Patent Publication Number: US-2012039417-A1

Title: Band pass sampling receiver

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 No. 10-2010-0076887, filed on Aug. 10, 2010, the entire contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention disclosed herein relates to a radio frequency receiver, and more particularly, to a band pass sampling receiver. 
     A superheterodyne receiver converts a received radio wave to an intermediate frequency having a certain frequency. And, by amplifying the converted intermediate frequency, sufficient amplification degree and selectivity are obtained. By using the amplified intermediate frequency, a baseband signal is down-converted. 
     In the case of receiving a Radio Frequency (RF) signal which is an analog signal, for applying an existing sampling theory, the RF signal is sampled by using a Nyquist sampling rate which is a sampling rate larger than at least twice as much as a carrier frequency. The more the carrier frequency of the RF signal is increased, the more the sampling rate is increased. However, a bandwidth of the RF signal, where a signal wanted to be received exits, is just about 0.03% to about 2% of the carrier frequency of the RF signal. In the case that the carrier frequency of the RF signal is a high frequency, the receiver should sample the RF signal with a higher sampling rate. In this case, a quantity of the sampled data increases exponentially, and the receiver should perform a data process very inefficiently. 
     For overcoming this limitation, a band pass sampling is proposed. According to the band pass sampling, the RF signal may be sampled with a lower sampling rate than the Nyquist sampling rate of the RF signal. The band pass sampling is also called a harmonic sampling or a sub-sampling. 
     The sampling may be performed with a lower sampling rate than the Nyquist sampling rate using the band pass sampling. Accordingly, the data quantity generated while the RF signal is sampled is reduced. According to the band pass sampling, aliasing is intentionally generated by performing the sampling with a lower rate in comparison with the Nyquist sampling rate. The band pass sampling basically has a sampling rate depending on a bandwidth of data. 
     The band pass sampling is generally applied to a digital direct conversion or an RF direct conversion. If the band pass sampling is applied to the digital direct conversion, the sampling is performed right after the RF signal received by an antenna is amplified at a Low Noise Amplifier (LNA). Therefore, a low-priced and small-sized receiver may be implemented. 
     SUMMARY OF THE INVENTION 
     The present invention provides a band pass sampling receiver which performs downward conversion, quantization, signal separation, signal detection and signal suppression by referencing a phase shift of first and second stream signals, sampling frequency and frequency bands of the RF signals. 
     Embodiments of the present invention provide band pass sampling receivers including a sampling process unit configured to generate first and second stream signals sampled by applying a sampling rate having a time lag to a combined signal of first and second RF signals of different frequency bands; and a signal process unit configured to perform an operation to a first interpolant function and the first stream signal and to a second interpolant function and the second stream signal, and separate the first and second RF signals by adding results of the two operations, wherein the first and second interpolant functions are determined based on the time lag, the sampling rate and frequency bands of the first and second RF signals. 
     In some embodiments, the signal process unit may detect one of the first and second RF signals. 
     In other embodiments, the signal process unit may eliminate the first or second RF signals. 
     In still other embodiments, the first and second interpolant functions may be determined based on a phase shift of the first and second stream signals generated according to the time lag. 
     In even other embodiments, the first and second interpolant functions may be determined based on carrier frequencies of the frequency bands of the first and second RF signals. 
     In yet other embodiments, the carrier frequency of the frequency band of the first RF signal corresponds to a multiple of the sampling rate and a first constant, and the carrier frequency of the frequency band of the second RF signal corresponds to a multiple of the sampling rate and a second constant, and the first and second interpolant functions may be determined based on the first and second constants. 
     In further embodiments, the detecting the first RF signal may detect the first RF signal down-converted to a base band. 
    
    
     
       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 block diagram illustrating a second-order band pass sampling receiver; 
         FIG. 2  is a graph illustrating a positive frequency spectrum in the case that the second-order band pass sampling receiver receives first and second signals; 
         FIG. 3  is a block diagram illustrating a second-order band pass sampling receiver which receives a plurality of RF signals; 
         FIG. 4  is a graph illustrating a positive frequency spectrum in the case that first to Rth signals are inputted to the second-order band pass sampling receiver of  FIG. 3 ; and 
         FIG. 5  is a graph illustrating a positive frequency spectrum in the case that 4 RF signals are received by the second-order band pass sampling receiver of  FIG. 3 . 
         FIG. 6  is a table exemplarily showing the value of the complex constant |C k,x |. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The following explanations are just exemplary as a matter of fact, and they are not to limit the scope of the technical concept of the present invention. It should be understood that the above-given general explanations and the following explanations are exemplary, and it should be considered that additional explanations of the present invention are provided. Reference symbols are shown at the preferred embodiments of the present invention in detail, and examples of them are shown at the accompanying drawings. In any of possible cases, same reference numerals refer to same or like elements. 
     The expression “at least one of A, B and C” is interpreted as meaning logic (A or B or C) not using exclusive logic OR. It should be understood that steps of a method may be performed in different orders unless the principle of the present invention is changed. 
     Hereinafter, it will be described about an exemplary embodiment of the present invention in conjunction with the accompanying drawings. 
       FIG. 1  is a block diagram illustrating a second-order band pass sampling receiver  100 . Referring to  FIG. 1 , the second-order band pass sampling receiver  100  includes an RF filter unit  110 , a sampling and quantization process unit  120 , a clock generation unit  130  and a signal process unit  140 . 
     The RF filter unit  110  selects an RF signal transmitted from a transmitter side (not shown). The RF filter unit  110  includes first and second RF filters  111  and  112 . For instance, the first and second RF filters  111  and  112  may be tunable RF filters. The RF filter unit  110  selects a frequency band corresponding to first and second RF signals R 1 (f) and R 2 (f) by using the first and second RF filters  111  and  112 . In  FIG. 1 , it is illustrated that the RF filter unit  110  selects two RF signals. However, this is just exemplary, i.e., the RF filter unit  110  may select a plurality of signals by using a plurality of RF filters. 
     The first signal R 1 (f) is selected by the first filter  111 . And, the second signal R 2 (f) is selected by the second filter  112 . Although not illustrated in  FIG. 1 , the second-order band pass sampling receiver  100  may include a Low Noise Amplifier (LNA). The first and second signals R 1 (f) and R 2 (f) may be amplified and transferred to the sampling and quantization process unit  120 . 
     The sampling and quantization process unit  120  includes first and second sampling units  121  and  122 , and first and second quantization units  125  and  126 . The sampling and quantization process unit  120  converts an analog signal to a digital signal. That is, the sampling and quantization process unit  120  performs a sub-sampling operation to the first and second signals R 1 (f) and R 2 (f). 
     The first and second sampling units  121  and  122  perform the sampling operation to the selected signal in synchronization with a clock signal provided by the clock generation unit  130 . The first sampling unit  121  performs the sampling operation to a signal which is a combined signal of the first and second signals R 1 (f) and R 2 (f) with nT s  as a unit, where T s  is a sampling time. The second sampling unit  122  performs the sampling operation to the combined signal of the first and second signals R 1 (f) and R 2 (f) with nT s +TΔ as a unit. That is, the sampling operation of the second sampling unit  122  is delayed from that of the first sampling unit  121  as much as the delay time TΔ. Herein, n is an integer. 
     If the sampling operation is performed to the combined signal of the first and second signals R 1 (f) and R 2 (f), the aliasing is generated between the first and second signals down-converted to a baseband. For example, the baseband may be 1 st  Nyquist zone. This will be explained in detail referring to  FIG. 2 . 
     The first and second quantization units  125  and  126  perform a quantization operation to signals sampled at the first and second sampling units  121  and  122  respectively. The first and second quantization units  125  and  126  perform the quantization operation based on the clock signal with nT s  as a unit received from the clock generation unit  130 . 
     And, the first and second quantization units  125  and  126  generate a first stream signal R δA (f) and a second stream signal R δB (f). That is, the processed and outputted signal from the first sampling unit  121  and the first quantization unit  125  is the first stream signal R δA (f). The processed and outputted signal from the second sampling unit  122  and the second quantization unit  126  is the second stream signal R δB (f). 
     The first quantization unit  125  transfers the first stream signal R δA (f) to the signal process unit  140 . The second stream signal R δB (f) may be sampled after being delayed as much as TΔ in comparison with the first stream signal R δA (f). In this case, there occurs a phase shift between the first and second stream signals R δA (f) and R δB (f). 
     The clock generation unit  130  generates the clock signal with nT s  as a unit and the clock signal with nT s +TΔ as a unit. And, the generated clock signals are provided to the sampling and quantization unit  120 . 
     The signal process unit  140  includes a first interpolant unit  141 , a second interpolant unit  142  and an adder  143 . The first interpolant unit  141  performs a multiplication operation to the first stream signal R δA (f) and a first interpolant function S A (f). The second interpolant unit  142  performs the multiplication operation to the second stream signal R δB (f) and a second interpolant function S B (f). 
     The adder  143  receives operation results of the first interpolant unit  141  and the second interpolant unit  142 . And, the adder adds the operation result of the first interpolant unit  141  to that of second interpolant unit  142 . 
     According to the band pass sampling receiver according to the embodiment of the present invention, the band pass sampling receiver selects the one frequency band among the plurality of frequency bands including the RF signals respectively by reconstituting of the signal process unit. That is, by performing a digital signal processing by using the phase shift of the first and second stream signals R δA (f) and R δB (f), only one of the first and second signal R 1 (f) and R 2 (f) may be recovered. Herein, the digital signal processing means a process of multiplying the first and second stream signals R δA (f) and R δB (f) by the first and second interpolant functions S A (f) and S B (f) respectively and adding the results of the multiplication. 
       FIG. 2  is a graph illustrating a positive frequency spectrum in the case that the second-order band pass sampling receiver  100  of  FIG. 1  receives the first and second signals R 1 (f) and R 2 (f). Referring to  FIG. 2 , a horizontal axis represents a frequency, and a vertical axis represents amplitude of a signal. At a band divided by a predetermine frequency interval, the first and second signals R 1 (f) and R 2 (f) are positioned at first and second frequency bands {circle around (a)} and {circle around (b)} corresponding n 1  and n 2  respectively. Bandwidths of the first and second frequency bands {circle around (a)} and {circle around (b)} correspond to bandwidths of the first and second RF filters  111  and  112 . And, the bandwidths of the first and second RF filters  111  and  112  are determined by the largest bandwidth among bandwidths of the first and second signals R 1 (f) and R 2 (f). 
     In  FIG. 2 , it is exemplarily illustrated that the first and second signals R 1 (f) and R 2 (f) are located at a bandwidth divided by an interval of a sampling rate f s . The sampling rate f s  is 1/T s  (refer to the output of the clock generation unit  130  of  FIG. 1 ). The sampling rate f s  may be determined by the bandwidths of the first and second frequency bands {circle around (a)} and {circle around (b)}. 
     In  FIG. 2 , the RF signal R 1 (f) represents RF signals received in first frequency band {circle around (a)}. For example, a transmitter can transmit a plurality of RF signals in one frequency band. In this case, the RF signal R 1 (f) means the plurality of RF signals in one frequency band. Furthermore, the RF signal R 2 (f) represents all RF signals received in second frequency band {circle around (b)}. 
     Signals of different frequency bands are transmitted and received based on the carrier frequency. For instance, the carrier frequency may be a center carrier frequency. The first signal R 1 (f) included in the first frequency band {circle around (a)} is received based on a first carrier frequency n 1 ·f s . The second signal R 2 (f) included in the second frequency band {circle around (b)} is received based on a second carrier frequency n 2 ·f s . n 1  and n 2  may be integers. Hereinafter, it is assumed that n 1  and n 2  are integers for convenience. 
     In the case that the first and second signals R 1 (f) and R 2 (f) are down-converted to the base band, there occurs the aliasing at the base band. According to the embodiment of the present invention, one of the first and second signals R 1 (f) and R 2 (f) down-converted to the base band may be selected, or both of them may be eliminated. 
         R   δ1B ( f )=β n1   ·R   δ1A ( f )
 
         R   δ2B ( f )=β n2   ·R   δ2A ( f )  (1)
 
     Equation (1) shows a relation between the first and second stream signals R δA (f) and R δB (f). In Equation (1), β=e −j2πTΔf     s   , R δ1A (f) corresponds to the first signal R 1 (f) included in the first stream signal R δA (f). R δ1B (f) corresponds to the first signal R 1 (f) included in the second stream signal R δB (f). Likewise, R δ2A (f) corresponds to the second signal R 2 (f) included in the first stream signal R δA (f). R δ2B (f) corresponds to the second signal R 2 (f) included in the second stream signal R δB (f). 
     That is, the first stream signal R δA (f) may include R δ1A (f) which is a sub-sampled signal of the first signal R 1 (f), and R δ2A (f) which is a sub-sampled signal of the second signal R 2 (f). The second stream signal R δB (f) includes R δ1B (f) which is a sub-sampled signal of the first signal R 1 (f), and R δ2B (f) which is a sub-sampled signal of the second signal R 2 (f). 
     A relation between R δ1A (f) and R δ1B (f) depends on the delay time TΔ, the sampling rate f s  and n 1 . A relation between R δ2A (f) and R δ2B (f) depends on the delay time TΔ, the sampling rate f s  and n 2 . 
     Hereinafter, it is assumed that the first and second signals R 1 (f) or R 2 (f) are eliminated. The first and second interpolant functions S A (f) and S B (f) may be configured to satisfy Equations (2) and (3). 
         B·[S   A ( f )· R   +δ1A ( f )+ S   B ( f )· R   +δ1B ( f )]= C·R   +1A ( f−n 1 ·B )
 
         B·[S   A ( f )· R   −δ1A ( f )+ S   B ( f )· R   −δ1B ( f )]= C·R   −1A ( f+n 1 ·B )  (2)
 
         B·[S   A ( f )· R   +δ2A ( f )+ S   B ( f )· R   +δ2B ( f )]=0
 
         B·[S   A ( f )· R   −δ2A ( f )+ S   B ( f )· R   −δ2B ( f )]=0  (3)
 
     In Equation (2), C is a complex constant. In Equations (2) and (3), B represents a larger bandwidth between the bandwidths of the first and second RF filters  111  and  112 . C·R +1A (f−n 1 ·B) and C·R −1A (f+n 1 ·B) respectively represent a positive frequency spectrum and a negative frequency spectrum of the first signal down-converted to the base band. 
     R +δ1A (f) and R −δ1A (f) respectively represent the positive frequency spectrum and the negative frequency spectrum of R δ1A (f). R +δ1B (f) and R −δ1B (f) respectively represent the positive frequency spectrum and the negative frequency spectrum of R δ1B (f). Likewise, R +δ2A (f) and R −δ2A (f) respectively represent the positive frequency spectrum and the negative frequency spectrum of R δ2A (f). R +δ2B (f) and R −δ2B (f) respectively represent the positive frequency spectrum and the negative frequency spectrum of R δ2B (f). 
     In Equation (3), since the second signal R 2 (f) is eliminated, the right side is 0. And, amplitude of the first signal (C·R +1A (f−n 1 ·B) and C·R −1A (f+n 1 ·B)) down-converted to the base band is proportional to the complex constant C. 
     For obtaining the first and second interpolant functions S A (f) and S B (f) which satisfy Equations (2) and (3), exemplarily, the first interpolant function S A (f) may be selected as expressed in Equation (4) for convenience of computation. 
     
       
         
           
             
               
                 
                   
                     
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                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
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                   4 
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     Meanwhile, referring to Equation (1), a relation of the first and second stream signals to the second signal R 2 (f) (R δ2A (f) and R δ2B (f)) is expressed as Equation (5). 
     
       
         
           
             
               
                 
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     By substituting Equations (4) and (5) for Equation (3), Equation (6) is obtained. 
     
       
         
           
             
               
                 
                   
                     
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     Equation (6) represents a relation of the first and second interpolant functions S A (f) and S B (f). Since β=e −j2πTΔf     s   , the relation of the first and second interpolant functions S A (f) and S B (f) may be determined by the delay time TΔ, the sampling rate f s  and a value of n 2 . 
     Meanwhile, like Equation (1), a relation of the first and second stream signals to the first signal R 1 (f) (R δ1A (f) and R δ1B (f)) is expressed as Equation (7). 
     
       
         
           
             
               
                 
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     By substituting Equations (6) and (7) for Equation (2), Equation (8) is obtained. 
         R   +δ1A ( f )·[1−β n2 ·β −n1   ·R   +δ1A ( f )]= C·R   +1A ( f−n 1 ·B )
 
         R   −δ1A ( f )·[1−β −n2 ·β n1   ·R   −δ1A ( f )]= C·R   −1A ( f+n 1 ·B )  (8)
 
     In Equation (8), it is assumed that the sampling rate f s  is a bandwidth B. And, it may be that β=e −j2πTΔf     s   =e −j2πTΔB . 
     The amplitude of the first signal down-converted to the base band is proportional to the complex constant C. According to the embodiment of the present invention, an absolute value of the complex constant C is determined based on the delay time TΔ, the sampling rate f s  and the first and second frequency bands {circle around (a)} and {circle around (b)}. For instance, the absolute value of the complex constant C is calculated as expressed in Equation (9). 
       | C|=| 1−β ±(n2−n1) |=√{square root over (2·(1−cos [2 π·TΔ·f   s   ·|n 2 −n 1|]))}  (9)
 
     Referring to Equation (9), the value of the complex constant C is determined based on the delay time TΔ, the sampling rate f s  and |n 2 −n 1 |. 
     In the case of |C|=0, the amplitude of the first signal down-converted to the base band may be 0. In this case, the first and second signals down-converted to the base band may be eliminated. The case of |C|=0 is called an interpolant null. 
     In the case of |C|≠0, the amplitude of the first signal down-converted to the base band may have a certain value. In detail, in the case of 2π·TΔ·f s ·|n 2 −n 1 |=2π·m, the amplitude of the first signal down-converted to the base band may be 0. And, in the case of 2π·TΔ·f s ·|n 2 −n 1 |≠2π·m, the amplitude of the first signal down-converted to the base band may have a certain value. Herein, m is an integer. 
       FIG. 3  is a block diagram illustrating a second-order band pass sampling receiver  200  which receives a plurality of RF signals. The second-order band pass sampling receiver  200  includes an RF filter unit  210 , a sampling and quantization process unit  120 , a clock generation unit  130  and a signal process unit  140 . Referring to  FIG. 3 , the second-order band pass sampling receiver  200  is configured in the same manner as the second-order band pass sampling receiver  100  except that the RF filter  210  selects more than two frequency bands. 
     The RF filter unit  210  includes first to Rth RF filters  211  to  21 R. The first to Rth RF filters  211  to  21 R respectively select predetermined frequency bands and output first to Rth signals R 1 (f) to R R (f). 
     A signal generated by combining the first to Rth signals R 1 (f) to R R (f) is sequentially inputted to the first sampling unit  121  and the first quantization unit  125 , and outputted as the first stream signal R δA (f). And, the signal generated by combining the first to Rth signals R 1 (f) to R R (f) is sequentially inputted to the second sampling unit  122  and the second quantization unit  126 , and outputted as the second stream signal R δB (f). 
     The signal process unit  140  includes the first and second interpolant units  141  and  142 , and the adder  143 . According to the embodiment of the present invention, the first and second interpolant functions S A (f) and S B (f) are selected referring to the sampling rate f s , the delay time TΔ, and frequency bands of the first to Rth signals R 1 (f) to R R (f). 
     According to the embodiment of the present inventions, one RF signal is obtained among a plurality of RF signals by reconstructing of the signal process unit. 
     Furthermore, assume that some of the first to Rth signals R 1 (f) to R R (f) are interference signals, and not regular signals. By reconstructing of the signal process unit, the interference signals are eliminated, and signal in desired frequency band may be obtained. 
       FIG. 4  is a graph illustrating a positive frequency spectrum in the case that the first to Rth signals R 1 (f) to R R (f) are inputted to the second-order band pass sampling receiver  200 . Referring to  FIG. 4 , a horizontal axis represents a frequency, and a vertical axis represents amplitude of a signal. At a band divided by interval of the sampling rate f s , the first to Rth signals R 1 (f) and R R (f) are positioned at first to Rth frequency bands {circle around (c)} to {circle around (d)} corresponding n 1  to nR respectively. 
     The signals included in the first to Rth frequency bands {circle around (c)} to {circle around (d)} are transmitted and received based on carrier frequencies n 1 ·f s  to nR·f s  respectively. n 1  to nR may be integers. Hereinafter, it is assumed that n 1  to nR are integers for convenience. 
     As above-described referring to Equations (2) to (9), the signal process unit  140  performs the signal processing to the first stream signal R δA (f) and the second stream signal R δB (f), and may detect a signal of a desired frequency band. For instance, an output result of the adder  143  is expressed as Equation (10). 
         F =( S   A ( f )· R   δ1A ( f )+ S   B ( f )· R   δ1B ( f )+ . . .
 
       +S A (f)·R δRA (f)+S B (f)·R δRB (f)  (10)
 
     In Equation (10), F represents an output signal of the adder  143 . Like Equation (1), the relation between the first and second stream signals R δA (f) and R δB (f) is expressed as Equation (11). 
         R   δkB ( f )=β nk   ·R   δkA ( f )  (11)
 
     In Equation (11), 1≦k≦R, β=e −j2πTΔf     s   . Equation (11) shows the relation between the first and second stream signals R δA (f) and R δB (f). That is, the relation between the first and second stream signals R δA (f) and R δB (f) of the kth signal R k (f) may be determined according to the delay time TΔ, the sampling rate f s  and nk. By substituting Equation (11) for Equation (10), Equation (12) is obtained. 
     
       
         
           
             
               
                 
                   
                     
                       
                         F 
                         = 
                           
                          
                         
                           
                             
                               R 
                               
                                 δ1 
                                  
                                 
                                     
                                 
                                  
                                 A 
                               
                             
                             · 
                             
                               ( 
                               
                                 f 
                                 - 
                                 
                                   n 
                                    
                                   
                                       
                                   
                                    
                                   
                                     1 
                                     · 
                                     B 
                                   
                                 
                               
                               ) 
                             
                             · 
                             
                               ( 
                               
                                 
                                   
                                     S 
                                     A 
                                   
                                    
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       S 
                                       B 
                                     
                                      
                                     
                                       ( 
                                       f 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     β 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           … 
                           + 
                           
                             
                               R 
                               
                                 δ 
                                  
                                 
                                     
                                 
                                  
                                 RA 
                               
                             
                             · 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ( 
                             
                               f 
                               - 
                               
                                 nR 
                                 · 
                                 B 
                               
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               
                                 
                                   S 
                                   A 
                                 
                                  
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   
                                     S 
                                     B 
                                   
                                    
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 · 
                                 
                                   β 
                                   nR 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               C 
                               
                                 1 
                                 , 
                                 x 
                               
                             
                             · 
                             
                               
                                 R 
                                 
                                   1 
                                    
                                   A 
                                 
                               
                                
                               
                                 ( 
                                 
                                   f 
                                   - 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     
                                       1 
                                       · 
                                       B 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           … 
                           + 
                           
                             
                               C 
                               
                                 k 
                                 , 
                                 x 
                               
                             
                             · 
                             
                               
                                 R 
                                 kA 
                               
                                
                               
                                 ( 
                                 
                                   f 
                                   - 
                                   
                                     nk 
                                     · 
                                     B 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             C 
                             
                               R 
                               , 
                               x 
                             
                           
                           · 
                           
                             
                               R 
                               RA 
                             
                              
                             
                               ( 
                               
                                 f 
                                 - 
                                 
                                   nR 
                                   · 
                                   B 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The output signal of the adder  143  may be expressed as Equation (12) at the base band. C 1,x ·R 1A (f−n 1 ·B) to C R,x ·R RA (f−nR·B) respectively represent the first to Rth signal down-converted to the base band. C k,x ·R kA (f−nk·B) (1≦k≦R) represents the kth signal down-converted to the base band. Absolute values of C 1,x ·R 1A (f−n 1 ·B) to C R,x ·R RA (f−nR·B) may be respectively proportional to those of the complex constants C 1,x  to C R,x . 
     That is, the absolute value of the kth signal down-converted to the base band may be proportional to the absolute value of the complex constant C k,x . Accordingly, based on the absolute value of the complex constant C k,x , the RF signals of different frequency bands may be recovered or eliminated. 
     The relation between the first interpolant function S A (f) and the second interpolant function S B (f) is exemplarily expressed as Equation (13). 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       B 
                     
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               - 
                               
                                 β 
                                 
                                   - 
                                   nx 
                                 
                               
                             
                              
                             
                               
                                 S 
                                 A 
                               
                                
                               
                                 ( 
                                 f 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               B 
                             
                             &lt; 
                             f 
                             &lt; 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 β 
                                 nx 
                               
                             
                              
                             
                               
                                 S 
                                 A 
                               
                                
                               
                                 ( 
                                 f 
                                 ) 
                               
                             
                           
                         
                         
                           
                             0 
                             &lt; 
                             f 
                             &lt; 
                             B 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In Equation (13), the relation between the first and second interpolant functions S A (f) and S B (f) may be determined according to the delay time TΔ, the sampling rate f s  and a value of nx. 
     Referring to Equation (13), the absolute value of the complex constant C k,x  (1≦k≦R) of Equation (12) is expressed as Equation (14). 
       | C   k,x |=|1−β ±(nk−nx) |=√{square root over (2·(1−cos [2 π·TΔ·f   s   ·|nk−nx |]))}  (14)
 
     Referring to Equation (14), the absolute value of the complex constant C k,x  is determined according to the delay time TΔ, the sampling rate f s , nk and nx. nk (1≦k≦R) may correspond to the carrier frequencies of the first to Rth frequency bands {circle around (c)} to {circle around (d)}. 
     According to the embodiment of the present invention, it is determined whether to recover a signal at the base band according to the absolute value of the complex constant C k,x . In the case of |C k,x |=0, the absolute value of the kth signal down-converted to the base band may be 0. And, in the case of |C k,x |≠0, the absolute value of the kth signal down-converted to the base band may have another value but 0. 
     In detail, in the case of 2π·TΔ·f s ·|nk−nx|=2π·m, the absolute value of the kth signal down-converted to the base band may be 0. And, in the case of 2π·TΔ·f s ·|nk−nx|≠2π·m, the absolute value of the kth signal down-converted to the base band may have a certain value. Herein, m is an integer. 
     According to Equation (14), in the case that the RF signals of different frequency bands are received, an undesired signal may be eliminated by using the delay time TΔ, the sampling rate f s , and |nk−nx|. 
       FIG. 5  is a graph illustrating a positive frequency spectrum in the case that 4 RF signals are received by the second-order band pass sampling receiver  200  of  FIG. 3 . Referring to  FIGS. 3 and 5 , the RF signals of 4 frequency bands are received by the second-order band pass sampling receiver  200 . The different 4 RF signals R 1 (f) to R 4 (f) are respectively positioned at different frequency bands n 1 , n 2 , n 3  and n 4  divided by interval of the sampling rate f s . 
     In  FIG. 5 , the first to fourth RF signals R 1 (f) to R 4 (f) represents RF signals received in first to fourth frequency bands i to iv respectively. For example, a transmitter can transmit a plurality of RF signals in one frequency band. In this case, the RF signal R 1 (f) may represent the plurality of RF signals in one frequency band. 
     The RF filter unit  210  may select the first to fourth RF signals R 1 (f) to R 4 (f). For instance, the RF filter unit  210  may include 4 RF filters, and select the first to fourth RF signals R 1 (f) to R 4 (f) through a band pass filtering process. 
     The sampling and quantization unit  120  may perform the sampling and quantization operation to the first to fourth RF signals R 1 (f) to R 4 (f). The sampling and quantization unit  120  may perform the sampling and quantization operation in synchronization with the clock signal of the clock generation unit  130 . The sampling and quantization unit  120  may generate the first and second stream signals R A (f) and R B (f). 
     The signal process unit  140  receives the first and second stream signals R A (f) and R B (f). The signal outputted from the adder  143  is expressed as Equation (15) at the base band. 
     
       
         
           
             
               
                 
                   
                     
                       
                         F 
                         = 
                           
                          
                         
                           
                             
                               R 
                               
                                 δ1 
                                  
                                 
                                     
                                 
                                  
                                 A 
                               
                             
                             · 
                             
                               ( 
                               
                                 f 
                                 - 
                                 
                                   n 
                                    
                                   
                                       
                                   
                                    
                                   
                                     1 
                                     · 
                                     B 
                                   
                                 
                               
                               ) 
                             
                             · 
                             
                               ( 
                               
                                 
                                   
                                     S 
                                     A 
                                   
                                    
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       S 
                                       B 
                                     
                                      
                                     
                                       ( 
                                       f 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     β 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           … 
                           + 
                           
                             
                               R 
                               
                                 δ4 
                                  
                                 
                                     
                                 
                                  
                                 A 
                               
                             
                             · 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ( 
                             
                               f 
                               - 
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 
                                   4 
                                   · 
                                   B 
                                 
                               
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               
                                 
                                   S 
                                   A 
                                 
                                  
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   
                                     S 
                                     B 
                                   
                                    
                                   
                                     ( 
                                     f 
                                     ) 
                                   
                                 
                                 · 
                                 
                                   β 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     4 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               C 
                               
                                 1 
                                 , 
                                 x 
                               
                             
                             · 
                             
                               
                                 R 
                                 
                                   1 
                                    
                                   A 
                                 
                               
                                
                               
                                 ( 
                                 
                                   f 
                                   - 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     
                                       1 
                                       · 
                                       B 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           … 
                           + 
                           
                             
                               C 
                               
                                 4 
                                 , 
                                 x 
                               
                             
                             · 
                             
                               
                                 R 
                                 
                                   4 
                                    
                                   A 
                                 
                               
                                
                               
                                 ( 
                                 
                                   f 
                                   - 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     
                                       4 
                                       · 
                                       B 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Referring to  FIG. 5  again, first to fourth frequency bands i to iv respectively correspond to n 1 ·f s  to n 4 ·f s . 
     For instance, it is assumed that carrier frequencies of the first to fourth frequency bands i to iv are respectively about 1.11 GHz, about 1.22 GHz, about 1.43 GHz and about 1.64 GHz. And, it is assumed that only the signal of 1.11 GHz is to be recovered. According to absolute values of the complex constants C 1,x  to C 4,x , it is determined whether to recover the signal at the base band. 
     For instance, if the sampling rate is selected so that f s =100 MHz, n 1 , n 2 , n 3  and n 4  may be respectively determined as 11, 12, 14 and 16. And, in the case that the delay time TΔ is selected as 5 ns, exemplarily, the first and second interpolant functions S A (f) and S B (f) may be designed as 1 and −β 10 . That is, in Equations (13) and (14), nx is 10. Referring to Equation (14), a table of  FIG. 6  is obtained. 
       FIG. 6  is a table exemplarily showing the value of the complex constant |C k,x |. Referring to  FIG. 6 , in the case of n 1 =11, |C 1,x |=2. Accordingly, the first signal transitioned to the base band is recovered. On the contrary, |C 2,x |, |C 3,x | and |C 4,x | are 0. Therefore, the second to fourth signals transitioned to the base band may be eliminated. 
     Assume that some of the second to fourth signals R 2 (f) to R R (f) are interference signals, and not regular signals. And, by reconstructing of the signal process unit, the interference signals are eliminated, and signal in desired frequency band may be obtained. 
     According to the band pass sampling receiver and the method for operating the same according to the embodiment of the present invention, the first and second stream signals are generated by performing the sampling process to the signal which is a combined signal of the plurality of RF signals of different frequency bands with a time lag. And, by referencing the phase shift of the first and second stream signals, the sampling frequency and the frequency bands of the RF signals, the downward conversion, quantization, signal separation, signal detection and signal suppression are performed to the RF signals. Accordingly, the band pass sampling receiver which detects one RF signal and the method for operating the same are provided. 
     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.