Separation of signals and cross-terms in the Wigner distribution using adaptive filtering

A frequency domain least-mean-squares (LMS) algorithm is used to both track and suppress cross terms in a Wigner distribution, allowing a much better reading of the time-varying distribution of power over frequency. In the adaptive filtering approach, the desired input (primary) takes the Pseudo Wigner distributions (PWDs) for different data blocks, while the filter input (reference) is assigned unit values. Due to the nature of the primary and reference data, the frequency domain filter adapts to the constant sinusoidal peak values. However, because of the uncorrelatedness, it fails to track the time-varying components in the desired signal, leaving out the cross terms to propagate to the output filter error. The authors introduce the general approach of separating constant and time-varying components in the desired signal, leaving out the cross terms to propagate to the output filter error. The authors introduce the general approach of separating constant and time-varying spectral terms via the LMS harmonic canceler, in which the Fourier transform (FT) is applied to the data rather than the data kernel. It is shown that the problem translates into separating two sets (partition over [0,2π]) of spectral components according to their frequency. One set has constant values, and includes all frequencies which are integer multiples of 1/N (harmonics), where N is the transform block length