Efficient computation of the discrete Wigner distribution function through a new iterative algorithm

This paper presents a new iterative method to speed up the DWDF computation. At the present it has been considered from a computational point of view as an 1-D section of the Wigner Kernel (WK) N points FT's [1],[4]. We purpose a new way to compute the DWDF based on the symmetry properties of the WK and the cosine function. The proposed algorithm is doubly based on a subdivision procedure: on the one hand we have subdivided for each m-value the sum over the k variable into log(2)N/4-PL partial sums, where PL is the k parity level. And the other hand for each n-value the algorithm computes the DWDF elements by grouping its in group depending on the m FL. The algorithm has been optimized to reduce the accesses of memory, and it improves the FFT algorithms when the number of samples is less than 256 and for this number the algorithm match the FFT algorithms.