Estimation of random spectral misadjustment of an adaptive filter

In most applications of adaptive filters, it is sufficient to have an rms measure of the error signal between the filter output and the desired signal. In an application of loop stability control, it is necessary to determine the spectral misadjustment, which will be a function of the input signal and any corrupting noise on the desired signal. For the case of a Gaussian input the spectral misadjustment can be shown to have a Rayleigh distribution. When the input signal is speech the spectral misadjustment must be determined by statistical methods.