Infinite impulse response adaptive digital filters and their applications

Abstract

The main objective of this dissertation work is to develop an improved infinite impulse response (IIR) adaptive digital filter (ADF) that must be stable during the adaptation process, and always convergent. Recently, IIR ADF``s have attracted much attention because of its several advantages over the FIR ADF``s. For example, an IIR filter can have small number of coefficients than an FIR filter for the same performance, and the delay produced by an IIR filter is usually small. But, the IIR ADF also has a few problems that must be resolved for the practical usage. Unlike an FIR ADF, it can be unstable during the adaptation process. Also it has a non-quadratic error surface, and consequently a local minimum solution can be obtained. Furthermore, it is known that an IIR ADF usually converges more slowly than an FIR ADF. In order to resolve or at least alleviate the problems stated above, we first propose a nonlinear least-squares (NLS) algorithm that may be regarded as an improved least-squares-based IIR ADF algorithm. In the NLS algorithm, a posteriori outputs and their filtered signals are used. And a weighting factor is considered in order to increase the convergence speed for stationary input signals. To avoid the instability problem of the IIR ADF, a filter bank structure is used. In this scheme, a high-order filter is decomposed into parallel low-order sub-filters using the discrete Fourier transform (DFT), thereby the stability of the IIR ADF can be maintained by keeping the magnitudes of poles of each sub-filter be less than unity. We also analyze the global convergence of the NLS algorithm under a sufficient-order condition and white Gaussian measurement noise assumption. We then compare the performances of various IIR ADF algorithms and the proposed NLS algorithm in the convergence speed, stability and the computational complexities. We show that, unlike the LMS or a self-orthogonaling-type algorithm in which an optimal convergence factor is normally chos...