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An adaptive, recursive, least mean-square-digital filter is heuristically derived that has the computational simplicity of existing transversal adaptive filters, with the additional capability of producing poles in the filter transfer function. Simulation results are presented to demonstrate its capability.

A parallel form adaptive pole-zero filter implemented in the frequency domain is presented. This filter can exactly model any proper rational system with distinct poles and it permits direct monitoring of pole trajectories during adaptation so that instability of the filter is easily prevented.

The authors formulate a block-based least-squares problem in the frequency domain. They then develop computationally efficient block least-squares algorithms that can be realized using the fast Fourier transform. They also present computer simulation results demonstrating the convergence characteristics of the proposed algorithms. >

The real and complex LMS adaptive algorithms are compared. In general, it is shown that, with respect to the weights, the real algorithm is not equivalent to the real part of the complex algorithm. However, when the algorithm is configured as an ALE with sinusoidal inputs, the mean weight behavior of the real algorithm is identical to the real part of the mean weight of the complex algorithm. This result is useful because there are simplicities in the analysis of the complex model that do not exist in the analysis of the real model Some of these simplicities are discussed.

Adaptive filtering in the frequency domain can be accomplished by Fourier transformation of the input signal and independent weighting of the contents of each frequency bin. The frequency-domain filter performs similarly to a conventional adaptive transversal filter but promises a significant reduction in computation when the number of weights equals or exceeds 16.

The purpose of this note is to demonstrate significant analytical simplifications for studying the behavior of adaptive filtering in the frequency domain as opposed to studying the behavior of adaptive filtering in the time domain. A closed form expression, for the single complex weight in the frequency domain adaptive filter, is presented which allows significant statistical analysis to be performed. The mean-square error of the filter is evaluated as a function of the algorithm step size and the signal and noise powers.

In this letter, we propose a frequency-weighted block LMS (FWBLMS) algorithm that is based on minimization of the frequency-weighted block mean-squared error. The FWBLMS algorithm has an important advantage over the time-domain LMS algorithm in that it can be designed with different frequency weighting on error signal depending on the relative significance of various frequency bands. Application of the FWBLMS algorithm in adaptive linear prediction of speech is discussed.