Transform Domain Adaptive Filter Research Articles

Simulation of active noise control using transform domain adaptive filter algorithms linked with the inhomogeneous Helmholtz equation

An iterative approach is presented that couples the inhomogeneous Helmholtz equation with transform domain active noise control algorithms. The Boundary Element Method is utilized to provide solutions of the inhomogeneous Helmholtz equations for three dimensional pressure wave fields. The source terms in the inhomogeneous Helmholtz equations are adapted iteratively by the algorithm to achieve convergence in the noise cancelling process. The approach can be used to study the impact of active noise control systems based on transform domain algorithms on the wavefield for specific application environments. Additionally, this approach allows for numerical frequency-dependent performance evaluation of multichannel active noise control systems even in acoustically challenging environments. Ill-posed control problems can be identified. The required calculation steps for the integration of the method into existing numerical simulation environments are presented step by step. The study is supplemented by numerical experiments and convergence studies that show good agreement with acoustic theory and analytical results reported in literature.

The wavelet transform-domain adaptive filter for nonlinear acoustic echo cancellation

The usage of low-quality components in communicating devices introduces acoustic nonlinearity. The presence of nonlinearity creates challenges in noise cancellation applications, especially the acoustic echo cancellation (AEC) that requires an adaptive filter of a very high order. However, the functional link adaptive filter (FLAF) algorithm models the acoustic nonlinearity efficiently but shows slow convergence performance due to a very high filter order. To improve the convergence performance of the FLAF, the wavelet transform-domain FLAF (WTD-FLAF) is proposed for nonlinear AEC (NAEC) applications. The convergence rate is improved by decomposing a higher-order adaptive filter into smaller-order subfilters. The convergence speed improvement is gained at the expense of increased computational complexity. A low complexity version of the WTD-FLAF, named as selective update WTD-FLAF (SU-WTD-FLAF) algorithm, is also presented. The SU-WTD-FLAF algorithm is based on the selective coefficient update approach. Computer simulations demonstrate that the convergence performance of the proposed algorithms outperforms the standard FLAF.

Identification of sparse impulse responses – design and implementation using the partial Haar block wavelet transform

This paper proposes an implementation for identifying sparse impulse responses. The new scheme follows the approach in which the location of the channel response peak is estimated in the wavelet domain. A short time-domain adaptive filter is then located about the estimated peak to identify the sparse response. The primary purpose of this paper is to present an efficient design of such a system. The use of a new block wavelet transform results in up to 70% less computational complexity and improved peak detection, as compared to previous solutions. A new robust time-domain adaptive filtering location and update scheme is also proposed that significantly reduces the occurrence of jitter problems and leads to improved residual mean-square error performance. The behavior of the transform-domain adaptive filter is analyzed, the Wiener solution is determined, and an accurate analytical model is obtained for the mean-square deviation of the adaptive coefficients. Monte Carlo simulations show excellent echo cancellation performance for typical ITU-T echo channels.

Fast convergence transform domain adaptive filter algorithm

Fast convergence transform domain adaptive filter algorithm

A Unified View of Adaptive Variable-Metric Projection Algorithms

We present a unified analytic tool named variable-metric adaptive projected subgradient method (V-APSM) that encompasses the important family of adaptive variable-metric projection algorithms. The family includes the transform-domain adaptive filter, the Newton-method-based adaptive filters such as quasi-Newton, the proportionate adaptive filter, and the Krylov-proportionate adaptive filter. We provide a rigorous analysis of V-APSM regarding several invaluable properties including monotone approximation, which indicates stable tracking capability, and convergence to an asymptotically optimal point. Small metric-fluctuations are the key assumption for the analysis. Numerical examples show (i) the robustness of V-APSM against violation of the assumption and (ii) the remarkable advantages over its constant-metric counterpart for colored and nonstationary inputs under noisy situations.

Krylov-Proportionate Adaptive Filtering Techniques Not Limited to Sparse Systems

This paper proposes a novel adaptive filtering scheme named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. KPNLMS exploits the benefits (i.e., fast convergence for sparse unknown systems) of the proportionate NLMS algorithm, but its applications are not limited to sparse unknown systems. A set of orthonormal basis vectors is generated from a certain Krylov sequence. It is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data. Different adaptation gain is allocated to a coefficient of each basis vector, and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate. KPNLMS enjoys i) fast convergence, ii) linear complexity per iteration, and iii) no use of any a priori information. Numerical examples demonstrate significant advantages of the proposed scheme over the reduced-rank method based on the multistage Wiener filter (MWF) and the transform-domain adaptive filter (TDAF) both in noisy and silent situations.

Transform domain adaptive linear phase filter

Describes a new adaptive linear-phase filter whose weights are updated by the normalized least-mean-square (LMS) algorithm in the transform domain. This algorithm provides a faster convergence rate compared with the time domain linear phase LMS algorithm. Various real-valued orthogonal transforms are investigated such as the discrete cosine transform (DCT), discrete Hartley transform (DHT), and power of two (PO2) transform, etc. By using the symmetry property of the transform matrix, an efficient implementation structure is proposed. A system identification example is presented to demonstrate its performance.

Acoustic echo cancellation with a transform domain adaptive filter

The adaptive filtering technique is one of the major approaches to control the acoustic echoes in teleconferencing systems or hands‐free telephony systems. A brief overview of the performance of different adaptive algorithms for acoustic echo cancellation [cf, S. M. Kuo and H. Zhao, J. Acoust. Soc. Am. Suppl. 1 86, S56 (1989)] will be presented. A transform domain adaptive filter (TDAF) algorithm is proposed to construct an acoustic echo canceler that has a convergence rate faster than that of the conventional LMS adaptive transversal filter with colored signals. The proposed approach does not introduce extra delay during the process so that it can be used in the application where delay is not allowed. Different orthogonal transforms such as the discrete Fourier transform (DFT), discrete cosine transform (DCT), and discrete Hartley transform (DHT) are used for signals with different eigenvalue spread. Real‐time implementations of this class of canceler with digital signal processors (DSP) will also be discussed.