A Spectral Analyzer Based on Dual Coprime DFT Filter Banks and Sub-Decimation

Abstract

Coprime (pair of) DFT filter banks (coprime DFTFB), which process signals like a spectral analyzer in time domain, divides the power spectrum equally into MN bands by employing two DFT filter banks (DFTFBs) of size only M and N respectively, where M and N are coprime integers. With coprime DFTFB, frequencies in wide sense stationary (WSS) signals can be effectively estimated with a much lower sampling rates than the Nyquist rates. However, the imperfection of practical FIR filter and the correlation based detection mode give rise to two kinds of spurious peaks in power spectrum estimation, that greatly limit the application of coprime DFTFB. Through detailed analysis of the spurious peaks, this paper proposes a modified spectral analyzer based on dual coprime DFTFBs and sub-decimation, which not only depresses the spurious peaks, but also improves the frequency estimation accuracy. The mathematical principle proof of the proposed spectral analyzer is also provided. In discussion of simultaneous signals detection, an O-extended MN-band coprime DFTFB (O_Ext M-N coprime DFTFB) structure is naturally deduced, where M, N, and O are coprime with each other. The original MN-band coprime DFTFB (M-N coprime DFTFB) can be seen a special case of the O_Ext M-N coprime DFTFB with extending factor O equals ‘1’. In the numerical simulation section, BPSK signals with random carrier frequencies are employed to test the proposed spectral analyzer. The results of detection probability versus SNR curves through 1000 Monte Carlo experiments verify the effectiveness of the proposed spectrum analyzer.