Transform Domain LMS Algorithm Research Articles

A New Post-whitening Transform Domain LMS Algorithm

A New Post-whitening Transform Domain LMS Algorithm

A new pre-whitening transform domain LMS algorithm and its application to speech denoising

In this paper, we propose a new pre-whitening transform domain LMS algorithm. The main idea is to introduce a pre-whitening using a simple finite impulse response decorrelation filter of order one before applying the transform to reinforce its decorrelation. The resulting algorithm has the advantage of using any transform even with low decorrelation. This advantage can be exploited to consider transforms having lower computational and structural complexities than those of the classical transforms. For this purpose, we also investigate the use of other transforms, namely the parametric Fourier and Hartley transforms. This investigation is accomplished by studying the eigenvalue spreads obtained by a given parametric transform and then finding the value of the parameter corresponding to the minimum eigenvalue spread, which is equivalent to the best mean square error (MSE) convergence behavior. This approach provides new attractive transforms for the proposed algorithm. Moreover, we consider the adaptive speech denoising as an application to evaluate the performance of the proposed algorithm. The comparisons between the proposed and conventional algorithms for different transforms are performed in terms of the computational complexity, MSE convergence speed, reached steady state level, residual noise in the denoised signal, steady state excess MSE, misadjustment and output SNR.

New Variable Step-Sizes Minimizing Mean-Square Deviation for the LMS-Type Algorithms

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms.

The wavelet transform-domain LMS adaptive filter with partial subband-coefficient updating

In this paper, we propose and analyze the wavelet transform-domain LMS (WTDLMS) algorithm where only a subset of the adaptive filter coefficients are updated at each iteration. The use of wavelets or subband filterbanks can lead to several novel schemes whose combinations can lead to other sub-schemes as well. In the proposed scheme, the coefficients can be selected altogether as a block and not just individually as done earlier in the literature. This algorithm is then tested in the context of system identification and equalization

PIPELINED ARCHITECTURES FOR TRANSFORM DOMAIN LMS ADAPTIVE FILTERING

In this paper, efficient pipelined architectures for the implementation of the Transform Domain LMS (TD-LMS) adaptive filter are considered. Pipelining of the TD-LMS algorithm is achieved by introducing an amount of time delay into the original adaptive scheme. The resulting algorithm, called thereafter the delayed TD-LMS, performs adaptive filtering with delayed coefficients adaptation. A statistical performance analysis of the proposed delayed TD-LMS adaptive algorithm is presented, both for the mean error and the mean squared error of the filter coefficients. A closed form expression is derived for the estimation of the steady state excess mean squared error, in terms of the adaptation delay and the input signal characteristics. The adaptation delay introduced to the delayed TD-LMS algorithm is subsequently utilized for the development of pipelined architectures. By retiming the delays existing in the error signal feedback loop, efficient pipelined implementations of the delayed TD-LMS algorithm are developed. The proposed architectures are suitable for parallel implementation on a general-purpose parallel machine, or on dedicated hardware, integrated on ASIC or ASIP VLSI processors.

ANALYSIS OF THE TRANSFORM DOMAIN LMS ALGORITHM WITH INSUFFICIENT LENGTH ADAPTIVE FILTER

Though, in most practical applications, the length of the adaptive filter is less than that of the unknown system impulse response, analysis of adaptive filtering algorithms almost always assumed a sufficient length adaptive filter whose length is equal to that of unknown system. Theoretical results on the sufficient length adaptive algorithm do not necessarily apply to the realistic insufficient length case and, therefore, it becomes extremely desirable for practical purposes that we quantify the statistical behavior of the insufficient length adaptive algorithm. In this paper, we analyze the popular Transform Domain LMS (TDLMS) algorithm with insufficient length adaptive filter for Gaussian input data and using the common independence assumption. Analysis yields exact theoretical expressions that describe the mean and mean-square convergence of the algorithm, which lead to a better understanding to the performance properties of the insufficient length TDLMS adaptive algorithm. Simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm.

Reduced-Complexity Transform-Domain Adaptive Algorithm With Selective Coefficient Update

This paper proposes a new low-complexity transform-domain (TD) adaptive algorithm for acoustic echo cancellation. The algorithm is based on decomposing the long adaptive filter into smaller subfilters and employing the selective coefficient update (SCU) approach in each subfilter to reduce computational complexity. The resulting algorithm combines the fast converging characteristic of the TD decomposition technique and the benefits of the SCU of low complexity with minimal performance losses. The improvement in convergence speed comes at the expense of a corresponding increase in misadjustment. To overcome this problem, a hybrid of the proposed algorithm and the standard TD LMS algorithm (TDLMS) is presented. The hybrid algorithm retains the fast convergence speed capabilities of the original algorithm while allowing for low final MSE. Simulations show that the hybrid algorithm offers a superior performance when compared to the standard TDLMS algorithm with less computational overhead.

Transform domain LMS-based adaptive prediction for lossless image coding

This paper is concerned with adaptive prediction for lossless image coding. A new predictor is proposed. This predictor involves two major steps: constructing a good predictor for each pixel using the transform domain LMS algorithm and adaptively combining it with a set of fixed predictors. The first step is targeting areas where simple predictors do not perform well, while the second step is an effective method to reduce the modelling costs associated with the uncertainty of the models. When a context-based arithmetic encoder is used to encode the prediction error, the compression performance of the proposed algorithm is better than or comparable to that of other published algorithms.

GSC realisations using the two-dimensional transform-domain LMS algorithm

The authors propose two new realisations of the broadband generalised sidelobe canceller (GSC) which are based on a two-dimensional (2D) extension of the transform-domain LMS algorithm. In the first realisation, the tap-input matrix of the GSC (following the blocking network) is mapped into the transform-domain via a 2D unitary image transform. Following this step, the transformed data are weighted and summed to produce the GSC output and the processor weights are updated via the self-orthogonalising LMS algorithm in the transform-domain. The second realisation uses a separable 2D transform and provides a narrowband decomposition of the GSC. The computational complexity of these new GSC realisations is analysed and shown to be comparable to that of the fast FLMS-GSC recently proposed by Chen and Fang (see J. Acoust. Sec. Am., vol.91, p.3354, 1992). However, as demonstrated by computer simulations, the new GSC realisations have a much faster convergence rate than the FLMS-GSC when the eigenvalue spread of the tap-input correlation matrix is large.

Transform domain LMS algorithm

The concept of transform domain adaptive filtering is introduced. In certain applications, filtering in the transform domain results in great improvements in convergence rate over the conventional time-domain adaptive filtering. The relationship between several existing frequency domain adaptive filtering algorithms is established. Applications of the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed.