Least mean square, finite length, predictive digital filters

Useful analytic solutions of the discrete Wiener-Hopf (W-H) matrix equation (using the method of undetermined coefficients (UC)) are presented for general rational input spectra. For the specific case of N sinusoids in white noise, the W-H equation is transformed via the UC method into a set of N coupled linear equations which decouple as the filter length becomes large. For all pole input spectra, the W-H equation transforms into a pxp Vandermonde matrix equation where p is the number of poles in the input spectra.