Tracking Behaviour of Lattice Filters for Linear and Quadratic FM Signals

Abstract

In practical applications, the statistics of the signal are unknown and time-varying. Hence, the coefficients of an adaptive filter converge towards the optimal values and track the time-varying statistics of the input signal during the steady state time. In order to analyse the performance of adaptive filters, the behaviour of optimal and adaptive coefficients as well as the resulting output error signals need to be carefully studied. Frequency modulated (FM) input signals in noise are a well-known class of nonstationary random processes with time-varying spectra. They possess a structure which facilitates the theoretical analysis and are also encountered in many real applications. In investigating the behaviour of adaptive filters tracking linear FM signals, a great effort has been devoted to transversal filters [9], [1]. However, an alternative structure is the lattice filter with its attractive properties. Some of these properties include high convergence speed, easy computations, less sensitivity to eigenvalues spread, ease of implementations, and providing a Gram-Schmidt type of orthogonali-sation of the input signal [8].