Fast computation of the Wigner distribution for finite-length signals

L. Cohen´s class (1989) of time-frequency distributions (TFDs), which includes the spectrogram and Wigner distribution (WD), has been widely used to analyze a variety of signals, including EMGs, EEGs, sonar data and speech. The WD is noted for its ability to localize mono-component signals in time and frequency, and, other than the spectrogram, is perhaps the most often-used TFD. An approach for the evaluation of the discrete-time WD (DTWD) of a finite-length signal which requires 25% less computation time than traditional schemes is introduced. Traditional fast DTWD algorithms rely on the fast Fourier transform (FFT), which shifts autocorrelation slices (decimates in frequency) in order to minimize multiplications. The approach uses a decimation scheme which shifts the signal rather than autocorrelation slices, effectively moving blocks of the autocorrelation, so that the resulting twiddle multiplications are reduced