On the convergence behaviour of frequency-domain LMS adaptive digital filters

In this paper we analyze the convergence behavior of the frequency-domain LMS(FLMS) adaptive digital filter(ADF) using discrete Fourier transform. We obtain the optimum Wiener solution, the minimum mean-squared-error(MSE), the convergence condition, and the excess MSE in the steady state. Also, we study the convergence behavior of the FLMS ADFbased on the concept of a self-orthogonalizing algorithm. By approximating the input autocorrelation matrix as a circulant matrix, we compare the results ofthe LMS and FLMS ADF's.