The use of orthogonal transforms for improving performance of adaptive filters

Marshall, D. F.; Jenkins, W.K.; Murphy, James J.

doi:10.1109/31.92880

Cited by 156 publications

(62 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Here, the input signal is assumed real and it is practically convenient for implementation purposes to utilize a real-valued orthogonal transform T [12]. The output error of the TD system is given by…”

Section: Algorithm Formulationmentioning

confidence: 99%

“…The TDLMS algorithm attempts to decorrelate the input signal where gains in convergence speed are obtained only after power normalization of the transformed input vector is applied to reduce the eigenvalue disparity of the transformed signal autocorrelation matrix [13], [10], [12], [2]. The optimal transform, known as the Karhunen-Loeve transform (KLT), can completely diagonalize the algorithm autocorrelation matrix but, unfortunately, is signal dependent and computationally prohibitive.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A New Variable Step Size Control Method for the Transform Domain LMS Adaptive Algorithm

Mayyas

2005

Circuits Syst Signal Process

View full text Add to dashboard Cite

This paper develops a new adaptive step size control method for the transform domain least mean-square (TDLMS) adaptive algorithm. The time-varying step size is an efficient approximation of an optimal step size based on a proposed cost function, therefore leading to significant improvements in the performance characteristics of the TDLMS algorithm. Mean-square analysis is provided, and an expression for the steadystate excess mean-squared error (MSE) is derived. Simulation experiments confirm the algorithm's enhanced convergence properties and verify the theoretical steady-state MSE results.

show abstract

Section: Algorithm Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Variable Step Size Control Method for the Transform Domain LMS Adaptive Algorithm

Mayyas

2005

Circuits Syst Signal Process

View full text Add to dashboard Cite

show abstract

“…In both cases, the orthogonal transform is used as a means for decomposing the input signal into approximately decorrelated components [5]- [7]. Moreover, in both approaches, the variables that are explicitly adapted are the transform domain coefficients of the adaptive filter.…”

Section: Classical Approaches Using a Square Orthogonal Transformmentioning

confidence: 99%

Adaptive filtering in subbands using a weighted criterion

Courville¹,

Duhamel²

1998

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-Transform-domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence, thus improving the convergence rate. However, a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input/output delay as small as possible, thus imposing short transforms. This dilemma has been alleviated by the so-called "short-block transform domain algorithms" but is still apparent. This paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms (e.g., critically subsampled, lossless, perfect reconstruction filter banks), thus allowing better tradeoffs between algorithm improvement, arithmetic complexity, and input/output delay.The method proposed here makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm. This method leads to improvements in the convergence rate compared with both LMS and classical frequency domain algorithms.

show abstract

“…Driven by the practical advantages of the TDNLMS family, there is also considerable interest in the performance analysis of these algorithms [8,9]. Results concerning the performance behaviors of the TDNLMS algorithm were studied in [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…An important class of NLMS is the transform domain NLMS (TDNLMS) algorithms [6][7][8][9][10][11] where unitary transformations such as the discrete Fourier transform (DFT), the discrete cosine transform (DCT), and the wavelet transform (WT) are employed to pre-whiten the input signal. Prewhitening and element-wise normalization usually help to reduce the eigenvalue spread of the input autocorrelation matrix and hence significantly improve the convergence speed.…”

Section: Introductionmentioning

confidence: 99%

On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

Chan

Zhou

2010

J Sign Process Syst

View full text Add to dashboard Cite

This paper studies the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm with general nonlinearity and the transform domain normalized least mean M-estimate (TDNLMM) algorithm in Gaussian inputs and additive Gaussian and impulsive noise environment. The TDNLMM algorithm, which is derived from robust M-estimation, has the advantage of improved performance over the conventional TDNLMS algorithm in combating impulsive noises. Using Price's theorem and its extension, the above algorithms can be treated in a single framework respectively for Gaussian and impulsive noise environments. Further, by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations which describe the mean and mean square behaviors of the TDNLMS and TDNLMM algorithms. These analytical results reveal the advantages of the TDNLMM algorithm in impulsive noise environment, and are in good agreement with computer simulation results.

show abstract

The use of orthogonal transforms for improving performance of adaptive filters

Cited by 156 publications

References 10 publications

A New Variable Step Size Control Method for the Transform Domain LMS Adaptive Algorithm

A New Variable Step Size Control Method for the Transform Domain LMS Adaptive Algorithm

Adaptive filtering in subbands using a weighted criterion

On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

Contact Info

Product

Resources

About