Elimination of interference terms of the discrete Wigner distribution using nonlinear filtering

Methods for interference reduction in the Wigner distribution (WD) have traditionally relied on linear filtering. This paper introduces a new nonlinear filtering approach for the removal of cross terms in the discrete WD. Realizing that linear smoothing kernels are unable to completely cancel the cross-terms without compromising time-frequency concentration and resolution of the auto-terms, a nonlinear filtering algorithm is devised where the filter automatically adapts to the rapidly changing nature of the WD plane. Varying the filter behavior from an identity operation at one extreme to a lowpass linear filter at the other, a near-optimal removal of cross terms is achieved. Unlike traditional smoothing and optimal kernel design techniques, this algorithm does not reduce the time-frequency resolution and concentration of the auto-terms and performs equally well for a very large variety of signals.