Complexity comparison between FFT and DCT based real data Wigner processors

Abstract

The symmetry of the discrete Wigner distribution (DWD) kernel input and the corresponding DWD output is used to develop an N-point DWD processor that outputs two DWD slices per N/2-point fast Fourier transform (FFT) subsystem. The overhead associated with FFT size reduction and kernel generation are shown to be less than that of the short-time Fourier transform magnitude (STFTM), given an equivalent reduction in FFT size, and the conclusion of double throughput for the DWD over that of the STFTM is validated. An alternative discrete-cosine-transform-based DWD processor is proposed where factorization is performed directly on the cosine matrix and compared in terms of computational complexity to radix-two, radix-four, and radix-2/4 FFT-based DWD processors.<>