Convergence analysis and a synchronized learning algorithm for a joint lattice predictor and FIR adaptive filter

Abstract

SUMMARYSince the transfer function of a two-stage adaptive filter combining a lattice predictor and a FIR filter includes the reflection coefficients and the filter coefficients, a conventional learning algorithm does not integrate the updates of the reflection coefficients and the filter coefficients. Therefore, error reduction could not be guaranteed. To solve this problem, we proposed a learning algorithm that corrects the coefficients of the adaptive filter synchronized to updating the reflection coefficients. The filter coefficients w(n + 1) are corrected so that the transfer function based on the filter coefficients w(n + 1) updated by using the reflection coefficients k(n) updated at sample time n is identical for the reflection coefficients k(n + 1) updated at sample time n + 1, and the filter coefficients w(n + 1) are used in the output calculation for sample n + 1. The computational complexity required for updating is 2 (prediction order × filter order). We conducted a simulation to estimate an unknown system by using white noise, colored noise, and speech as the input signal and compared the performance to a conventional method. We verified the following. The conventional method that does not correct the filter coefficients in response to fluctuations in the reflection coefficients cannot adequately reduce the estimation errors. The proposed method converges 4 to 5 times faster than NLMS for speech input, and its errors are equivalent to those of RLS. When the prediction order << the filter order, the computational complexity can be substantially less than RLS.

Block implementation of a synchronized learning algorithm in adaptive lattice filters

“…From the discussions in [7], [8], Û´Ò · ½ µ is updated using ôҵ, therefore, the following output at the next sample can reduce the cost function.…”

“…This problem was analyzed, and the "Synchronized Learning Algorithm" was proposed. The filter coefficients are compensated for taking the reflection coefficient updating into account [7], [8].…”