A spectral magnitude analysis theorem and applications

Spectral magnitude analysis can be performed with identical results by computing the short-time Fourier transform magnitude (|STFT|) of a real signal, or by analyzing the signal with a filter/detector (F/D) bank. In the latter approach, analysis is performed by a bank of bandpass filters, each of which is followed by a detector consisting of a square law device. The equivalence between |STFT| and F/D bank analysis is extended to complex signals. New applications such as complex signal reconstruction from spectral magnitude and pulse-Doppler radar signal processors are discussed. A new equivalence between wavelet analysis and the generalized STFT is presented, and it is shown that speech spectrograms are not equivalent to the |STFT|