(A) study on efficient frequency-domain adaptive filter algorithms

Abstract

The main objective if this dissertation is to develop computationally efficient realization methods for a class of block algorithms of finite impulse response (FIR) adaptive digital filters (ADF``s) in the frequency domain. ADF``s based on least mean square (LMS) with optimum convergence factor have been implemented efficiently and their convergence performances have been improved considerably, in several algorithms proposed in this dissertation works. First, we have discussed various realization methods in the frequency domain. A normalized frequency-domain optimum block algorithm (NFOBA) has been investigated in order to improve the convergence performance of the optimum block algorithm (OBA) or the frequency-domain optimum block algorithm (FOBA). In the OBA, the convergence factor is optimized in an LS sense, and thus the OBA converges fast. However, when the OBA ADF is of high-order and/or the input signal is colored, the convergence speed deteriorates. To alleviate this problem, in the NFOBA we use a scheme of individual adaptation of the convergence factor, separately in each frequency-bin. The NFOBA yields significant convergence improvement. Second, in the NFOBA we propose two robust normaliziation methods which can stabilize the normalization process with usual power estimators in each frequency-bin. Since the initial values of the power estiamtors are not given in most practical environments and usually selected as zeros, the normalization in the initial stages can yield instability. Therefore, we propose a delayed normalization method in which we do not normalize during the initial few iterations. And, for the non-stationary noisy input signals, the stability can be assured if we control the unstable normalizations by a flooring method which modifys the relative power estimator. This flooring method can compromise the noisy estimation of input spectral power, especially when the fast Fourier transform (FFT) size is small or the signal is speech-like....