A class of FIR filters and blind identification of SIMO systems

In signal processing problems involving quadratic performance functional and stationary signals, solutions often involve a first stage of filtering called whitening. The whitening filter obtained by Yule-Walker equations uncorrelates N samples of the output with the past input samples (beyond the zero lag) as seen by the orthogonality principle. It does not constrain the output samples to be uncorrelated with each other or to have pre-defined autocorrelation values for finite number of samples. In this thesis we present finding the unique minimum order, invertible FIR filter FM(z) from the input and output autocorrelation equations directly such that for the colored input process u(n) with finite number of autocorrelation samples the output y(n) has N desired zero or nonzero autocorrelation samples. The N output lags may or may not be equidistance samples. The input-output autocorrelation equation is quadratic in the coefficients of FM( z) but is solved linearly. We term this the Quadratic filter (QF) problem and its special case the Semi-Whitening filter (SWF). (Abstract shortened by UMI.)...