On filter order in fir adaptive filters. - Aoyagi, Thiago Yuji (2021)
A practical problem faced when designing an FIR (Finite Impulse Response) adaptive filter is to set an appropriate filter length. The best choice for the length is application dependent, and is common practice to determine it by some rough approximation, such as by trial-and-error. By setting a small number of coefficients, the filter has a reduced complexity and may benefit from an increased convergence rate, but its steady-state per formance is degraded by undermodeling. By setting a large number of coefficients, we ensure the filter suffers negligible or no undermodeling effects, but we limit the maximum stable convergence rate, increase the computational complexity and also decrease the fil ter ability to respond in nonstationary scenarios. In this work, we analyze how the filter length affects the performance of adaptive algorithms, in particular, for the LMS and the -NLMS algorithms. For stationary scenarios, we analyze both transient and steady-state performance, and propose a method for selecting the filter length that ensures fast con vergence rate and low undermodeling effects, assuming that the system impulse response follows an exponential decay envelope. We show that a filter with the proposed length is particularly interesting to operate as the fast filter within a combination of filters. For nonstationary scenarios, we focus our study on the steady-state performance, and show through simulations that a short filter may outperform a longer one in both convergence and tracking performance.