the same distance, and the area between two transitions represents a magnetic bit. The bits having mid-transitions (e.g.,  31 ,  33  and  36 ) between the transitions represent 1s, and the bits without the mid-transitions represent 0s. Thus, the magnetic bits from the transitions  30  to  39  represent 110100 from left to right. 
   It is important to note that the present invention preferably derives the magnetic stripes&#39;remanent noise characteristics from the magnetized regions, such as the regions denoted  30   a – 36   a . When sensed by the sensing unit  105 , these regions  30   a – 36   a  generate analog signals that are less dominated by the data signal than the magnetic transition regions  30 – 39 . 
     FIG. 4  illustrates a grossly enlarged fragment  400  of the magnetic stripe track  200  of  FIG. 2 . A pair of magnetic transitions  401  (N/S interface) and  402  (S/N interface) (representing data) define a magnetized region  403  therebetween. Incidentally, individual magnetic particles  406  also are indicated in the cross section (right). As has generally been recognized in the past, it is the inherent variations and orientations of these particles  406  that account for the magnetic characteristic (magnetic fingerprint) of the stripe  200 . Interval  405  illustrates a preferred sampling interval in the middle of the magnetic transitions  401  and  402 . 
     FIG. 5  illustrates an analog signal  160  (as shown in  FIG. 1 ) sensed from the magnetic transitions  401  and  402  of  FIG. 4 . The analog signal  160  comprises signal peaks, some of which are denoted as  500 ,  502 ,  504 ,  506  at the extreme ends of the interval  403  (as shown in  FIG. 4 ), separated by signal portions of much lower amplitude. The peaks  500 ,  502 ,  504 ,  506  and so on correspond to the data stored magnetically on the card. The magnetized regions  30   a  to  36   a  (shown in  FIG. 3 ) in the preferred interval  405  (Shown in  FIG. 4 ) translate to the central portion  508  of  FIG. 5  between peaks  500  and  502  of the analog signal. 
   The remanent noise characteristic gives rise to the low amplitude fluctuations in the analog signal, appearing throughout the length of the analog signal central portion  508 , as well as the next central portions, such as  510 . The central portions, such as  508  and  510 , are the portions from which the remanent noise characteristic is preferably identified. 
   Still referring to  FIG. 5 , in one embodiment, the analog signal is sampled between a positive peak  500  and the closest negative peak  502  from the positive peak. Each peak will act as a marking point for the samples of interest representing the remanent noise characteristic to be captured. Thus, when digital samples representing the captured analog signal are compared against a reference signal at the transaction unit of  FIG. 1 , it is assumed that the digital samples and the reference signals were extracted from substantially similar peak intervals (the difference in registration being approximately ½ um). In this embodiment, the distance of separation between two peaks, such as  512  and  520 , determines the encoding of the measured analog signal. For example, for a long separation, such as  512 , 0 is encoded and for a short separation, such as  520 , 1 is encoded. 
     FIG. 6  illustrates an expanded view of the analog signal within the window  514  of  FIG. 5 . The peaks, such as  500  and  504 , have an amplitude of approximately 2 mV per inch per second (ips) for a typical inductive read head. The amplitude of the remanent noise signal ranges from 0.05% to 2% of the peak amplitude, ranging from 1 uV to 40 uV per ips. Thus the data-to-remanent noise magnitude ratio ranges from approximately 2000:1 to 50:1. 
   The remanent magnetic characteristic signal component from the interspersed portions, such as  508  and  510  ( FIGS. 5 and 6 ) of the waveform  160  ( FIG. 5 ) may be isolated or extracted from the analog signal  160  ( FIG. 1 ) using a variety of techniques. 
   Referring back to  FIG. 1 , in one embodiment, prior to extracting the remanent magnetic characteristic signal component, the compressive amplifier  110  receives the analog signal  160  from the sensing unit  105  and preferentially amplifies the remanent noise characteristic of the analog signal. The compressive amplifier  110  is configured to provide different levels of amplification for the relatively high amplitude input signals (peaks) and the relatively low amplitude input signals (remanent magnetic characteristic signal component). For example, the portion of the analog readback signal from which the remanent noise characteristic is determined (a portion that has a relatively low signal amplitude) receives greater amplification than the portion of the analog readback signal corresponding to the data signal (a portion that has a relatively high signal amplitude). 
   Accordingly, the range of the amplified signal corresponding to the remanent noise characteristic is expanded relative to the range of the amplified signal corresponding to the data signal. Thus, without resorting to more expensive wider bit digitizers, a high degree of resolution is available in the expression of the signal portions corresponding to the remanent noise characteristic. A greater percentage of the digitizer bit values are focused within the remanent noise characteristic&#39;s dynamic range. Accordingly, precise quantization of the magnetic medium&#39;s remanent noise characteristic can be achieved using a lower bit width digitizer than would have been previously needed to obtain such a high degree of resolution. 
   More specifically,  FIG. 7  illustrates a plot of the output signal strength versus the input signal strength for a linear amplifier (denoted as  710 ) and a compressive amplifier (in solid lines, denoted as  706  and  708 ) of the present invention. The gain provided to the input signal is discernible from the slope of the plot; a steeper slope corresponds to a higher gain than a gentler slope. Thus in  FIG. 7 , the gain characteristic of the compressive amplifier, denoted as  706  and  708 , indicates that the gain  706  provided to input signals with levels in range  700  is greater than the gain  708  provided to input signals with levels in ranges  702  and  704 . 
   Range  700  corresponds to relatively low level input signals. The width of range  700  is preferably set to substantially coincide with the amplitude of the magnetic medium&#39;s sensed remanent noise, which typically ranges from 1 uV to 40 uV per ips. Ranges  702  and  704  correspond to relatively high level input signals. The width of ranges  702  and  704  are preferably set to substantially coincide with the amplitude of the data portions of the analog signal, which is approximately 2 mV per ips. The level of remanent noise gain  706  and data gain  708  may be selected and adjusted as needed. In one embodiment, the level of remanent noise gain  706  is 40, whereas the level of data gain  708  is 6. 
     FIG. 7  also depicts the gain characteristics of a linear amplifier as a straight line  710 . Unlike the dynamically configured gain characteristics of a compressive amplifier, the linear amplifier provides the same level of amplification for the entire range of the input analog signal. Thus, for both the data portions and the remanent noise portions of the analog signal, the slope of the gain  710  remains the same, equally amplifying both the data portions and the remanent noise portions. As previously discussed, when using a linear amplifier, the amount of amplification should be limited to prevent “clipping” of the peaks, which results in less than desirable gain for the weaker remanent noise component of the analog signal. To compensate for the limited level of amplification provided by the linear amplifier, a wider bit digitizer (ADC) should be used. 
     FIG. 8  illustrates a comparison between an uncompressed analog signal  160  from the sensing unit  105  and a compressed signal  165  from the compressive amplifier  110  of the reader system of  FIG. 1 . In  FIG. 8 , the uncompressed signal is represented in a solid line  800 . The right vertical axis  810  corresponds to the amplitude of the uncompressed signal  800 . The compressed signal is represented in a dotted line  805 . The left vertical axis  815  corresponds to the amplitude of the compressed signal  805 . The horizontal axis corresponds to time for both uncompressed and compressed signals. 
   In the example of  FIG. 8 , the analog signal corresponding to the data peaks has been amplified by a factor of 13, whereas the analog signal corresponding to the remanent noise characteristic has been amplified by a factor of 25. As demonstrated in portion  820 , a high degree of resolution is available for the remanent noise characteristic that has been compressively amplified. Once the signal portion corresponding to the remanent noise characteristic is enhanced by the compressive amplifier, the relatively flat remanent noise signal in portion  820  is in fact a slightly down-sloping signal exhibiting various levels of amplitude fluctuations throughout the width of the portion  820 . 
     FIG. 9  illustrates an embodiment of a compressive amplifier  900  in accordance with the present invention with the gain characteristics as shown in  FIG. 7 . The compressive amplifier  900  of  FIG. 9  is a differential circuit comprising two op-amps  902  and  912 , each having an input voltage  914  applied to its positive (+) input. The input voltage  914  is the analog signal that has been generated by a transducer head of the sensing unit of  FIG. 1 . The feedback loop from the output of the op-amp  902  to the negative (−) input comprises parallel paths of (1) a resistor  918 , (2) a resistor  920  and a diode  904 , with the diode  904 &#39;s cathode connected to the resistor  920  and the diode  904 &#39;s anode connected to the negative (−) input of the op-amp  902 , and (3) a resistor  922  and a diode  906 , with the diode  906 &#39;s anode connected to the resistor  922  and the diode  906 &#39;s cathode connected to the op-amp  902 &#39;s negative (−) input. The resistor  918  has a value of R 2  and resistors  920  and  922  both have values of R 3 . The feedback paths also provide a resistor  930  to the negative (−) input of the op-amp  902 . The resistor  930  has a value of  2 R 1 . 
   The op-amp  912  is similar to the op-amp  902 . The feedback loop from the output of the op-amp  912  to the negative (−) input comprises parallel paths of (1) a resistor  928 , (2) a resistor  926  and a diode  910 , with the anode of the diode  910  connected to resistor  926  and the cathode of the diode  910  connected to the negative (−) input of the op-amp  912 , and (3) a resistor  924  and a diode  908 , with the cathode of the diode  908  connected to the resistor  924  and the anode of the diode  908  connected to the op-amp  912 &#39;s negative input. Resistor  928  has a value of R 2 , and resistors  924  and  926  both have values of R 3 . The feedback paths also couple the resistor  930  to the negative (−) input of the op-amp  912 . 
   The circuit of  FIG. 9  operates to compressively amplify the input signal  914  in accordance with the gain characteristics  706  and  708  of  FIG. 7 . For the portions of the input signal  914  having smaller amplitudes, corresponding to the remanent noise characteristic of the input signal, the diodes  904 ,  906 ,  908 , and  910  are not forward-biased, thus the gain for the remanent noise characteristics, denoted as G 1 , is: 
   
     
       
         
           
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   For the portions of the input signal  914  having larger amplitudes, corresponding to the data portions of the input signal, large input voltage causes the feedback diodes  904 ,  906 ,  908 , and  910  to become forward-biased, thus the gain for the data portions, denoted as G 2 , is determined by the parallel combination of R 2  and R 3 . The gain G 2  is calculated by: 
   
     
       
         
           
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   R 3  is selected to be less than R 2  to cause the gain for large voltage inputs to be less than that of small voltage inputs. For a preferred G 1  value of 25 and a preferred G 2  value of 3, and selecting R 3  value of 22 KΩ, algebraic processing of the calculations of G 1  and G 2  above provide values for R 1  and R 2  to achieve the desired gain values as follows: 
   
     
       
         
           
             
               
                 
                   
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   By entering the desired values for G 1  and G 2  and the selected value for R 3  into the above formulas for R 1  and R 2 , a preferred value for R 1  is 1.008×10 4 . Similarly, a preferred value for R 2  is 2.42×10 5 . 
   The differential circuit of  FIG. 9  can also be implemented as a single-ended circuit of  FIG. 10 .  FIG. 10  illustrates another architecture of a compressive amplifier. The compressive amplifier  900  of  FIG. 10  comprises an op-amp  940  that receives an input voltage  946  (the analog readback signal) at its positive (+) input, and produces an output voltage  948 . The compressive amplifier  900  comprises a resistor  950  having a value of R 1  connected between the negative (−) input of the op-amp  940  and ground. The compressive amplifier  900  also comprises a feedback loop from the output of the op-amp  940  to the negative (−) input of the op-amp  940  with three parallel paths (1) a path comprising a resistor  952 , having a value of R 2 , (2) a path comprising a resistor  954 , having a value of R 3  and a diode  942  with the diode  942 &#39;s cathode connected to the resistor  954  and the diode  942 &#39;s anode connected to the negative (−) input of the op-amp  940 , and (3) a path comprising a resistor  956 , having a value of R 3  and a diode  944 , with the diode  944 &#39;s anode connected to the resistor  956  and the diode  944 &#39;s cathode connected to the negative (−) input of the op-amp  940 . The gain for the remanent noise characteristics, denoted as G 1 , and the gain for the data portions, denoted as G 2 , can be determined from the same formulas used for the differential compressive amplifier of  FIG. 9 . 
   Referring back to  FIG. 1 , an analog-to-digital converter (ADC)  115  receives the amplified analog signal  165  from the compressive amplifier  110 . When an inductive magnetic reading head is used in the sensing unit  105 , the magnitude of the analog signal provided to the ADC  115  is proportional to the speed of the magnetic stripe as it is swiped past the magnetic reading head. Swipe speeds can vary and are typically measured in the range of 4–80 inches per second. The bandwidth of the analog signal is also directly proportional to the swipe speed. If the bandwidth of the system remains unmatched to that of the sensed analog signal, the system is left with extra bandwidth that can corrupt the output signal with unwanted noise. The problems created by extra bandwidth are most evident for slower swipes, where the relatively small signals generated are more readily corrupted by the unnecessary wideband noise signal. 
     FIG. 11A  illustrates an embodiment of an ADC with an adjustable bandwidth in accordance with aspects of the invention. The ADC  115  includes an over-sampled modulator  1100  that is connected to a tapped delay line  1105 . As known in the art, modulators may be of various orders, where the order of the modulator is determined by the number of integrators in it. The various outputs of the tapped delay line are connected to each of a plurality of channels. In the illustrated embodiment, two channels are shown. Other embodiments can include a single channel or more than two channels. 
   Each channel comprises a selector  1110  that is connected to a sinc n  filter and decimator  1115 . Sinc n  filters are “box-car” running average filters that are cascaded such that the order n of the sinc n  filter is one greater than the order of the modulator. For example, in one embodiment a second order modulator is employed in conjunction with a third order sinc (sinc 3  or sinc-cubed) filter. The sinc n  filter can also be referred to as a “sinc filter”. Both the selector  1110  and the sinc filter and decimator  1115  are connected to the controller  120 . The sinc filter and decimator is also connected to a half band filter  1120 . The half band filter  1120  is connected to an up sampler  1125 , which is connected to a low pass filter  1130 . The outputs of the low pass filters  1130  in each of the channels are connected to another selector (selector C)  1135 . Selector C  1135  is also connected to the controller via a channel select C connection. Selector C  1135  provides a digital output indicative of samples of the input analog signal at the decimated sampling rate. 
   In one embodiment, the over-sampled modulator  1100  receives the amplified analog input signal  165  from the compressive amplifier  110 . The amplified analog input signal  165  can include a high-amplitude data signal component and a low-amplitude remanent noise characteristic component. The over-sampled modulator  1100  samples the input signal at the sampling frequency (Fm). The sampling frequency (Fm) is much higher than the Nyquist frequency, which is at least twice the bandwidth of the input signal. 
   As described above, the output of the over-sampled modulator  1100  can be provided to a tapped delay line  1105 . In one embodiment, the tapped delay line  1105  includes a number of outputs (n) that provide the previous n−1 outputs of the over-sampled modulator  1100 . 
   In several embodiments, the ADC channels include a selector  1110  connected to each of the outputs of the tapped delay line. The selection of an output of the tapped delay line can be coordinated via a signal from the controller  120 . The selected output is provided to the channel&#39;s sinc filter and decimator  1115 . The reduction in the sampling rate caused by the decimator  1115  can be selected using a select line from the controller  120 . The reduction in sampling rate varies as the decimator  1115  attempts to match the sampling rate to the Nyquist frequency of the particular signal generated by a card swipe. The sinc filter removes the aliases created by the sampling process. 
   A sinc filter and decimator in accordance with an embodiment of the present invention is shown in  FIG. 11C . The sinc filter and decimator  1115 ′ includes an integrator  1150 , a decimator  1155  and a differencer  1160 . In several embodiments, the sinc filter&#39;s integrator length and the decimator rate are variable and can be selected to accommodate variable signal bandwidth. 
   Turning back to  FIG. 11A , the output of the sinc filter and decimator  1115  is provided to a half-band filter  1120 . In one embodiment, the bandwidth of the half-band filter  1120  is variable and can be selected (by selection of a suitable decimation rate) to accommodate variable signal bandwidth. Typically, the bandwidth of the half-band filter is chosen to attenuate as much of the noise in the unused portions of the frequency spectrum as possible. In embodiments where the decimator down samples to the Nyquist rate of the received signal, the half-band filter applies greater attenuation to frequencies greater than half the Nyquist frequency. 
   In several embodiments, an up-sampler  1125  is provided after the half-band filter  1120 . The up-samplers  1125  operate at a frequency, Fs, which is 4 times faster than Fd (i.e., the decimated operating rate of the half-band filter). The high sampling rate of the up-sampler  1125  interpolates new samples between successive values of the half-band filter  1120  output signal which provides a finer grid of samples. Aliasing within the interpolated samples can be removed by passing the signal through a low pass reconstruction filter  1130 . The up-sampled signal provides sufficient resolution that it can be used to extract information concerning the remanent noise characteristic of a magnetic stripe from the signal generated by the magnetic stripe. 
   The output of the low pass filter  1130  from each channel is provided to the selector C  1135 . The output chosen as the output of the ADC is determined based on an input select signal, which can be provided by the controller. 
   In operation, the bandwidth of the signal can change during the card swipe. The previous bit duration can be used to set an appropriate bandwidth and associated sampling rate for the ensuing bit. Determination of bit duration can be performed in a variety of ways. In one embodiment, the bit duration is measured as the time between peaks in the signal output. Peaks can be detected by determining whether a value is greater than previous values for a predetermined period of time. The length of the predetermined time period can influence the accuracy of peak detection. The shorter the period of time, the greater the possibility that a “detected” peak is an aberration. 
   The time required to determine that a peak has occurred can result in the bit duration remaining unknown for a predetermined period of time during the subsequent bit. In instances where the bit duration is unknown for a period during the subsequent bit and a single channel is used, the channel is flushed and restarted using the new bandwidth. During the additional time required for the channel&#39;s output to settle, the output of the channel may not be indicative of the magnetic field of the magnetic stripe. In several embodiments, the settling time is sufficiently short to enable data to be collected during the subsequent bit interval. 
   In instances where the bit duration is unknown for a period during the subsequent bit and a multiple channel system is used, a second channel can be started once the bit duration is known. During the time required for the output of the second channel to settle, the output of the first channel can be used as the output of the ADC. Once the second channel has settled, the output of the second channel can be used as the output of the ADC The output of the first channel and the second channel can be synchronized by choosing an appropriate relative delay between the first channel and the second channel from the tapped delay line  1105 . 
   In one embodiment, the data extraction unit (DEU)  125  determines the bit durations and provides this information to the controller  120 . The controller  120  uses the information concerning the bit duration to set the delay and sampling rate (and hence bandwidth) for a channel by using the selector  1110  to select an appropriate output from the tapped delay line and concurrently providing an appropriate select signal to the sinc filter, decimator  1115 , and half-band filter  1120 . The output of the channel can then be selected using the selector C  1135 . As indicated above, the bandwidth of the ADC can be modified during the swipe by the controller. The controller configures a second channel in the manner described above based on the most recent bit duration. When the next bit arrives, the controller  120  stops using the first channel to sample and digitize the incoming signal. Instead, the controller  120  selects the output of the second channel using the selector C  1135 . The tapped delay line  1105  maintains appropriate spacing between samples by delaying one channel relative to the other channel, so that both paths can be synchronized at the final selector C  1135 . By repeating the above process during each bit interval, the controller  120  is able to continually adjust (within bounds) the bandwidth of the ADC in response to variations in the speed at which a magnetic stripe is being swiped past an inductive magnetic reading head. 
   In one embodiment, the over-sampled modulator has a sampling frequency, Fm, at 8 MHz, which generates a sequence of 0s and 1s separated in time by 125 nsec. In addition, the outputs of the tapped delay line and the frequencies of each of the channels are configured to enable the control to select from the delays and frequencies shown in the table of  FIG. 11B .  FIG. 11B  illustrates a table listing the number of delayed samples (e.g., length of tapped delay), bandwidth (e.g., corner frequency, Fc), output sampling rate, and maximum swipe speed associated with each selection from 0 to 6. In other embodiments, more or fewer outputs can be provided by the tapped delay line and other combinations of delays and sampling rates can be used. 
   In other embodiments, other configurations are possible including using a sigma delta modulator in conjunction with a low pass filter. The ADC can be implemented by a variety of hardware components that enable modification of the ADC bandwidth and associated sampling rate in response to variation in speed during a card swipe. 
     FIG. 12  illustrates a graphical representation of the compressed and digitized signal produced by the ADC of  FIG. 11A . The vertical axis represents ADC counts and the horizontal axis represents the time in seconds. A positive peak  1200  reaches the ADC count of 27000 and a negative peak  1210  reaches the negative peak of −27000. The remanent noise component of the analog signal  160  is generally expressed within the window  1215  having the digital values from −3000 to 1500 between the peaks  1200  and  1210 . Even after the enhancement by the compressive amplifier  110  and digitization by the selectable ADC  115 , the recorded data component and the remanent noise characteristic component are still linked to one another. For example, as shown by the digital samples in the window  1215 , the digital samples corresponding to the remanent noise characteristic component ride on the slope of the heavily influential recorded data component, so that the digital signal exhibits various levels of fluctuation throughout the window  1215 . 
   As illustrated in  FIG. 12 , the digital samples in the region  1215  are tightly spaced without any visible gaps, such that the digital signal in the region  1215  substantially resembles the analog signal within the region  820  of  FIG. 8 . The digital signal within the region  1215  of  FIG. 12  shows virtually the same fluctuations in the amplitudes as the analog signal in the region  820 . 
   The filter  130  of  FIG. 1  receives the digital signal from the selectable ADC  115 , bit duration data and peak location information from the DEU  125 . The filter  130  forwards the filtered signal to the authentication extraction unit  135 . In some embodiments, the filter  69  is configured as a high pass filter, such that the low frequency, data dependent signal (also referred to as the recorded data signal) is substantially filtered out and the high frequency remanent noise characteristic signal remains in the digitized samples. 
   In one embodiment, as shown in  FIG. 13 , the filter  130  comprises a mean-smoothing filter. Referring to  FIG. 13 , input samples X(n), denoted as  1300 , are the digital samples produced by the selectable ADC  115  of  FIG. 1 . The input samples  1300  are forwarded to two processing units  1302  and  1304 . The first processing unit  1302  delays each sample X(n) and the second processing unit  1034  calculates a sliding average of the samples X(n). The respective outputs  1306  and  1308  are combined by a subtractor  1310 , which in turn generates filtered output samples  1312 . 
   In one embodiment, a single filter  1310  is used to process the digital samples X(n)  1300 . In some other embodiments, a cascade of filters  1310  are used to process the digital samples X(n)  1300 .  FIG. 14  illustrates the frequency response of a cascade of two mean smoothing filters, each of which is substantially similar to the filter of  FIG. 13 . In some embodiments, the filter length, which determines the frequency response of the filter, is adjustable based on the swipe speed. In one embodiment, the filter length is calculated at the end of each magnetic bit&#39;s traversal of the sensing unit and the length of the filter is set to be ⅛ of the length of the most recent magnetic bit. In some embodiments, if a cascade of two filters is used, the length of each filter is set to be an odd number so that the length of the cascaded filter is an even number. 
   Still referring to  FIG. 14 , the vertical axis of the frequency response is the magnitude in units of dB, and the horizontal axis is the spatial frequency in units of cycles per magnetic bit. In  FIG. 14 , the frequency response indicates a high pass filter, where the magnitude components at low frequencies (in units of cycles per magnetic bit) are greatly attenuated. 
     FIG. 15  illustrates a comparison between filtered and unfiltered digital samples. The dashed plot  1500  represents the unfiltered signal. The solid plot  1510  represents the filtered signal. As can be seen by the dashed plot  1500  (as well as  FIG. 12 ), the portion of interest  1504  between peaks of the signal is heavily dominated by data signal/peaks  1502 . Due to the heavily influential recorded data dependent signal with significantly higher amplitudes, the signal in the portion  1504  fluctuates along with the data dependent component of the signal, dominating over the relatively flat lower amplitude remanent noise signal. 
   However, when the signal is processed by the filters of  FIGS. 13 and 14 , a much flatter central portion  1514  results between the peaks  1512  of the filtered signal  1510 . The influence of the recorded data on the central portions  1514  of the signal is substantially negated, thus the portion  1514  representing the remanent noise characteristic can be easily distinguished from the peaks  1512 . In some other embodiments, an analog filter or a cascade of analog filters maybe used to isolate the remanent noise characteristic component of the amplified analog signal  165  from the recorded data component of the amplified analog signal  165 . 
     FIG. 16  illustrates an embodiment of the authentication extraction unit (AEU)  135  of  FIG. 1  in accordance with aspects of the invention. The AEU  135  identifies the magnetic zeros to use to capture the remanent magnetic characteristics of the magnetic stripe  155  ( FIG. 1 ). The AEU also communicates with the DEU  125  to receive the bit duration and peak location information, which is also provided to the controller  120  and the filter  130  by the DEU  125 . 
   In the embodiment of  FIG. 16 , the AEU comprises a sample buffer  1600 , an extractor  1605 , and a scaler  1610 . The sample buffer stores amplified and filtered digital samples of a magnetic bit as the magnetic stripe  155  ( FIG. 1 ) containing the magnetic bit is passing through the sensing unit  105  ( FIG. 1 ). T 0  denotes the duration of the most recent bit (Nth bit) that had already passed by the sensing unit  105  ( FIG. 1 ). Thus T 0 , which is provided by the DEU  125  of  FIG. 1 , denotes the time for the entire Nth magnetic bit to pass by the sensing unit  105 . At the end of the Nth bit, the buffer waits for the duration of ¼ of the previous bit duration (i.e., T 0 /4). Samples are collected into the sample buffer  1600  for the N+1st bit from the time T 0 /4 until the last peak is detected at the end of T 1  (denoting the duration of the N+1 st bit) or the buffer is fill, whichever occurs first. The size of the buffer  1600  should be large enough to hold the desired number of samples to accurately represent the remanent noise characteristic among the collected samples. 
   The AEU of  FIG. 16  also comprises an extractor  1605 . The extractor  1605  receives information regarding bit duration (e.g., the duration of the N+1th magnetic bit as T 1 ) and potential peak locations from the DEU  125  of  FIG. 1 . The DEU  125  merely indicates to the AEU  135  all of the potential peaks, not knowing for certain which one of the potential peaks detected by the DEU  125  is an actual peak. The peak detection algorithm ensures that the last potential peak declared is the actual peak. For example, the peak detection algorithm indicates a local maximum as a potential peak. The algorithm then searches for a potential peak with a higher value than the previous potential peaks and the subsequent potential peaks. Thus the global maximum from the local maxima is identified as the actual peak. Once the actual peaks are determined, the extractor determines which of the samples in the buffer  1600  are located closest to the desired points in the magnetic bit and therefore best represent the remanent noise characteristic. Referring back to  FIG. 15 , the samples best representing the remanent noise characteristic are extracted from the middle of the magnetic bit in region  1514  (post-filtered). 
   In an instance where more than one sample is to be extracted, the selected sample locations should be symmetric about the center of the magnetic bit so that they may be obtained regardless of the direction of the swipe. Because only a limited number of samples can be transmitted, (and hence, captured) due to the data/sample size restrictions imposed by banks, the spacing of the samples to be extracted should be sufficient to be statistically independent and therefore maximize their entropy and promote effective discrimination of fraudulent magstripes. If the samples are taken too close together, less information about the magstripe is garnered and inferior discrimination results. 
   In one example, samples representing the remanent noise characteristic are taken from 32 magnetic zeros and are collected by the sample buffer  1600 . For each group of samples collected from the 32 magnetic zeros, four samples are to be extracted and provided as an authenticity identifier for the card  150  of  FIG. 1 . The four samples extracted are the ones closest to (13/32)T 1 , (15/32)T 1 , (17/32)T 1 , and (19/32)T 1  points, where T 1  denotes the time the current magnetic bit passes through the sensing unit  105  of  FIG. 1 . For example, if a total of 400 samples are collected by the buffer  1600 , the first extracted sample was collected at (13/32)*400=the 162nd sample, second extracted sample was collected at (15/32)*400=the 187th sample, the third extracted sample was collected at the 212th sample and the 4th extracted sample was collected at the 237th sample. The Extractor  1604  passes along the four extracted samples as well as the maximum amplitude of all the samples between (13/32)T 1  and (19/32)T 1  to the scaler  1610 . 
   In one embodiment, the scaler  1610  scales each extracted sample having a 17 bit data value down to a 3-bit data value. More specifically, in this embodiment, the selectable ADC  115  outputs samples of a magnetic bit, where each sample representing the magnetic bit is comprised of 17 data bits. The four 17-bit samples extracted by the Extractor  1605  are then scaled down to four 3-bit data samples. Thus, four 3-bit samples are produced by the scaler  1610  for each of the 32 magnetic zero bits that form the authenticity identifier. In this embodiment, the total size of the authenticity identifier is 384 bits or 48 bytes (32 magnetic zeros each having 4 3-bit samples). 
   As previously mentioned, the authenticity identifier samples produced by the AEU  135  are encrypted by the encryption unit  145  and the card data samples produced by the DEU  125  are concatenated by the data combiner  140  with the encrypted authenticity identifier of the reader system  100 .  FIG. 17  illustrates a correlation coefficient histogram of authentic cards and forged cards after processing magstripes of both cards through the reader system  100  of  FIG. 1 . Dashed lines  1700  represent the correlation coefficients of authentic cards. The solid lines  1705  represent the correlation coefficients of forged cards. As illustrated in  FIG. 17 , no overlap exists between the authentic card and the forged card distributions because their respective correlation coefficients derived from the remanent noise characteristics are substantially different from each other. Because of the substantial differences between the remanent noise characteristics of the authentic cards and the forged cards, the forgery is easily and reliably detected. 
   Variations, modifications, and other implementations of what is described herein will occur to those of ordinary skill in the art without departing from the spirit and the scope of the invention as claimed. Although the invention has been described with respect to certain embodiments, it should be recognized that the invention includes the claims and their equivalents supported by this disclosure.