Convergence Analysis of Deficient-Length Frequency-Domain Adaptive Filters

The frequency-domain adaptive filter (FDAF) has been utilized in various applications where the length of the modeling filter is very long. The convergence behavior of the FDAF in the full-modeling case has been well analyzed. However, because the length of the true filter may be rather long and is unknown in practice, the length of the adaptive filter is usually less than that of the true system. In this paper, only the statistical behavior of the deficient-length constrained FDAF was analyzed for Gaussian inputs. This paper presents a unified approach to the stochastic analysis of a family of the FDAF in an under-modeling situation and for arbitrary input distributions. Specifically, the mean and mean-square convergence behaviors of FDAFs are presented, and the closed-form expression of the steady-state misalignment is given. Our theoretical results provide some new insights into the convergence property of deficient-length FDAFs. In addition, the analysis is carried out in the frequency domain directly. Computer simulations indicate an excellent agreement with our theoretical predictions.