Frequency measurement receiver with means to resolve an ambiguity in multiple frequency estimation

A frequency measurement receiver system capable of resolving up to M signal frequencies f.sub.m (1.ltoreq.m.ltoreq.M) appearing on an RF input line within a same measurement interval, comprising I FFT units and I spectrum peak detector units, M and I being positive integers with I being greater than M, each FFT unit having an input coupled to the RF input line via mixers and analog-to-digital (A/D) converter means to provide complex signals having digital in-phase and quadrature components, processor means for multiple frequency ambiquity resolution, each FFT unit having N outputs coupled to one of the peak detector units, and each of the peak detector units having outputs coupled to the processor means;

• the A/D converter means for each of the I FFT units having a different sampling speed F.sub.i (1.ltoreq.i.ltoreq.I), wherein for each signal frequency, f.sub.m, each FFT unit includes means for measuring a remainder, .alpha..sub.mi, which is related to f.sub.m for complex input as
• f.sub.m =.alpha..sub.mi +K.sub.mi F.sub.i ( 1)
• for the M signal frequencies, where K.sub.mi is an unknown integer and represents an aliasing ambiguity;
• wherein each spectrum peak detector unit includes means for scanning the magnitudes of the N outputs of the FFT unit to which it is coupled and identifying all frequency bins, n.sub.mi, where frequency magnitude exceeds a maximum anticipated sidelobe level;
• wherein the processor means includes a plurality of read-only memory units (ROM) having look-up tables for converting the n.sub.mi outputs of the spectrum peak detector units to corresponding remainders .alpha..sub.mi using the following transformation, ##EQU23## where a dedicated ROM generates .alpha..sub.mi, (1.ltoreq.m.ltoreq.M), for each of the I FFT units;
• wherein the processing means includes means coupled to the read-only memory units for solving the aliasing ambiquity for each subset of two FFT units and one signal frequency f.sub.m, which protects the remainder from a noise perturbation of q(Hz) and gives the correct resolved frequency to within q over a bandwidth, B, given as ##EQU24## wherein using properties from number theory, the F.sub.1 F.sub.2 are related as
• F.sub.1 =(4q+1)p.sub.1 ( 4)
• F.sub.2 =(4q+1)p.sub.2
• where p.sub.1, p.sub.2 are relatively prime integers;
• wherein the processing means includes means for exhaustively considering all possible ##EQU25## groupings of .alpha..sub.j.sbsb.l (1.ltoreq.j.ltoreq.M;
• 1.ltoreq.l.ltoreq.2) remainders for all the M remainders in the subset of 2 FFTs used in the single frequency resolution, wherein the symbol ##EQU26## represents a binomial coefficient which gives the number of unique groups of FFT units out of a total number of I FFT units, there being M.sup.2 possible groupings or combinations of remainders or resolved frequencies for each of the ##EQU27## possible groups of 2 FFT units out of a total of I FFT units, each of these remainder combinations producing one resolved frequency using the single frequency method, wherein of the ##EQU28## frequencies, ##EQU29## represent true frequencies, while ##EQU30## represent incorrect frequencies resulting from a false or spurious grouping of remainders;
• wherein the bandwidth of the multiple frequency resolution algorithm, B.sub..mu., will equal the minimum of all ##EQU31## bandwidths, B, as given by equation (3);
• wherein the processing means further includes sorting means for selecting the M true frequencies based on the number of repeats, from the ##EQU32## output frequencies generated.