Decorrelating MVDR Filterbanks Using the Non-Uniform Discrete Fourier Transform

Abstract

Minimum variance distortionless response (MVDR) is a classic design criteria in signal adaptive spectral analysis as well as filter design. We extend this approach to filterbanks with the constraint that transform domain signal components must be uncorrelated. Our analysis shows that filterbanks based on Vandermonde decomposition of the autocorrelation matrix correspond to the non-uniform discrete Fourier transform and satisfies the MVDR criteria. Namely, the columns of the inverse Vandermonde matrix corresponds to filters with unit response at the pass-band while leakage is minimized with the constraint that components remain uncorrelated. In the special case that the autocorrelation matrix is rank deficient, the proposed filterbank coincides with Pisarenko's harmonic decomposition, which thus also satisfies the MVDR criteria.