Frequency-domain FIR and IIR adaptive filters
A discussion of the adaptive filter relating to its convergence characteristics and the problems associated with disparate eigenvalues is presented. This is used to introduce the concept of proportional convergence. The use of the FFT to implement fast convolution and FIR adaptive filters is presented. It is shown that the several frequency-domain filters currently in the literature are special cases of a general frequency-domain block adaptive filter. An analysis of the convergence of the Dentino filter for the case of two sinusoids is presented. In connection with this a closed form expression for the DFT of a general sinusoid and its derivation are given. A novel approach is used to analyze the convergence characteristics of block frequency-domain adaptive filters. This leads to a development showing how the frequency-domain FIR adaptive filter is easily modified to provide proportional convergence. These ideas are extended to the IIR adaptive filter. A new algorithm for high speed IIR convolution using the FFT is presented. This structure is developed into a block frequency-domain IIR adaptive filter and the idea of proportional convergence is applied. Experimental results illustrating proportional convergence in both FIR and IIR frequency-domain block adaptive filters is presented.