(A) class of adaptive digital filters and their applications

Abstract

The main objectives of this dissertation are to develop computationally efficient realization methods for a class of finite impulse response (FIR) adaptive digital filters (ADF``s) and to study the use of the developed ADF``s in practical appications. First, we have investigated various realization methods and convergence behabior of a class of FIR ADF``s including the time-domain least-mean-square (TLMS), frequency-domain least-square (FLMS), time-domain block least-mean-square (TBLMS), and frequency-domain block least-mean-square (FBLMS) ADF``s. We have studied the convergence behavior of these ADF``s in a common frame work based on block mean-squareerror performance criterion. In particular, the fast convergence behavior of the FLMS ADF have newly been analyzed based on the concept of a self-orthogonalizing algorithm. Then, efficient realization methods for the TBLMS and FBLMS ADF``s have been investigated, and the computational complexity of the ADF``s has been analyzed. It has been found that the structure of the FBLMS ADF with the block length of one reduces to that of the FLMS ADF. According to the computational complexity analysis, the TBLMS and FBLMS ADF``s for a complex input can be realized efficiently using FFT. The FBLMS ADF can be realized more efficiently than the TBLMS ADF. Efficient realization of the TBLMS ADF using Fermat number transform (FNT) has been studied. When computational complexities of two TBLMS ADF``s, one using the fixed-point FFT and the other using the FNT, are compared, the latter has been found out to be computationally more efficient. Also, the result of computer simulation of the two ADF``s reveals that the performances of the TBLMS ADF realized using the 16-bit FNT do not show appreciable differences from those using infinite precision arithmetic. To verify the analysis on the convergence behavior of the ADF``s under study, computer simulation has been done. According to the simulation results, the performances of the four...