Abstract:
A multi-band receiver according to an embodiment of the present invention includes an analog-to-digital converter configured to convert multi-band analog radio signals into a digital baseband signal, and a first signal extracting unit configured to generate a first path signal by changing a sampling rate of the digital baseband signal and sample-delaying the digital baseband signal, and generate a second path signal by bypassing the digital baseband signal, wherein the first signal extracting unit extracts a first baseband signal using a group delay difference between the first and second path signals caused by a sample delay difference between the first and second path signals.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This U.S. non-provisional patent application claims priority under 35 U.S.C. §119 of Korean Patent Application Nos. 10-2013-0140993, filed on Nov. 19, 2013, and 10-2014-0141532, filed on Oct. 20, 2014, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     The present invention disclosed herein relates to a wireless signal receiver for wireless communication, and more particularly, to a multi-band receiver for receiving and directly down-converting a plurality of signals transmitted at different bands. 
     Recently, terminals for wireless communication systems have become more compact and have been improved to satisfy new requirements of various standards of wireless communication. In particular, such terminals are required to support both a multi-band and a multi-mode for improving flexibility, adaptability and cognitivity. Moreover, next-generation wireless communication standards will provide dynamic spectrum allocation and sharing functions to improve the spectrum efficiency and the quality of service (QoS). Furthermore, non-contiguous frequency bands may be allocated to improve the efficiency of use of a spectrum. Such requirements need a technology for receiving signals transmitted at two or more different frequency bands using a single receiver. 
     Currently, it is required to simultaneously support two or more different communication standards in a single wireless receiver, or, in the case of a communication system such as a cognitive radio communication system, it is required to scan signals at an arbitrary frequency band, while receiving signals of another arbitrary frequency band. However, a typical receiver should be provided with separate receiver circuits or chips for respective modes and respective frequency bands or channels. Therefore, the circuit structure of the receiver is complicated and the unit price of the receiver is high. Therefore, a novel receiver for supporting a multi-band and a multi-mode using a single receiver circuit is required. 
     A band-pass sampling technology is considered as one of the best alternatives for satisfying such requirements. According to the band-pass sampling technology, sampling is performed at a sampling rate that is at least two times higher than a signal bandwidth so that an RF band signal is directly frequency-converted into a baseband signal. A typical band-pass sampling receiver applies two sampling clocks having relative time delays to two analog-to-digital converts (ADCs) respectively to perform sampling, and then removes an aliasing effect through signal processing. However, since such a band-pass sampling receiver needs two ADCs, the complexity of hardware increases. Furthermore, since a delay time difference between two paths is induced by using analog devices, the performance of hardware may be degraded due to an error of the delay time difference between the paths and irregular signal magnitude. 
     SUMMARY OF THE INVENTION 
     The present invention provides a multi-band receiver for simultaneously down-converting multi-band signals at arbitrary frequency bands to receive the signals, while using a single RF chain and a single ADC. 
     The present invention also provides a multi-band receiver for cancelling interference between two signals at a baseband to separate a desired signal using a single ADC. 
     The present invention also provides a multi-band receiver provided with a single ADC to have reduced complexity and reduced size compared to a typical receiver for which two ADCs should be used. 
     The present invention is also directed to preventing the performance degradation caused by a delay time error and signal magnitude irregularity between two paths which occur when using a second order band pass sampling technique for which two ADCs are used. 
     The present invention also provides a multi-band receiver for scanning a signal at an arbitrary frequency band, while receiving a signal of another arbitrary frequency band using a single receiver circuit. 
     Embodiments of the present invention provide multi-band receivers including an analog-to-digital converter configured to convert multi-band analog radio signals into a digital baseband signal, and a first signal extracting unit configured to generate a first path signal by changing a sampling rate of the digital baseband signal and sample-delaying the digital baseband signal, and generate a second path signal by bypassing the digital baseband signal, wherein the first signal extracting unit extracts a first baseband signal using a group delay difference between the first and second path signals caused by a sample delay difference between the first and second path signals. 
     In other embodiments of the present invention, multi-band receivers include an analog-to-digital converter configured to convert multi-band analog radio signals into a digital baseband signal, and a first signal extracting unit configured to generate a first path signal by sample-delaying the digital baseband signal and changing a sampling rate thereof, and generate a second path signal by changing the sampling rate of the digital baseband signal, wherein the first signal extracting unit extracts a first baseband signal using a group delay difference between the first and second path signals caused by a sample delay difference between the first and second path signals. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are included to provide a further understanding of the present invention, and are incorporated in and constitute a part of this specification. The drawings illustrate exemplary embodiments of the present invention and, together with the description, serve to explain principles of the present invention. In the drawings: 
         FIG. 1  is a graph illustrating analog spectra of two signals at arbitrary frequency bands; 
         FIG. 2  is a schematic block diagram illustrating a double-band receiver according to a first embodiment of the present invention; 
         FIG. 3  is a graph illustrating a spectrum R A   δ (f) of a first path signal DR A  output from the sampling rate down-converter of  FIG. 2 ; 
         FIG. 4  is a graph illustrating a spectrum R B   δ (f) of a second path signal DR B  illustrated in  FIG. 2 ; 
         FIG. 5  is a graph illustrating a spectrum of the first baseband signal DR 1  output from the adder  146  of  FIG. 2 ; 
         FIG. 6  is a graph illustrating a spectrum of the second baseband signal DR 2  output from the adder  156  of  FIG. 2 ; 
         FIG. 7  is a schematic block diagram illustrating a double-band receiver according to a second embodiment of the present invention; 
         FIG. 8  is a schematic block diagram illustrating a double-band receiver according to a third embodiment of the present invention; 
         FIG. 9  is a graph illustrating a spectrum R A   δ (f) of the first path signal DR A  output from the first sampling rate converter of  FIG. 8 ; 
         FIG. 10  is a graph illustrating a spectrum R B   δ (f) of the second path signal DR B  output from the second sampling rate converter of  FIG. 8 ; and 
         FIG. 11  is a schematic block diagram illustrating a double-band receiver according to a fourth embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will be described below in more detail with reference to the accompanying drawings. The present invention may, however, be embodied in 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 present invention to those skilled in the art. 
     The terminology used herein is not for delimiting the present invention but for describing specific embodiments. The terms of a singular form may include plural forms unless otherwise specified. It will be further understood that the terms “comprise”, “comprising,”, “include”, “including”, “have” and/or “having”, when used herein, specify the presence of stated features, numbers, steps, operations, elements, components or combinations thereof, but do not preclude the presence or addition of one or more other features, numbers, steps, operations, elements, components or combinations thereof. 
     The terms used herein, including technical or scientific terms, have the same meanings as understood by those skilled in the art. It will be further understood that terms in common usage should also be interpreted as is customary in the relevant art and not in an idealized or overly formal sense unless otherwise defined herein. 
     In the description, when it is described that a certain part includes certain elements, the part may further include other elements. The embodiments exemplified and described herein include complementary embodiments thereof. Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings. 
       FIG. 1  is a graph illustrating analog spectra of two signals at arbitrary frequency bands. Referring to  FIG. 1 , wireless signals transmitted through two frequency bands f c1  and f c2  may interfere with each other at a baseband after being sampled. 
     It may be assumed that a first analog RF signal AR 1  has a first carrier frequency f c1  and a first signal bandwidth B 1 . It may be assumed that a second analog RF signal AR 2  has a second carrier frequency f c2  and a second signal bandwidth B 2 . A spectrum R AR1+ (f) represents a positive frequency spectrum component of the first analog RF signal AR 1 , and a spectrum R AR1− (f) represents a negative frequency spectrum component of the first analog RF signal AR 1 . A spectrum R AR2+ (f) represents a positive frequency spectrum component of the second analog RF signal AR 2 , and a spectrum R AR2− (f) represents a negative frequency spectrum component of the second analog RF signal AR 2 . 
       FIG. 2  is a schematic block diagram illustrating a multi-band receiver according to a first embodiment of the present invention. A multi-band receiver  100  of the present invention may include a band-pass sampling receiver. In addition, although a double band is exemplarily illustrated as a multi-band, it may be understood that the present invention is applicable to a multi-band for receiving three or more signals. Referring to  FIG. 2 , the multi-band receiver  100  of the present invention may include an antenna  110 , first and second analog band pass filters  120  and  125 , an adder  127 , an analog-to-digital converter (ADC)  130 , a first signal extracting unit  140  and a second signal extracting unit  150 . 
     The antenna  110  receives an analog RF signal transmitted wirelessly. The received analog RF signal may include signals transmitted at two or more frequency bands. Here, although it is illustrated that the analog RF signal is transmitted through two or more different frequency bands, those skilled in the art could understand that the analog RF signal may be transmitted at three or more bands. 
     The first and second analog band pass filters  120  and  125  may include broadband pass filters for filtering broadband signals. The first analog band pass filter  120  may be such designed that a passband is limited to the first bandwidth B 1 . The first analog band pass filter  120  may generate, as a result of filtering, the first analog RF signal AR 1  having the first bandwidth B 1  and the first carrier frequency f c1 . The second analog band pass filter  125  may be such designed that a passband is limited to the second bandwidth B 2 . The second analog band pass filter  125  may generate, as a result of filtering, the second analog RF signal AR 2  having the second bandwidth B 2  and the second carrier frequency f c2 . In an exemplary embodiment, the passbands and the passband widths B 1  and B 2  of the first and second analog band pass filters  120  and  125  may have fixed values or may be adjusted to other values. To this end, the first and second analog band pass filters  120  and  125  may include tunable band pass filters (BPFs). 
     The adder  127  adds the filtering result of the first analog band pass filter  120  and the filtering result of the second analog band pass filter  125 . That is, the adder  127  adds the first analog RF signal AR 1  to the second analog RF signal AR 2  to generate a multi-band analog RF signal AR, and transfers the multi-band analog RF signal AR to the ADC  130 . 
     The ADC  130  converts the multi-band analog RF signal AR to a digital baseband signal DR. The ADC  130  samples the multi-band analog RF signal AR on the basis of a sampling rate f s . Furthermore, data obtained through the sampling is quantized by the ADC  130  and is output as the multi-band digital baseband signal DR. 
     The first signal extracting unit  140  and the second signal extracting unit  150  respectively separate a first signal signal — 1 and a second signal signal — 2 from the digital baseband signal DR output from the ADC  130 . 
     The first signal extracting unit  140  may include a sampling rate up-converter  141 , a sample delayer  142 , a sampling rate down-converter  143 , a first digital filter  144 , a second digital filter  145  and an adder  146 . The baseband signal DR obtained through the sampling of the ADC  130  may pass through two signal paths so as to be processed. That is, the baseband signal DR passes through a first path including the sampling rate up-converter  141 , the sample delayer  142 , the sampling rate down-converter  143  and the first digital filter  144  and passes through a second path including the second digital filter  145  so as to be added to each other in the adder  146 . The signals output from the first and second paths are added to each other in the adder  146  so as to be output as the first signal signal — 1. The first signal signal — 1 is a baseband signal obtained by removing one of signals transmitted at multiple bands. 
     In the first signal extracting unit  140 , the digital baseband signal DR output from the ADC  130  is divided into a first path signal processed through the first path and a second path signal processed through the second path. While the digital baseband signal DR passes through the first path, the sampling rate is increased by N times, a specific number of samples (e.g., one sample) is delayed, and then the sampling rate is decreased by N times. The first path signal is provided to the adder  146  after being processed by the first digital filter  144 . 
     In addition, the digital baseband signal DR passes through the second path so as to be transferred as the second path signal. The digital baseband signal DR passes through the second digital filter  145  in the second path without undergoing sample delay or change in a sampling rate. 
     Here, a value obtained by multiplying the up-sampling rate N of the sampling rate up-converter  141  included in the first path by the down-sampling rate 1/N of the sampling rate down-converter  143  may be 1. That is, the sampling rate of the first path signal that has passed through the sampling rate up-converter  141  and the sampling rate down-converter  143  is equal to the sampling rate of the output of the ADC  130 . Furthermore, the first path signal is delayed by the sample delayer  142  arranged between the sampling rate up-converter  141  and the sampling rate down-converter  143 . The sample delayer  142  delays the first path signal by as much as D samples. Here, a delay amount D of the sample delayer  142  may be an integer that is greater than 0 and smaller than the denominator of the down-sampling rate, i.e., N. 
     The signal that has been delayed by as much as D samples by the sample delayer  142  is down-sampled by the sampling rate down-converter  143  so that the sampling rate is decreased by 1/N times. An output signal of the sampling rate down-converter  143  is provided to the first digital filter  144 . The digital baseband signal DR output from the ADC  130  is processed by the second digital filter  145  included in the second path so as to be provided to the adder  146 . Here, the first digital filter  144  and the second digital filter  145  are designed on the basis of a relative sample delay difference between the first and second paths or fractional delay. A second baseband signal DR 2  may be removed and a first baseband signal DR 1  may be extracted using the first and second digital filters  144  and  145  and the adder  146 . 
     The relative sample delay difference between the first and second paths and the fractional delay are presented as different group delays in multi-band signals at different frequency bands. Even though two signals interfere with each other at a baseband, a multi-band signal may be separated using an effect of the different group delays. The first and second digital filters  144  and  145  are designed in consideration of such a characteristic. 
     The second signal extracting unit  150  may include a third digital filter  154 , a fourth digital filter  155  and an adder  156 . An output signal of the sampling rate down-converter  143  may pass through a third path including the third digital filter  154 . The baseband signal DR obtained through the sampling of the ADC  130  passes through a fourth path including the fourth digital filter  155  so as to be provided to the adder  156 . The signals output from the third and fourth paths are added to each other in the adder  156  so as to be output as the second signal signal — 2. 
     In the second signal extracting unit  150 , a baseband signal DR A  transferred to the third path affected by sample delay is processed by the third digital filter  154 . A baseband signal DR B  transferred to the fourth path where sample delay does not occur is processed by the fourth digital filter  155 . The third and fourth digital filters  154  and  155  may be such designed that one of the baseband signals DR A  and DR B  is removed using different fractional delay effects of the baseband signals DR A  and DR B . 
     When the output signals of the third and fourth digital filters  154  and  155  are added to each other by the adder  156 , the second signal signal — 2 is extracted. 
     According to the above-mentioned configurations of the first and second signal extracting units  140  and  150 , even though the first and second baseband signals DR 1  and DR 2  interfere with each other, such interference may be cancelled so that the first and second baseband signals DR 1  and DR 2  may be extracted substantially simultaneously and completely. Therefore, both a multi-band and a multi-mode may be supported using a single receiver circuit, without providing an additional receiver circuit for each signal band. In particular, since a single ADC is used in the receiver circuit of the present invention, the complexity of hardware of the receiver is decreased, the degree of integration of the circuit is increased, and the size of the receiver is decreased, so that the unit price of the receiver is decreased and the power consumption thereof is reduced. 
     Accordingly, the multi-band receiver of the present invention may simultaneously receive two or more signals having arbitrary frequency bands and signal bandwidths by using a single receiver circuit. Furthermore, in a communication system such as a cognitive ratio communication system, the multi-band receiver of the present invention may provide a function for scanning a signal at an arbitrary frequency band while receiving a signal of another arbitrary frequency band. 
     Hereinafter, a method of designing the first and second digital filters  144  and  145  using an effect of different fractional delays will be described. 
       FIG. 3  is a graph exemplarily illustrating a spectrum R A   δ (f) of the first path signal DR A  output from the sampling rate down-converter  143  of  FIG. 2 .  FIG. 4  is a graph exemplarily illustrating a spectrum R B   δ (f) of the second path signal DR B  corresponding to the spectrum of the digital baseband signal DR. Here, the spectrum R A   δ (f) of the first path signal DR A  represents the spectrum of a signal obtained by processing the digital baseband signal DR through the sampling rate up-converter  141 , the sample delayer  142  and the sampling rate down-converter  143 . The spectrum R A   δ (f) of the first path signal DR A  indicates a signal to which a fractional delay of D/N is applied compared to the second path signal. As a result, the first path signal DR A  has the same processing effect as that of applying a group delay to the second path signal DR B . 
     Referring to the spectra illustrated in  FIGS. 3 and 4 , it may be understood that interference may occur on the first and second baseband signals DR 1  and DR 2  constituting the first path signal DR A  and the first and second baseband signals DR 1  and DR 2  constituting the second path signal DR B . That is, the first and second baseband signals DR 1  and DR 2  may interfere with each other at a baseband. Nonetheless, the multi-band receiver  100  (see  FIG. 2 ) of the present invention may cancel the interference between the first and second baseband signals DR 1  and DR 2  and may correctly extract the first and second baseband signals DR 1  and DR 2 . 
     It is exemplarily described herein how the first and second baseband signals DR 1  and DR 2  are extracted when the first and second baseband signals DR 1  and DR 2  interfere with each other. Herein, the first and second path signals DR A  and DR B  have signal characteristics as described below. 
     An effect of group delay due to time delay of the first baseband signal DR 1  included in the first path signal DR A  may be expressed as Equation (1) and Equation (2). Equation (1) represents an image component of the first baseband signal DR 1  transitioned from a negative band, and Equation (2) represents an image component of the first baseband signal DR 1  transitioned from a positive band.
 
 e   jθ     1−     (f)   =e   j2πn     1     D/N   e   −j2πDf/f     s     (1)
 
 e   jθ     1+     (f)   =e   −j2πn     1     D/N   e   −j2πDf/f     s     (2)
 
     Where n 1  denotes a frequency band position index and may have an integer value of 0, 1, 2, 3, . . . . D denotes an amount of sample delay, and N denotes a conversion rate of the sampling rate down-converter  143 . 
     An effect of group delay of the second baseband signal DR 2  included in the first path signal DR A  may be expressed as Equation (3) and Equation (4). Equation (3) represents an image component of the first baseband signal DR 2  transitioned from a negative band, and Equation (4) represents an image component of the first baseband signal DR 2  transitioned from a positive band.
 
 e   jθ     2−     (f)   =e   j2πn     2     D/N   e   −j2πDf/f     s     (3)
 
 e   jθ     2+     (f)   =e   −j2πn     2     D/N   e   −j2πDf/f     s     (4)
 
     Where n 2  denotes a frequency band position index of the second analog RF signal AR 2  and may have an integer value of 0, 1, 2, 3, . . . . 
     n 1  and n 2  may be expressed as Equation (5) by the carrier frequencies f c1  and f c2  of the first and second analog RF signals AR 1  and AR 2  and the sampling rate f s  of the ADC  130  (see  FIG. 2 ). 
     
       
         
           
             
               
                 
                   
                     
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     Where a round function round(x) represents rounding off of x. 
     Signals of two bands may be separated using a delay difference between the first and second path signals DR A  and DR B  and an effect of group delay between the first and second baseband signals DR 1  and DR 2 . For the purpose of this process, the response characteristics of the first and second digital filters  144  and  145  and the third and fourth digital filters  154  and  155  are designed. 
     A spectrum R A   δ (f) of the first path signal DR A  output from the sampling rate down-converter  143  at a first Nyquist zone may be expressed as Equation (6). 
     
       
         
           
             
               
                 
                   
                     
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     Furthermore, a spectrum R B   δ (f) of the second path signal DR B  output from the ADC  130  at a first Nyquist zone may be expressed as Equation (7).
 
 R   B   δ ( f )= f   s   {R   1− ( f )+ R   1+ ( f )+ R   2− ( f )+ R   2+ ( f )}  (7)
 
     Spectra of signals processed by the first and second digital filters  144  and  145  may be expressed as Equation (8) and Equation (9). 
     
       
         
           
             
               
                 
                   
                     
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                                     ⁢ 
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                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       Df 
                                       / 
                                       
                                         f 
                                         s 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       2 
                                       - 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     j2π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       2 
                                     
                                     ⁢ 
                                     
                                       D 
                                       / 
                                       N 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       Df 
                                       / 
                                       
                                         f 
                                         s 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     2 
                                     + 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     n 
                                     2 
                                   
                                   ⁢ 
                                   
                                     D 
                                     / 
                                     N 
                                   
                                 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   
                                     - 
                                     2 
                                   
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Df 
                                     / 
                                     
                                       f 
                                       s 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       S 
                       B 
                       δ 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       f 
                       s 
                     
                     ⁢ 
                     
                       
                         H 
                         B 
                       
                       ⁡ 
                       
                         ( 
                         f 
                         ) 
                       
                     
                     ⁢ 
                     
                       { 
                       
                         
                           
                             R 
                             
                               1 
                               - 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         + 
                         
                           
                             R 
                             
                               1 
                               + 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         + 
                         
                           
                             R 
                             
                               2 
                               - 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         + 
                         
                           
                             R 
                             
                               2 
                               + 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     A spectrum of an output signal of the adder  146  is expressed as Equation (10).
 
 S ( f )= S   A   δ ( f )+ S   B   δ ( f )  (10)
 
     Here, Equation (11) may be satisfied to remove the second baseband signal DR 2  and extract the first baseband signal DR 1 . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               S 
                               A 
                               δ 
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                           + 
                           
                             
                               S 
                               
                                 B 
                                 ⁢ 
                                 
                                     
                                 
                               
                               δ 
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               R 
                               
                                 1 
                                 - 
                               
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                           + 
                           
                             
                               R 
                               
                                 1 
                                 + 
                               
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     By solving Equation (11), frequency responses of the first and second digital filters  144  and  145  may be expressed as Equation (12) and Equation (13). 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       A 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ⅇ 
                                 
                                   j2π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Df 
                                     / 
                                     
                                       f 
                                       s 
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           1 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                     - 
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           2 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               - 
                               
                                 
                                   f 
                                   s 
                                 
                                 2 
                               
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ⅇ 
                                 
                                   j 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Df 
                                     / 
                                     
                                       f 
                                       
                                         s 
                                         ⁢ 
                                         
                                             
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j2π 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           1 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                     - 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           2 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             
                               
                                 f 
                                 s 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       H 
                       B 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         
                                           π 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 n 
                                                 1 
                                               
                                               - 
                                               
                                                 n 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               - 
                               
                                 
                                   f 
                                   s 
                                 
                                 2 
                               
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               1 
                               
                                 
                                   f 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               n 
                                               1 
                                             
                                             - 
                                             
                                               n 
                                               2 
                                             
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             
                               
                                 f 
                                 s 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In the same manner, frequency responses of the third and fourth digital filters  154  and  155  may be expressed as Equation (14) and Equation (15). 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       C 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ⅇ 
                                 
                                   j 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Df 
                                     / 
                                     
                                       f 
                                       s 
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           2 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                     - 
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           1 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               - 
                               
                                 
                                   f 
                                   s 
                                 
                                 2 
                               
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ⅇ 
                                 
                                   j2π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Df 
                                     / 
                                     
                                       f 
                                       s 
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j2π 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           2 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                     - 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           1 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             
                               
                                 f 
                                 s 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       H 
                       D 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               n 
                                               2 
                                             
                                             - 
                                             
                                               n 
                                               1 
                                             
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               - 
                               
                                 f 
                                 2 
                               
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               1 
                               
                                 
                                   f 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               n 
                                               2 
                                             
                                             - 
                                             
                                               n 
                                               1 
                                             
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           D 
                                           / 
                                           N 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             
                               
                                 f 
                                 s 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Digital filters may be designed using the above-mentioned relationship between the first and second path signals DR A  and DR B  and the effect of relative group delay between the first and second baseband signals DR 1  and DR 2  included in the first path signal DR A . That is, the first to fourth digital filters  144 ,  145 ,  154  and  155  are designed in consideration of the group delay, so that the first and second baseband signals DR 1  and DR 2  are separated. In an exemplary embodiment, the first to fourth digital filters  144 ,  145 ,  154  and  155  may be implemented with finite impulse response (FIR) filters. 
     Furthermore, as shown in Equations (13) and (15), H B (f) and H D (f) are not frequency functions but constants. Therefore, it may be understood that the second and fourth digital filters  145  and  155  may be implemented with multipliers. In this case, a synchronous delayer may also be provided to make a delay by as much as a delay time caused by signal processing in the sampling rate up-converter  141 , the sampling rate down-converter  143  and the first or third digital filter  144  or  154 . 
       FIG. 5  is a graph illustrating a spectrum of the first baseband signal DR 1  output from the adder  146 . Referring to  FIG. 5 , it may be understood that the second baseband signal DR 2  is removed and only the first baseband signal DR 1  is extracted. According to the present invention, the first baseband signal DR 1  may be extracted using the first and second digital filters  144  and  145  and the adder  146 . 
       FIG. 6  is a graph illustrating a spectrum of the second baseband signal DR 2  output from the adder  156 . Referring to  FIG. 6 , it may be understood that the first baseband signal DR 1  is removed and only the second baseband signal DR 2  is extracted. The second baseband signal DR 2  may be extracted using the third and fourth digital filters  154  and  155  and the adder  156 . 
       FIG. 7  is a schematic block diagram illustrating a multi-band receiver  200  according to a second embodiment of the present invention. Referring to  FIG. 7 , the multi-band receiver  200  of the present invention may include an antenna  210 , first and second analog band pass filters  220  and  225 , an adder  227 , an ADC  230 , a first signal extracting unit  240  and a second signal extracting unit  250 . Here, the antenna  210 , the first and second analog band pass filters  220  and  225 , the adder  227 , the ADC  230  and the first signal extracting unit  240  are substantially the same as those of  FIG. 2 . Therefore, detailed descriptions of the foregoing elements are omitted. 
     A first signal signal — 1 may be generated by an adder  246  that adds outputs of first and second digital filters  244  and  245 . A second signal signal — 2 may be extracted by subtracting the first signal signal — 1 that is an output of the adder  246  from an output of the ADC  230 . Here, it is assumed that the first and second digital filters  244  and  245  are provided as FIR filters having a sampling rate tap length of K. In this case, the first signal signal — 1 that is the output of the adder  246  undergoes a sample delay of round(K/ 2 ) compared to the output of the ADC  230  which does not pass through a digital filter. Therefore, if the output of the ADC  230  is sample-delayed by as much as round(K/ 2 ) using a second layer  252 , it may be synchronized with the first signal signal — 1 in a subtractor  254 . When the first signal signal — 1 is subtracted from the output of the ADC  230 , which has been delayed by as much as round(K/ 2 ), by the subtractor  254 , the second signal signal — 2 is extracted. A spectrum of the second signal signal — 2 is illustrated in  FIG. 6 . 
       FIG. 8  is a schematic block diagram illustrating a multi-band receiver  300  according to a third embodiment of the present invention. In addition, although a double band is exemplarily illustrated as a multi-band, it may be understood that the present invention is applicable to a multi-band for receiving three or more signals. Referring to  FIG. 8 , the multi-band receiver  300  of the present invention may include an antenna  310 , first and second analog band pass filters  320  and  325 , an adder  327 , an ADC  330 , a first signal extracting unit  340  and a second signal extracting unit  350 . 
     The antenna  310  receives an analog RF signal transmitted wirelessly. The received analog RF signal may include at least two frequency bands. 
     The first and second analog band pass filters  320  and  325  may include broadband pass filters for filtering broadband signals. The first analog band pass filter  320  may be such designed that a passband is limited to the first bandwidth B 1 . The first analog band pass filter  320  may generate, as a result of filtering, the first analog RF signal AR 1  having the first bandwidth B 1  and the first carrier frequency f c1 . The second analog band pass filter  325  may be such designed that a passband is limited to the second bandwidth B 2 . The second analog band pass filter  325  may generate, as a result of filtering, the second analog RF signal AR 2  having the second bandwidth B 2  and the second carrier frequency f c2 . In an exemplary embodiment, the passbands and the passband widths B 1  and B 2  of the first and second analog band filters  320  and  325  may have fixed values or may be adjusted to other values. To this end, the first and second analog band pass filters  320  and  325  may include tunable band pass filters (BPFs). 
     The adder  327  adds the filtering result of the first analog band pass filter  320  and the filtering result of the second analog band pass filter  325 . The analog signals filtered by the adder  327  are transferred as a multi-band analog RF signal AR to the ADC  330 . 
     The ADC  330  samples the multi-band analog RF signal AR to output a digital baseband signal DR. The ADC  330  samples the multi-band analog RF signal AR on the basis of a sampling rate L. Furthermore, a sampled signal is quantized by the ADC  330  and is output as the multi-band digital baseband signal DR. 
     The first signal extracting unit  340  and the second signal extracting unit  350  respectively separate a first signal signal — 1 and a second signal signal — 2 from the digital baseband signal DR output from the ADC  330 . 
     The first signal extracting unit  340  includes a sample delayer  342 , a first sampling rate converter  343 , a first digital filter  344 , a second sampling rate converter  345 , a second digital filter  346  and an adder  347 . The output of the ADC  330  is allowed to pass through two signal paths by the first signal extracting unit  340 . That is, the output of the ADC  330  is divided to be transferred to a first path including the sample delayer  342  and a second path where delay does not occur. 
     The first and second paths include the first and second sampling rate converters  343  and  345  respectively. The first and second sampling rate converters  343  and  345  may adjust sampling rates of input signals by L/M times. That is, sampling rates f s ′ of baseband signals DR A  and DR B  obtained through the ADC  330  and the first and second sampling rate converters  343  and  345  may be expressed as Equation (16). 
     
       
         
           
             
               
                 
                   
                     f 
                     s 
                     ′ 
                   
                   = 
                   
                     
                       f 
                       s 
                     
                     ⁢ 
                     
                       L 
                       M 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Where L and M are natural numbers and L&lt;M. 
     Therefore, the baseband signal DR A  transferred to the first digital filter  344  has a fractional delay of LD/M due to the sample delayer  342  and the first sampling rate converter  343 . Such a fractional delay may greatly contribute to cancellation of interference. Furthermore, according to settings of the sampling rates of the first and second sampling rate converters  343  and  345 , sampling rate selection of the ADC  330  may be more flexible. 
     When the baseband signals DR A  and DR B  processed by the sampling rate converters  343  and  345  are filtered by the digital filters  344  and  346  and are added to each other by the adder  347 , an interfering baseband signal is removed. That is, the adder  347  outputs the first signal signal — 1 obtained by extracting one of the baseband signals. Response characteristics of the digital filters  344  and  346  will be described later with reference to  FIGS. 9 and 10 . 
     The second signal extracting unit  350  may include a third digital filter  354 , a fourth digital filter  356  and an adder  357 . An output signal of the first sampling rate converter  343  may pass through a third path including the third digital filter  354 . An output signal of the second sampling rate converter  345  passes through a fourth path including the fourth digital filter  356  and is added to another signal in the adder  357 . The signals output from the third and fourth paths are added to each other in the adder  357  so as to be output as the second signal signal — 2. 
     When the baseband signals DR A  and DR B  processed by the sampling rate converters  353  and  355  are filtered by the digital filters  354  and  356  and are added to each other by the adder  357 , an interfering baseband signal is removed. That is, the adder  357  outputs the second signal signal — 2 obtained by extracting one of the baseband signals. 
       FIG. 9  is a graph exemplarily illustrating a spectrum R A   δ (f) of the first path signal DR A  output from the first sampling rate converter  343  of  FIG. 8 .  FIG. 10  is a graph exemplarily illustrating a spectrum R B   δ (f) of the second path signal DR B  output from the second sampling rate converter  345  of  FIG. 8 . 
     The spectrum R A   δ (f) of the first path signal DR A  illustrated in  FIG. 9  represents the spectrum of a signal obtained by processing the digital baseband signal DR that is the output of the ADC  330  through the sample delayer  342  the first sampling rate converter  343 . That is, the spectrum R A   δ (f) of the first path signal DR A  indicates a signal to which a fractional delay of LD/M is applied. As a result, the first path signal DR A  has the same processing effect as that of applying a group delay to the second path signal DR B . 
     Referring to the spectra illustrated in  FIGS. 9 and 10 , the first and second baseband signals DR 1  and DR 2  constituting the first path signal DR A  may interfere with each other. Furthermore, it may be understood that the first and second baseband signals DR 1  and DR 2  constituting the second path signal DR B  may interfere with each other. That is, the first and second baseband signals DR 1  and DR 2  may interfere with each other at a baseband. Nonetheless, the multi-band receiver  300  (see  FIG. 8 ) of the present invention may cancel the interference between the first and second baseband signals DR 1  and DR 2  and may correctly extract the first and second baseband signals DR 1  and DR 2 . 
     It is exemplarily described herein how the first and second baseband signals DR 1  and DR 2  are extracted when the first and second baseband signals DR 1  and DR 2  interfere with each other. Herein, the first and second path signals DR A  and DR B  have signal characteristics as described below. 
     An effect of group delay due to time delay of the first baseband signal DR 1  included in the first path signal DR A  may be expressed as Equation (17) and Equation (18). Equation (17) represents an image component of the first baseband signal DR 1  transitioned from a negative band, and Equation (18) represents an image component of the first baseband signal DR 1  transitioned from a positive band.
 
 e   jθ     1−     (f)   =e   j2πn     1     LD/M   e   −j2πLDf/(Mf     s     ′)   (17)
 
 e   jθ     1+     (f)   =e   −j2πn     1     LD/M   e   −j2πLDf/(Mf     s     ′)   (18)
 
     Furthermore, an effect of group delay of the second baseband signal DR 2  included in the first path signal DR A  may be expressed as Equation (19) and Equation (20). Equation (19) represents an image component of the second baseband signal DR 2  transitioned from a negative band, and Equation (20) represents an image component of the second baseband signal DR 2  transitioned from a positive band.
 
 e   jθ     2−     (f)   =e   j2πn     2     LD/M   e   −j2πLDf/(Mf     s     ′)   (18)
 
 e   jθ     2+     (f)   =e   −j2πn     2     LD/M   e   −j2πLDf/(Mf     s     ′)   (19)
 
     Where n 1  and n 2  denote frequency band position indices of the first and second analog RF signal AR 1  and AR 2  and may have an integer value of 0, 1, 2, 3, . . . . 
     n 1  and n 2  may be expressed as Equation (21) by the carrier frequencies f c1  and f c2  of the first and second analog RF signals AR 1  and AR 2  and the sampling rates (f s ′=Lf s /M) of the sampling rate converters  343  and  345 . 
     
       
         
           
             
               
                 
                   
                     
                       n 
                       1 
                     
                     = 
                     
                       round 
                       ⁡ 
                       
                         ( 
                         
                           
                             f 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           
                             
                               Lf 
                               s 
                             
                             / 
                             M 
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       n 
                       2 
                     
                     = 
                     
                       round 
                       ⁡ 
                       
                         ( 
                         
                           
                             f 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           
                             
                               Lf 
                               s 
                             
                             / 
                             M 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     Where a round function round(x) represents rounding off of x. 
     Signals of two bands may be separated using a delay difference between the first and second path signals DR A  and DR B  and an effect of group delay between the first and second baseband signals DR 1  and DR 2 . That is, by designing the first and second digital filters  344  and  346  and the third and fourth digital filters  354  and  356  as described above, interference between two signals may be cancelled. 
     Hereinafter, a method of designing the digital filters  344  and  346  for cancelling interference between the first and second path signals DR A  and DR B  and extracting a desired signal will be described. A spectrum R A   δ (f) of the first path signal DR A  output from the first sampling rate converter  343  at a first Nyquist zone may be expressed as Equation (22). 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       A 
                       δ 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       f 
                       s 
                       ′ 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       1 
                                       - 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       1 
                                     
                                     ⁢ 
                                     
                                       LD 
                                       / 
                                       M 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       LDf 
                                       / 
                                       
                                         ( 
                                         
                                           Mf 
                                           s 
                                           ′ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       1 
                                       + 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       1 
                                     
                                     ⁢ 
                                     
                                       LD 
                                       / 
                                       M 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       LDf 
                                       / 
                                       
                                         ( 
                                         
                                           Mf 
                                           s 
                                           ′ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       2 
                                       - 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       2 
                                     
                                     ⁢ 
                                     
                                       LD 
                                       / 
                                       M 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       LDf 
                                       / 
                                       
                                         ( 
                                         
                                           Mf 
                                           s 
                                           ′ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     2 
                                     + 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     n 
                                     2 
                                   
                                   ⁢ 
                                   
                                     LD 
                                     / 
                                     M 
                                   
                                 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     LDf 
                                     / 
                                     
                                       ( 
                                       
                                         Mf 
                                         s 
                                         ′ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Furthermore, a spectrum R B   δ (f) of the second path signal DR B  output from the second sampling rate converter  345  at a first Nyquist zone may be expressed as Equation (23).
 
 S   B   δ ( f )= f   s   ′{R   1− ( f )+ R   1+ ( f )+ R   2− ( f )+ R   2+ ( f )}  (23)
 
     Spectra of signals processed by the first and second digital filters  344  and  345  may be expressed as Equation (24) and Equation (25). 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       A 
                       δ 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       f 
                       s 
                       ′ 
                     
                     ⁢ 
                     
                       
                         H 
                         A 
                       
                       ⁡ 
                       
                         ( 
                         f 
                         ) 
                       
                     
                     ⁢ 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       1 
                                       - 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       1 
                                     
                                     ⁢ 
                                     
                                       LD 
                                       / 
                                       M 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       LDf 
                                       / 
                                       
                                         ( 
                                         
                                           Mf 
                                           s 
                                           ′ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       1 
                                       + 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       1 
                                     
                                     ⁢ 
                                     
                                       LD 
                                       / 
                                       M 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       LDf 
                                       / 
                                       
                                         ( 
                                         
                                           Mf 
                                           s 
                                           ′ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     R 
                                     
                                       2 
                                       - 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     j 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       n 
                                       2 
                                     
                                     ⁢ 
                                     
                                       LD 
                                       / 
                                       M 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   ⅇ 
                                   
                                     
                                       - 
                                       j 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       LDf 
                                       / 
                                       
                                         ( 
                                         
                                           Mf 
                                           s 
                                           ′ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     2 
                                     + 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     n 
                                     2 
                                   
                                   ⁢ 
                                   
                                     LD 
                                     / 
                                     M 
                                   
                                 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     LDf 
                                     / 
                                     
                                       ( 
                                       
                                         Mf 
                                         s 
                                         ′ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       S 
                       B 
                       δ 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       f 
                       s 
                       ′ 
                     
                     ⁢ 
                     
                       
                         H 
                         B 
                       
                       ⁡ 
                       
                         ( 
                         f 
                         ) 
                       
                     
                     ⁢ 
                     
                       { 
                       
                         
                           
                             R 
                             
                               1 
                               - 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         + 
                         
                           
                             R 
                             
                               1 
                               + 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         + 
                         
                           
                             R 
                             
                               2 
                               - 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         + 
                         
                           
                             R 
                             
                               2 
                               + 
                             
                           
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     A spectrum of an output signal of the adder  347  is expressed as Equation (26).
 
 S ( f )= S   A   δ ( f )+ S   B   δ ( f )  (26)
 
     Here, Equation (27) may be satisfied to remove the second baseband signal DR 2  and extract the first baseband signal DR 1 . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               S 
                               A 
                               δ 
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                           + 
                           
                             
                               S 
                               B 
                               δ 
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               R 
                               
                                 1 
                                 - 
                               
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                           + 
                           
                             
                               R 
                               
                                 1 
                                 + 
                               
                             
                             ⁡ 
                             
                               ( 
                               f 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     By solving Equation (27), frequency responses of the first and second digital filters  344  and  346  may be expressed as Equation (28) and Equation (29). 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       A 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ⅇ 
                                 
                                   j 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     LDf 
                                     / 
                                     
                                       ( 
                                       
                                         Mf 
                                         s 
                                         ′ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   s 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ⅇ 
                                       
                                         j2π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           1 
                                         
                                         ⁢ 
                                         
                                           LD 
                                           / 
                                           M 
                                         
                                       
                                     
                                     - 
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           2 
                                         
                                         ⁢ 
                                         
                                           LD 
                                           / 
                                           M 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               - 
                               
                                 
                                   f 
                                   s 
                                   ′ 
                                 
                                 2 
                               
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ⅇ 
                                 
                                   j2π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     LDf 
                                     / 
                                     
                                       ( 
                                       
                                         Mf 
                                         s 
                                         ′ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   s 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           1 
                                         
                                         ⁢ 
                                         
                                           LD 
                                           / 
                                           M 
                                         
                                       
                                     
                                     - 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j2π 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           n 
                                           2 
                                         
                                         ⁢ 
                                         
                                           LD 
                                           / 
                                           M 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             
                               
                                 f 
                                 s 
                                 ′ 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       H 
                       B 
                     
                     ⁡ 
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               
                                 
                                   f 
                                   s 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       ⅇ 
                                       
                                         j 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               n 
                                               1 
                                             
                                             - 
                                             
                                               n 
                                               2 
                                             
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           LD 
                                           / 
                                           M 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               - 
                               
                                 
                                   f 
                                   2 
                                   ′ 
                                 
                                 2 
                               
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               1 
                               
                                 
                                   f 
                                   2 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       ⅇ 
                                       
                                         
                                           - 
                                           j 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               n 
                                               1 
                                             
                                             - 
                                             
                                               n 
                                               2 
                                             
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           LD 
                                           / 
                                           M 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             
                               
                                 f 
                                 s 
                                 ′ 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     In the same manner, the third and fourth digital filters  354  and  356  may be designed. 
     The above-mentioned relationship between the first and second path signals DR A  and DR B  and the effect of relative group delay between the first and second baseband signals DR 1  and DR 2  included in the first path signal DR A  may be used to digital filters. Since the first to fourth digital filters  344 ,  346 ,  354  and  356  are designed using group delay, the first and second baseband signals DR 1  and DR 2  may be separated. In an exemplary embodiment, the first to fourth digital filters  344 ,  346 ,  354  and  356  may be implemented with FIR filters. 
     Furthermore, as shown in Equation (29), H B (f) is not a frequency function but a constant. Therefore, it may be understood that the second and fourth digital filters  346  and  356  may be implemented with multipliers. In addition, a synchronous delayer may also be provided to make a delay by as much as a delay time generated during the filtering process performed by the first digital filter  344 . 
     The first to fourth digital filters  344 ,  346 ,  354  and  356  may be implemented with filters having an operating frequency (f s ′=Lf s /M). Furthermore, the coefficients of the digital filters may be recalculated according to the two wireless frequency bands B 1  and B 2 . The first to fourth digital filters  344 ,  346 ,  354  and  356  may be reconfigured using the recalculated coefficients so as to receive multi-band signals at arbitrary bands. 
       FIG. 11  is a schematic block diagram illustrating a multi-band receiver  400  according to a fourth embodiment of the present invention. Referring to  FIG. 11 , the multi-band receiver  400  of the present invention may include an antenna  410 , first and second analog band pass filters  420  and  425 , an adder  427 , an ADC  430 , a first signal extracting unit  440  and a second signal extracting unit  450 . Here, the antenna  410 , the first and second analog band pass filters  420  and  425 , the adder  427 , the ADC  430  and the first signal extracting unit  440  are substantially the same as those of  FIG. 8 . Therefore, detailed descriptions of the foregoing elements are omitted. 
     A first signal signal — 1 may be generated by an adder  447  that adds outputs of first and second digital filters  444  and  446 . A second signal signal — 2 may be extracted by subtracting the first signal signal — 1 that is an output of the adder  447  from an output of the ADC  430 . Here, it is assumed that the first and second digital filters  444  and  446  are provided as FIR filters having a tap length of K. Then, the first signal signal — 1 that is the output of the adder  447  undergoes a sample delay of round(K/ 2 ) compared to an output of a second sampling rate converter  445  which does not pass through a digital filter. Therefore, if the output of the second sampling rate converter  445  is sample-delayed by as much as round(K/ 2 ) using a second layer  452 , it may be synchronized with the first signal signal — 1 in a subtractor  454 . When the first signal signal — 1 is subtracted from the output of the second sampling rate converter  445 , which has been delayed by as much as round(K/ 2 ), by the subtractor  454 , the second signal signal — 2 is extracted. 
     According to the present invention, multi-band signals at arbitrary frequency bands may be simultaneously down-converted to be received, while using a single RF chain and a single ADC. 
     According to the present invention, interference between two signals at a baseband may be cancelled to separate a desired signal using a single ADC. 
     Furthermore, since a single ADC is used, the complexity and size of hardware and the cost for manufacturing the same are reduced compared to a typical technology for which two ADCs are used. 
     Moreover, the present invention may resolve the performance degradation caused by a delay time error and signal magnitude irregularity between two paths which occur when using a second order band pass sampling technique for which two ADCs are used. 
     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 of the present invention. Thus, to the maximum extent allowed by law, the scope of the present invention 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.