Block implementation of a synchronized learning algorithm in adaptive lattice filters

Abstract

In order to achieve fast convergence and less computation for adaptive filters, a joint method combining a whitening process and the NLMS algorithm is a hopeful approach. However, updating the filter coefficients is not synchronized with the reflection coefficient updating resulting in unstable behavior. We analyzed effects of this, and proposed the "Synchronized Learning Algorithm" to solve this problem. Asynchronous error between them is removed, and fast convergence and small residual error were obtained. This algorithm, however, requires Ç´Åĵ computations, where Å is an adaptive filter length, and Ä is a lattice predictor length. It is still large compared with the NLMS algorithm. In order to achieve less computation while the fast convergence is maintained, a block implementation method is proposed. The reflection coefficients are updated at some period, and are fixed during this interval. The proposed block implementation can be effectively applied to parallel form adaptive filters, such as sub-band adaptive filters. Simulation using speech signal shows that a learning curve of the proposed block implementation a little slower than the our original algorithm, but can save the computational complexity.

A lattice predictor based adaptive volterra filter and its convergence property analysis

“…This phenomenon is caused by asynchronous update of the reflection coefficients and the filter coefficients, just the same as the linear lattice adaptive filters [13], [14]. 3) Lattice-AVF with Updated Reflection Coefficients: Figure 5 shows the learning curves, in which the reflection coefficients are updated following Eqs.…”

“…Updating the reflection coefficients and the filter coefficients are not synchronized, and some error remain. The synchronized learning algorithm has been proposed [13], [14], which is briefly described here.…”

“…In linear lattice predictor based adaptive filters [12], a problem of asynchronous update of the reflection coefficients and the filter coefficients is pointed out, and the residual error is not well reduced. A synchronization method has been proposed [13], [14]. In this paper, this asynchronous problem is analyzed.…”