An efficient real-time implementation of the Wigner-Ville distribution

TLDR: To evaluate the analytic signal required by the WVD analysis system, it is shown that the time domain definition implemented as a finite impulse response (FIR) filter is practical and more efficient than the frequency domain definition of the analytical signal.

Abstract: The Wigner-Ville distribution (WVD) is a valuable tool for time-frequency signal analysis. In order to implement the WVD in real time, an efficient algorithm and architecture have been developed which may be implemented with commercial components. This algorithm successively computes the analytic signal corresponding to the input signal, forms a weighted kernel function, and analyzes the kernel via a discrete Fourier transform (DFT). To evaluate the analytic signal required by the algorithm, it is shown that the time domain definition implemented as a finite impulse response (FIR) filter is practical and more efficient than the frequency domain definition of the analytic signal. The windowed resolution of the WVD in the frequency domain is shown to be similar to the resolution of a windowed Fourier transform. A real-time signal processor has been designed for evalution of the WVD analysis system. The system is easily paralleled and can be configured to meet a variety of frequency and time resolutions. The arithmetic unit is based on a pair of high-speed VLSI floating-point multiplier and adder chips.