Efficient computation of the discrete Wigner-Ville distribution

To ensure that the discrete Wigner-Ville distribution (DWVD) does not contain aliasing terms, the analytic signal is normally used instead of the real signal. However, the computation of the analytic signal amounts to most of the computation time. Eilouti and Khadra (1989) made use of the overlapping between two successive sequences to develop a recursive algorithm for updating the analytic signal. The time difference between the successive sequences was taken to be one. The more general case with a time difference (lag) of P is considered. It is shown that the analytic signal can effectively be updated by computing an aperiodic convolution. For small lag, the convolution is evaluated directly, while for a transform with larger lag, the convolution is evaluated by a real-valued pruning FFT (fast Fourier transform) based on the split-radix FFT. The DWVD is then obtained from the DFT (discrete Fourier transform) of a conjugate symmetric sequence of reduced length which can be computed with the real-valued split-radix FFT algorithms.<>