A statistical Wiener filter using complex analysis of variance.

The Wiener filter is a digital filter in the frequency domain which enables the detection of signals in noise on the basis of a relatively small number (N) of signals-in-noise series. However, the variance associated with the Wiener filter increases sharply with low N or low signal-to-noise ratio, sometimes resulting in large negative transfer coefficients (H(w)'s). This causes an unacceptable distortion of the extracted signal. The classical solution for this problem is rather arbitrary; clipping all H(w)'s less than zero. It can be shown that this approach has limited practical value and does not lead to optimal filtering of the signal. The solution presented in this paper is based on the fact that the large negative H(w)'s in the case of a small N are caused by using an estimate for the noise-power which deviates from the actual noise-power. This makes the use of a statistical procedure feasible. By using complex analysis of variance it is possible to test which part of the spectrum is due to the signal and which part of the spectrum is due to the noise. H(w)'s not reaching a preset significance criterion are set to zero. The statistical Wiener filter acts as an adaptive multi-band-pass filter with band-passes determined by (a posteriori) detected signal components. It is demonstrated that this procedure leads to better suppression of the noise in signal-in-noise series.