Efficient computation of the discrete pseudo-Wigner distribution

A description is given of a novel algorithm, the fast Fourier transform in part (FFTP), for the computation of the discrete pseudo-Wigner distribution (DPWD). The FFTP computes the cosine and sine parts of the discrete Fourier transform (DFT) separately by employing real inverse sinusoidal twiddle factors. Unlike the conventional methods which directly utilize the complex DFT, the FFTP yields real output since the DPWD is always real. In addition, the new method reduces the computational cost by making full use of symmetries and removing redundancies in the FFTP computation. The authors also describe a simple algorithm for computing the discrete Hilbert transform (DHT) to produce the nonaliased DPWD. A pipeline structure for real-time and a bulk processing technique for offline implementations of the method are presented