Patent ID: 6031879
Filing Date: 2000-02-29
Classification: H04B,H04L

Abstract:
A method for digitally processing a signal derived from an analog waveform of frequency f, comprising the steps of:receiving the analog waveform with a receiving antenna to produce an analog signal indicative of the amplitude and frequency of the analog waveform;processing the analog signal in a plurality of r parallel digital processing channels each arranged to digitize the analog signal at a corresponding sampling frequency f.sub.si to produce a plurality of digital signals;applying a discrete Fourier transform to directly utilize the relationship of the discrete Fourier transform (DFT) and the symmetrical number system (SNS) to resolve frequency aliases .function.>.function..sub.si /2 (ambiguities due to undersampling a real signal) that occur within a plurality of r parallel ADC-DFT channels where after sampling, the DFT in each channel naturally encodes the frequency information of the signal in m.sub.i indices (number of samples within the DFT) that are pairwise relatively prime, ##EQU63## for m.sub.i even, and ##EQU64## for m.sub.i odd, and this is a format that is in the same form as the SNS so that the indices within each channel containing the detected frequency a.sub.1, a.sub.2, a.sub.3, . . . a.sub.r are used to evaluate the original (single) frequency,detecting the frequency bin (a.sub.i) within each discrete Fourier transform output;processing the bin numbers a.sub.i (i=1, 2, . . . , r) to resolve the single frequency ambiguity;setting M=m.sub.1, m.sub.2, m.sub.3, . . . , m.sub.r ;evaluating.function..tbd.(a.sub.1)Mb.sub.1 /m.sub.1 .+-.(a.sub.2)Mb.sub.2 /m.sub.2 .+-.(a.sub.3)Mb.sub.3 /m.sub.3 .+-. . . . (a.sub.r)Mb.sub.r /m.sub.r mod(M )where b.sub.i is such that ##EQU65## picking the one value that lies within the dynamic range M of the SNS where ##EQU66## when m.sub.1 is even and where j ranges from 2 to r-1 and i.sub.2, i.sub.3, . . . , i.sub.r range over all permutations of (2, 3, . . . , r). ##EQU67## when all of the m.sub.i s are odd and where j ranges from 1 to r-1 and i.sub.1, i.sub.2, . . . , i.sub.r range over all permutations of (1, 2, . . . , r).