Zero sensitivity properties of the digital lattice filter

Abstract

The first-order movement of zeros given small perturbations of the PARCOR coefficients in the all-zero digital lattice filter is determined analytically. This is an extension of previous work characterizing sensitivity by integral spectral deviation measures, and is of interest since much is known about the perceptual effects of deviations in formant frequency location. The principal insight is the role that the frequency of the zero plays in its sensitivity and a better understanding of the quite different sensitivity properties of the first and last PARCOR coefficients. Comparison is made to the transversal filter structure, and further interpretation of the effect of preemphasis is given. By examining individual terms of the zero sensitivity equations, an understanding may be gained of the factors responsible for large zero movements and the methods which may be used to decrease these movements. As an example, a computationally simple bilinear type of transformation of the original PARCOR's to a new set of PARCOR's is proposed, which decreases the zero sensitivity at low frequency and increases it at high frequency. The perceptual advantage is estimated by listening tests and spectral deviation plots to be comparable to that of preemphasis, about 2 bits/frame.