A New Rapid Frequency-Domain Adaptation of Causal FIR Filters

The frequency domain Newton algorithm was introduced by Elliott and Rafaely in an effort to improve the convergence speed as well as to generate an unbiased steady-state solution for the case of a strict causality-constrained adaptive filter. However, their proposed frequency domain Newton algorithm requires that we split the normalized convergence coefficients into constituent causal and non-causal components via spectral factorization. This process, of course, requires significant and complicated exponential and logarithm computations. Furthermore, due to circular convolution effects, their proposed Newton adaptation will also introduce bias in some cases. In this paper, we introduce a new rapid frequency-domain adaptive and causal FIR filters. Our algorithm only requires the estimation of the input signal power spectral density. When our algorithm is compared to the Newton algorithm, we find that our proposed algorithm shares its fast convergence rate, but also generates robust unbiased solutions while requiring significantly lower computational complexity. We provide simulation results that confirm the effectiveness of our proposed new algorithm