Patent Publication Number: US-10763906-B1

Title: Cognitive radio technique for efficiently receiving multiple signals using polyphase downconverter channelizers

Description:
FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT 
     The United States Government has ownership rights in this invention. Licensing inquiries may be directed to Office of Research and Technical Applications, Naval Information Warfare Center, Pacific, Code 72120, San Diego, Calif., 92152; telephone (619) 553-5118; email: ssc_pac_t2@navy.mil. Reference Navy Case No. 104985. 
    
    
     BACKGROUND OF THE INVENTION 
     Multiple radio frequency (RF) signal reception is becoming and will certainly be a key capability in current and future radio communications. It has already begun to be used in Long-Term Evolution (LTE)-Advanced and is a key feature of 5G New Radio (NR) (the next major cellular standard after LTE) because of the high data rates it enables; specifically, carrier aggregation allows for the use of up to five carriers in LTE-Advanced and up to sixteen carriers in 5G NR to increase data rates. With the overcrowded nature of frequency spectrum due to limited spectrum resources, cognitive radios will need to be able to dynamically receive multiple signals at carrier frequencies that change with time. While the prior art does not address this issue, it may be desirable to consider methods of reducing computational complexity in RF receivers from a holistic perspective for multiple signal reception applications. Typically others try to minimize the complexity at each stage of the signal reception process which does not necessarily result in the lowest complexity when looked at from a larger perspective. For example, using the smallest valid sampling rate to sample multiple signals without considering where the signals are placed after sampling. Another example is taking the signal placement at the input to a polyphase downconverter channelizer as a given and introducing additional computational complexity in the channelizer or at its output to process signals not falling entirely within one of the input channels. 
     Bandpass sampling of a single analog RF signal is well known. This will be described with reference to  FIG. 1 . 
       FIG. 1  illustrates a prior art bandpass-filtering system  100 , which includes an antenna  102  and a receiving portion  104 . Receiving portion  104  includes a bandpass filter, and LNA component  106  and an ADC component  108 . 
     In operation, antenna  102  receives an analog radio frequency (RF) signal  118 , having a carrier frequency. Antenna  102  passes analog RF signal  118  to receiving portion  104  via line  112 . Bandpass filters and LNA component  106  bandpass-filters and amplifies analog RF signal  118  so as to output amplified filtered analog RF signal  120  to ADC component  108  via line  114 . ADC component  108  samples amplified filtered analog RF signal  120  at a predetermined sample rate that is below its Nyquist rate and that is still able to reconstruct the signal. ADC component  108  outputs an intermediate frequency (IF) digital signal  122  that corresponds to amplified filtered analog RF signal  120  via an output line  116  for further processing (not shown). 
     Further using a polyphase downconverter channelizer to separate a plurality of received signals is well known. What is needed is a system and method that determines a minimum sampling frequency, F s , for use in the bandpass sampling of a plurality of received signals. 
     SUMMARY OF THE INVENTION 
     An aspect of the present disclosure is drawn to a system for receiving a plurality N of analog radio frequency signals. The system includes a bandpass-filtering component, an analog to digital converter (ADC), an M-path polyphase downcoverter channelizer, a range-finding component and a frequency-setting component. The bandpass-filtering component is operable to bandpass filter the plurality N of analog radio frequency signals. The ADC is operable to generate digitally sampled signals based on the bandpass-filtered plurality N of analog radio frequency signals. The N-path polyphase downcoverter channelizer is operable to output converted intermediate frequency N signals based on the digitally sampled signals, respectively. The range-finding component is operable to determine a minimum sample frequency range, [F s,min1 , F s,min2 ], for sampling the bandpass-filtered plurality of analog radio frequency signals. The frequency-setting component is operable to determine the minimum sampling frequency, F s , and to provide a sampling frequency instruction to the ADC. F s,min1  is the smallest sampling frequency that results in no aliasing of the N signals when bandpass sampling is performed, whereas F s,min2  is larger than F s,min1  and additionally results in no aliasing of the N signals when bandpass sampling is performed, wherein F s,min1 ≤F s ≤F s,min2 . The ADC is operable to sample the bandpass-filtered plurality N of analog radio frequency signals using the minimum sampling frequency, F s , indicated in the sampling frequency instruction to generate digitally sampled signals, wherein N is an integer greater than one. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and form a part of the specification, illustrate example embodiments and, together with the description, serve to explain the principles of the disclosure. A brief summary of the drawings follows. 
         FIG. 1  illustrates a prior art bandpass-filtering system. 
         FIG. 2  illustrates a receiver in accordance with aspects of the present disclosure. 
         FIG. 3  illustrates a method of determining F s  in accordance with aspects of the present disclosure. 
         FIG. 4A  illustrates the example of M=2 and the associated channel inputs. 
         FIG. 4B  illustrates the example of M=2 and the associated channel inputs in accordance with aspects of the present disclosure. 
         FIG. 5A  illustrates the example of M=3 and the associated channel inputs. 
         FIG. 5B  illustrates the example of M=4 and the associated channel inputs. 
         FIG. 5C  illustrates the example of M=5 and the associated channel inputs. 
         FIG. 6  illustrates an example of five input channels to the M-path polyphase downconverter channelizer in accordance with aspects of the present disclosure. 
         FIG. 7  illustrates an example of five input channels to the M-path polyphase downconverter channelizer in accordance with aspects of the present disclosure, wherein the signals are centrally disposed in each respective input channel. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     An aspect of the present disclosure is drawn to a computationally efficient procedure for selecting a sampling frequency in a system that performs bandpass sampling and that uses a polyphase downconverter channelizer to receive multiple RF signals. The procedure finds a sampling frequency that positions all or a subset of the sampled signals such that the sampled signals fall entirely within the input channels of the polyphase downconverter channelizer. 
     In the case of multiple RF signal reception, there are N real, continuous-time bandpass signals denoted as x 1 (t), x 2 (t), . . . , x N (t). Each x i (t) i=1, . . . , N has an arbitrary carrier frequency f Ci  and bandwidth B i  (i.e., X i (f) is only nonzero on the intervals (−f Ci −B i /2, −f Ci +B i /2) and (f Ci −B i /2, f Ci +B i /2)). A system in accordance with aspects of the present disclosure uses bandpass sampling and a polyphase downconverter channelizer to receive the signals. The signals are received with an antenna, which is then followed by bandpass filters and amplifiers before being sampled by an analog-to-digital converter (ADC). The sampled signals are then processed using a polyphase downconverter channelizer to bring the signals to baseband. As in traditional bandpass-sampling literature, the RF hardware (i.e. antenna, bandpass filters, amplifiers, and ADC) are such that they enable bandpass sampling to be used. As a result, the bandpass filters attenuate all signals outside of the N frequency bands. Moreover, as a result, the low noise amplifier(s) amplify the signals such that they can be sampled by the ADC. Further, as a result, analog bandwidth of the ADC is sufficient to sample the signals at the carrier frequencies of the N signals. 
     At a high level, a method of receiving signals in accordance with aspects of the present disclosure includes four steps. In the first step, the minimum sampling frequency range is found. In the second step, within the sampling frequency range from the first step, it is determined whether each of the N sampled signals can fall entirely within an input channel of the polyphase downconverter channelizer. In the third step, if a signal can fall within an input channel, it is determined whether the signal can be placed at the center of the input channel. Finally, in the fourth step, based on the second and third steps, a sampling frequency is selected. These steps are described in more detail below. 
     Aspects of the present disclosure are drawn to bandpass sampling and using a polyphase downconverter channelizer to receive multiple RF signals. In particular, an aspect of the present disclosure is drawn to determining a minimum sampling frequency, F s , for use in the bandpass sampling. The procedure finds a sampling frequency that positions all or a subset of the sampled signals such that the sampled signals fall entirely within the input channels of the polyphase downconverter channelizer. Aspects of a bandpass sampling system and method in accordance with the present disclosure will now be described with additional reference to  FIGS. 2-7 . 
       FIG. 2  illustrates a receiver  200  in accordance with aspects of the present disclosure. As shown in the figure, receiver  200  includes an antenna  202  and a receiving portion  204 . Receiving portion  204  includes a combined bandpass filters/LNA component  206 , an ADC component  208 , a range-finding component  210 , a frequency-setting component  212  and an M-path polyphase downconverter channelizer  214 . 
     In this example, combined bandpass filters/LNA component  206 , ADC component  208 , range-finding component  210  frequency-setting component  212  and M-path polyphase downconverter channelizer  214  are illustrated as individual devices. However, in some embodiments, at least two of combined bandpass filters/LNA component  206 , ADC component  208 , range-finding component  210 , frequency-setting component  212 , and M-path polyphase downconverter channelizer  214  may be combined as a unitary device. Further, in some embodiments, at least one of combined bandpass filters/LNA component  206 , ADC component  208 , range-finding component  210 , frequency-setting component  212 , and M-path polyphase downconverter channelizer  214  may be implemented as a computer having tangible computer-readable media for carrying or having computer-executable instructions or data structures stored thereon. Such tangible computer-readable media can be any available media that can be accessed by a general purpose or special purpose computer. Non-limiting examples of tangible computer-readable media include physical storage and/or memory media such as RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer. For information transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a computer, the computer may properly view the connection as a computer-readable medium. Thus, any such connection may be properly termed a computer-readable medium. Combinations of the above should also be included within the scope of computer-readable media. 
     In operation, antenna  202  receives a plurality, n, of analog radio frequency (RF) signals  226 , each with a different respective carrier frequency, wherein n is an integer greater than 1. Antenna  202  passes analog RF signals  226  to receiving portion  204  via line  216 . Combined bandpass filters/LNA component  206  bandpass-filters and amplifies analog RF signals  226  so as to output N amplified filtered analog RF signals  228  to ADC component  208  via line  218 , wherein N is equal to n. 
     Range-finding component  210  determines a minimum sample frequency range, [F s,min1 , F s,min2 ], for which ADC component  208  should sample the bandpass-filtered plurality of analog radio frequency signals. F s,min1  is the smallest sampling frequency that results in no aliasing of the N amplified filtered analog RF signals  228  when bandpass sampling is performed. F s,min2  is larger than F s,min1  and additionally results in no aliasing of the N amplified filtered analog RF signals  228  when bandpass sampling is performed. 
     Frequency-setting component  212  determines the minimum sampling frequency, F s , for which ADC component  208  should sample the bandpass-filtered plurality of analog radio frequency signals, wherein F s,min1 ≤F s ≤F s,min2 . Frequency-setting component  212  provides a sampling frequency instruction  230  to ADC component  208  via line  222 . Sampling frequency instruction  230  instructs ADC component  208  to sample the bandpass-filtered plurality of analog radio frequency signals using F s . 
     ADC component  208  down-samples the amplified filtered analog RF signals  228  and converts them to IF digital signals  232  using F s  as indicated by sampling frequency instruction  230 , which is provided by frequency-setting component  212 . IF digital signals  232 , being a single digital bit stream, correspond to the amplified filtered analog RF signals  228  as separated in the frequency domain. M-path polyphase downconverter channelizer  214  separates the IF digital signals  232  into M different respective channels, separated in the time domain, for distribution as M output signals, wherein M is an integer greater than or equal to two (2). In this example embodiment, M is equal to five (5), such that the output signals are output signals  234 ,  236 ,  238 ,  240  and  242 . 
     It should be noted that a system and method in accordance with aspects of the present disclosure do not require M to equal N. On the contrary, M is determined elsewhere. Because M-path polyphase downconverter channelizer  214  operates on digital samples, for example with software, the size M may easily be configured/changed for example by way of a radio. 
     The technique of bandpass sampling is known and includes the function of a bandpass filter and ADC. However, a novel feature of the present disclosure is the determination of F s  by frequency-setting component  212  that enables efficient sampling by ADC component  208 . 
     The standard M-path polyphase downconverter channelizer as known in the prior art can be commonly used to efficiently downconvert multiple signals when their carrier frequencies are equally spaced apart and they have equal bandwidths. If the carrier frequencies of the signals can be equal to integer multiples of F S /M (i.e. the output sampling rate of the M channels of the polyphase channelizer), then all of the signals will be shifted to baseband by the channelizer. If the signals have arbitrary carrier frequencies and bandwidths, a receiver design can be used, which consists of a modified version of the standard M-path polyphase downconverter channelizer followed by additional processing. When bandpass sampling is performed in a receiver followed by a polyphase downconverter, the carrier frequencies of the input to the downconverter can be the IFs of the sampled signals. 
     In a scenario where one or more of the IF signals falls within two input channels of M-path polyphase downconverter channelizer  214 , additional processing after M-path polyphase downconverter channelizer  214  may be required to shift the signals to baseband. However (depending on the particular carrier frequencies and bandwidths of the signals before being sampled by ADC component  208 ), a sampling frequency F S  may be selected in accordance with aspects of the present disclosure. 
     A method  300  of determining F S  in accordance with aspects of the present disclosure will now be described in greater detail with reference to  FIG. 3 . As shown in the figure, method  300  starts (S 302 ) and a minimum sampling frequency range is determined (S 304 ). For example, range-finding component  210  may find the minimum sampling frequency range based on the respective carrier frequencies of the received analog RF signals  226 . 
     Example algorithms to find the minimum sampling frequency that results in no aliasing of the N signals when bandpass sampling is performed are well known. Non-limiting examples of such algorithms include Lin et al, “Finding the minimum sampling frequency of multi-band signals: an efficient iterative algorithm,” in  Proc. of IEEE Int. Symposium on Circuits and Systems , pp. 57-60, 30 May-2 Jun. 2010 and Lin et al, “A new iterative algorithm for finding the minimum sampling frequency of multiband signals,”  IEEE Trans. Signal Processing , vol. 58, no. 10, pp. 5446-5450, October 2010, the entire disclosures of which are incorporated herein by reference. Methods of how to find the smallest valid range of sampling frequencies as well as all valid ranges are additionally well known. Any of these known algorithms may be used to find the minimum sampling frequency that results in no aliasing of the N signals when bandpass sampling. The determined minimum sampling frequency range is denoted as [F s,min1 , F s,min2 ]. Range-finding component  210  then provides the minimum sampling frequency range to frequency-setting component  212  via line  220 . 
     After the minimum sampling frequency range is determined (S 304 ), all possible sampling frequencies are found within the sampling frequency range that will place at least one signal within an input channel of M-path polyphase downconverter channelizer  214  (S 306 ). 
     In an example embodiment, frequency-setting component  212  determines whether the amplified filtered analog RF signals  228  are within the input channels of M-path polyphase downconverter channelizer  214  by using the linear equation (1), which was derived in S. Ramlall, “On the IF spectral placement of bandpass sampled signals,” IEEE DSP Workshop, pp. 164-168, 11-14 Aug. 2013, the entire disclosure of which in incorporated herein by reference. The equation is: 
                     f   IF     =         (     -   1     )       n   +   1       ⁢     (         -     ⌊     n   2     ⌋       ⁢     F   S       +     f   C       )               (   1   )               
where f IF  is the intermediate frequency (i.e. frequency the signal is at after sampling), n is an integer, and └ ┘ denotes the mathematical floor operation. Each of the N signals will have a value of n associated with it based on the sampling frequencies obtained in the sampling frequency range found in S 304 . Specifically,
 
                       n   i     =         ⌈       2   ⁢     (       f   Ci     +       B   i     2       )         F     S   ,     min   ⁢           ⁢   1           ⌉     ⁢           ⁢   i     =   1       ,   …   ⁢           ,   N           (   2   )               
where ┌ ┐ denotes the mathematical ceiling operation.
 
     By using equation (2) to calculate n i , the frequency location where each of the N signals are placed after sampling can be determined using (1). M-path polyphase downconverter channelizer  214  has M input channels as shown in  FIGS. 4A-5C . 
       FIG. 4A  illustrates the example of M=2, wherein a function  402  represents the channel inputs. In this example, there are two (2) valid input channels. However, it is not possible to place a bandpass sampled signal at the very center of the two channels. This example shows two signals, signal  404  and signal  406 . Ideally, it is desirable to place the signals at the center of the channels, but it is more important that each signals falls somewhere entirely inside of a single channel. As shown in the figure, signal  404  falls entirely inside of a single channel, whereas signal  406  extends into two different channels. If a signal falls entirely inside of a single channel, then a system in accordance with aspects of the present disclosure determines whether the signal can be placed at the center of the channel. 
     Further, if a signal does not fall within a single channel, then additional processing after M-path polyphase downconverter channelizer  214  may be performed to place the signal entirely within a single channel. This will be shown in  FIG. 4B . As shown in  FIG. 4B , signal  406  has been moved so as to fall entirely within a single channel. 
     It should be noted that only two signals are illustrated in  FIGS. 4A-B . However, more signals may have been included. In particular, in accordance with aspects of the present disclosure, the number of signals do not have be less than or equal to the number of valid channels. Examples of additional channels will now be described 
       FIG. 5A  illustrates the example of M=3, wherein a function  502  represents the channel inputs. In this example, there are two valid input channels for use, the center of the second valid channel is indicated by m=1, which is disposed between F s /4 and F s /2.  FIG. 5B  illustrates the example of M=4, wherein a function  504  represents the channel inputs. In this example, there are three valid input channels for use, the center of the second valid channel is indicated by m=1, which is disposed at F s /4.  FIG. 5C  illustrates the example of M=5, wherein a function  508  represents the channel inputs. In this example, there are three valid input channels for use, the center of the second valid channel is indicated by m=1, which is disposed at less than F s /4, whereas the center of the third valid channel is indicated by m=2, which is disposed at 3F s /10. 
     For a given M, the input channel intervals given by 
               [     0   ,         F   S     /   2     M       ]     ,     [           F   S     /   2     M     ,       3   ⁢       F   S     /   2       M       ]     ,     [         3   ⁢       F   S     /   2       M     ,       5   ⁢       F   S     /   2       M       ]     ,         
etc., up to the interval ending with F s /2 are relevant. Note that only the input channels that contain positive frequencies are considered since the sampled signals are real and thus their Fourier transforms are conjugate symmetric. It is desirable to place signals such that they fall within the center of the input channels intervals mentioned above; otherwise, additional processing may be required to reassemble signal components that are split among multiple channels.
 
     To determine if a signal falls entirely within an input channel, a linear set of equations needs to be solved. These can be solved efficiently using linear programming techniques. Denote the input channel interval as [LFs, UFs]. It is determined whether f IFi +B i /2&lt;UFs and LFs&lt;f IFi −B i /2 for the signal to fall within the input channel. This results in the following linear set of equations depending on if n, is odd or even: 
     
       
         
           
             
               
                 
                   
                     
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     Equations (3a) (or (4a)) determine the maximum sampling frequency within the range from S 304  that positions the signal within the input channel, and equations (3b) (or (4b)) determine the minimum sampling frequency within the range that still positions the signal within the input channel. It can be shown that for a given choice of M, there are 
               ⌊     M   2     ⌋     +   1         
input channels that are applicable. Worst case,
 
             2   ⁢     N   ⁡     (       ⌊     M   2     ⌋     +   1     )             
linear programming problems need to be solved to determine all possible sampling frequencies within the range from S 304  that will place all N (or a subset of N) signals within input channels of M-path polyphase downconverter channelizer  214 . However, if a solution to one linear programming problem is not found, then its counterpart does not need to be solved; i.e., if a solution to equation (3a) does not exist then equation (3b) does not need to be solved. So the minimum number of linear programming problems that need to be solved is
 
             N   ⁡     (       ⌊     M   2     ⌋     +   1     )           
which occurs when none of the signals can be placed within any of the input channels.
 
     The output of S 306  is all possible sampling frequencies within the range from S 304  that will place all N (or a subset of N) signals within input channels of M-path polyphase downconverter channelizer  214 . 
       FIG. 6  illustrates an example of five input channels to M-path polyphase downconverter channelizer  214 , including a channel  602 , a channel  604 , a channel  606 , a channel  608  and a channel  610 . In this example, signals  612 ,  614 ,  616 ,  618  and  620  are disposed in the respective channels. However, it should be noted that signals  614 ,  616  and  620  are not centered in their respective channels. 
     It is then determined whether the signals are placed at the center of the input channels (S 308 ). If they are not, and if possible, it is desirable to place signals at the center of the input channels to the polyphase downconverter channelizer because then the signals will be at baseband at the output of M-path polyphase downconverter channelizer  214  and no further downconversion would be necessary (Y at S 308 ). The center of the input channels to M-path polyphase downconverter channelizer  214  are given by mFs/M for m=0, 1, 2, . . . . However, note that for bandpass sampling, only some of the input channels need to be checked due to the conjugate symmetry of the sampled signal&#39;s Fourier transform. It can be shown that only the following values of m need to be checked: 
     
       
         
           
             
               
                 
                   m 
                   = 
                   
                     { 
                     
                       
                         
                           
                             1 
                             , 
                             2 
                             , 
                             … 
                             ⁢ 
                             
                                 
                             
                             , 
                             
                               
                                 M 
                                 2 
                               
                               - 
                               1 
                             
                           
                         
                         
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             even 
                           
                         
                       
                       
                         
                           
                             1 
                             , 
                             2 
                             , 
                             … 
                             ⁢ 
                             
                                 
                             
                             , 
                             
                               ⌊ 
                               
                                 M 
                                 2 
                               
                               ⌋ 
                             
                           
                         
                         
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             odd 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     For illustration, the values of m from equation (5) are also shown in  FIGS. 4A-5C . Equation (1) allows a simple calculation to be used to determine if the IF signals can be placed at the center of the input channels: 
     
       
         
           
             
               
                 
                   
                     F 
                     S 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               f 
                               Ci 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     n 
                                     i 
                                   
                                   2 
                                 
                                 ⌋ 
                               
                               - 
                               
                                 m 
                                 M 
                               
                             
                           
                         
                         
                           
                             
                               n 
                               i 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             even 
                           
                         
                       
                       
                         
                           
                             
                               f 
                               Ci 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     n 
                                     i 
                                   
                                   2 
                                 
                                 ⌋ 
                               
                               + 
                               
                                 m 
                                 M 
                               
                             
                           
                         
                         
                           
                             
                               n 
                               i 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             odd 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Note that equation (6) only needs to be calculated if a solution was found in S 306  for the given signal and input channel. 
       FIG. 7  illustrates the example of five input channels to M-path polyphase downconverter channelizer  214 , of  FIG. 6 . In this example, the signals  702 ,  704 ,  706 ,  708  and  710  have been sampled so as to be centrally disposed in the respective channels. 
     If the signals are not centrally disposed in the input channels, then additional known processing may be required (S 310 ). 
     Looking at the sampling frequencies found in S 306 , the intersection of the sampling frequency intervals is found that results in the most signals falling within input channels of M-path polyphase downconverter channelizer  214 . Then, it is determined whether any of the sampling frequencies found in S 308  are within the intersection. If so, this sampling frequency is selected (S 312 ). Otherwise, the smallest sampling frequency in the intersection is selected (S 312 ). 
     If no signals fall within input channels of M-path polyphase downconverter channelizer  214 , return to S 304  and repeat the process one more time using the next highest range of sampling frequencies from S 304 . In an example embodiment, this process is only repeated this one time because repeating more than once may result in significantly higher sampling frequencies that will then outweigh the computational savings provided by S 306 -S 310 . If after this one additional iteration of the process, still no signals fall within input channels of M-path polyphase downconverter channelizer  214 , then the smallest sampling frequency obtained from the first iteration of S 304  is selected (S 312 ). 
     Once the F s  is selected by frequency-setting component  212  using method  300 , sampling frequency instruction  230  is sent to ADC component  208 . As discussed above, ADC component  208  down-samples the amplified filtered analog RF signals  228  and converts them to IF digital signals  232  using F s  as indicated by sampling frequency instruction  230 . M-path polyphase downconverter channelizer  214  then separates the IF digital signals into different respective channels, separated in the time domain, for distribution as output signals  234 ,  236 ,  238 ,  240  and  242   
     With the ongoing research in software-defined radio (SDR), cognitive radio, and dynamic spectrum access, a radio may have to receive a signal whose carrier frequency changes over time using bandpass sampling (assuming the radio has a tunable bandpass filter at its RF front end). This may be due to either changes in the environment or due to action taken by the operator. But, no matter what the reasons for a change in carrier frequency, the systems and methods of the present disclosure can be used to quickly and dynamically determine a minimum sampling frequency that would place the IFs at a desired location. 
     The foregoing description of various embodiments has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The example embodiments, as described above, were chosen and described in order to best explain the principles of the disclosure and its practical application to thereby enable others skilled in the art to best utilize the disclosure in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the disclosure be defined by the claims appended hereto.