Update Equation

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Walter Kellermann - One of the best experts on this subject based on the ideXlab platform.

  • on the causality problem in time domain blind source separation and deconvolution algorithms
    International Conference on Acoustics Speech and Signal Processing, 2005
    Co-Authors: Robert Aichner, H Buchner, Walter Kellermann
    Abstract:

    Using a recently presented generic framework for multichannel blind signal processing for convolutive mixtures, we investigate the problem of incorporating acausal delays which are necessary with certain geometric constellations. Starting from a generic Update Equation which is applicable to blind source separation (BSS), multichannel blind deconvolution (MCBD), and multichannel blind partial deconvolution (MCBPD) for dereverberation of speech signals, two formulations of the natural gradient are derived. It is shown that one expression is applicable to mere causal filters whereas the other also allows an implementation of noncausal filters. Moreover, proper initialization methods for both cases are given. For the implementation of these algorithms, cross-relation estimation techniques, known from linear prediction, are discussed. Based on these results, relationships between traditional MCBD algorithms can be established. Experimental results of different acoustic scenarios show the applicability of the presented algorithms.

  • a generalization of blind source separation algorithms for convolutive mixtures based on second order statistics
    IEEE Transactions on Speech and Audio Processing, 2005
    Co-Authors: H Buchner, Robert Aichner, Walter Kellermann
    Abstract:

    We present a general broadband approach to blind source separation (BSS) for convolutive mixtures based on second-order statistics. This avoids several known limitations of the conventional narrowband approximation, such as the internal permutation problem. In contrast to traditional narrowband approaches, the new framework simultaneously exploits the nonwhiteness property and nonstationarity property of the source signals. Using a novel matrix formulation, we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms by generalizing a known cost-function which inherently allows joint optimization for several time-lags of the correlations. Based on the broadband approach time-domain, constraints are obtained which provide a deeper understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both the time-domain and the frequency-domain versions, we discuss links to well-known, and also, to novel algorithms that constitute special cases. Moreover, using the so-called generalized coherence, links between the time-domain and the frequency-domain algorithms can be established, showing that our cost function leads to an Update Equation with an inherent normalization ensuring a robust adaptation behavior. The concept is applicable to offline, online, and block-online algorithms by introducing a general weighting function allowing for tracking of time-varying real acoustic environments.

Aykut Hocanin - One of the best experts on this subject based on the ideXlab platform.

  • Recursive inverse adaptive algorithm: a second-order version, a fast implementation technique, and further results
    Signal Image and Video Processing, 2015
    Co-Authors: Mohammad Shukri Salman, Osman Kukrer, Aykut Hocanin
    Abstract:

    A variable step-size and first-order recursive estimate of the autocorrelation matrix have been used in the Update Equation of the recently proposed recursive inverse (RI) algorithm. These lead to an improved performance of the RI algorithm compared with some well-known adaptive algorithms. In this paper, the RI algorithm is first briefly reviewed. An improved version of the RI algorithm, which uses a second-order recursive estimation of the correlations, is introduced. A general fast implementation technique for the RI algorithms is presented. The performances of the fast RI and fast second-order RI algorithms are compared to that of the RLS algorithm in stationary white and correlated noise environments in a noise cancellation setting. The simulation results show that the fast RI algorithms outperform the others compared either in speed of convergence and/or the computational complexity when the MSE is held constant. The performance of the original RI algorithms is compared to that of the RLS algorithm in a system identification setting. Simulations show that the RI algorithms perform similar or better than the other algorithms.

  • recursive inverse adaptive filtering algorithm
    Digital Signal Processing, 2011
    Co-Authors: Mohammad Shukri Ahmad, Osman Kukrer, Aykut Hocanin
    Abstract:

    In this paper, a new FIR adaptive filtering algorithm is proposed. The approach uses a variable step-size and the instantaneous value of the autocorrelation matrix in the coefficient Update Equation that leads to an improved performance. Convergence analysis of the algorithm has been presented. Simulation results show that the algorithm performs better than the Transform Domain LMS with Variable Step-Size (TDVSS) in stationary Additive White Gaussian Noise (AWGN) and Additive Correlated Gaussian Noise (ACGN) environments in a system identification setting. It is shown that the algorithm has a performance better than RLS and very similar to RRLS algorithm with a considerable reduction in computational complexity. Additionally, the performance of the proposed algorithm is shown to be superior to that of the Stabilized Fast Transversal Recursive Least Squares (SFTRLS) algorithm under the same conditions.

  • recursive inverse adaptive filter with second order estimation of autocorrelation matrix
    International Symposium on Signal Processing and Information Technology, 2010
    Co-Authors: Mohammad Shukri Ahmad, Osman Kukrer, Aykut Hocanin
    Abstract:

    The recently proposed Recursive Inverse (RI) Adaptive Filtering algorithm uses a variable step-size and the first order recursive estimation of the correlation matrices in the coefficient Update Equation which lead to an improved performance. In this paper, a new FIR adaptive filtering algorithm is introduced. This algorithm uses the second order recursive estimation of the correlation matrices in the coefficient Update Equation which leads to an improved performance over the RI algorithm. The simulation results show that the algorithm outperforms the Transform Domain LMS with Variable Step-Size (TDVSS), the RI and the RLS algorithms in stationary environments. The performance of the algorithms is tested in Additive White Gaussian Noise (AWGN) and Correlated Noise environments.

  • recursive inverse adaptive filtering algorithm
    Conference on Decision and Control, 2009
    Co-Authors: Mohammad Shukri Ahmad, Osman Kukrer, Aykut Hocanin
    Abstract:

    In this paper, a new FIR adaptive filtering algorithm is introduced. This algorithm is based on the Quasi-Newton (QN) optimization algorithm. The approach uses a variable step-size in the coefficient Update Equation that leads to an improved performance. The simulation results show that the algorithm has very similar performance to the Robust Recursive Least Squares Algorithm (RRLS) while performing better than the Transform Domain LMS with Variable Step-Size (TDVSS) in stationary environments. The algorithm is tested in Additive White Gaussian Noise (AWGN) and Correlated Noise environments.

Robert Aichner - One of the best experts on this subject based on the ideXlab platform.

  • on the causality problem in time domain blind source separation and deconvolution algorithms
    International Conference on Acoustics Speech and Signal Processing, 2005
    Co-Authors: Robert Aichner, H Buchner, Walter Kellermann
    Abstract:

    Using a recently presented generic framework for multichannel blind signal processing for convolutive mixtures, we investigate the problem of incorporating acausal delays which are necessary with certain geometric constellations. Starting from a generic Update Equation which is applicable to blind source separation (BSS), multichannel blind deconvolution (MCBD), and multichannel blind partial deconvolution (MCBPD) for dereverberation of speech signals, two formulations of the natural gradient are derived. It is shown that one expression is applicable to mere causal filters whereas the other also allows an implementation of noncausal filters. Moreover, proper initialization methods for both cases are given. For the implementation of these algorithms, cross-relation estimation techniques, known from linear prediction, are discussed. Based on these results, relationships between traditional MCBD algorithms can be established. Experimental results of different acoustic scenarios show the applicability of the presented algorithms.

  • a generalization of blind source separation algorithms for convolutive mixtures based on second order statistics
    IEEE Transactions on Speech and Audio Processing, 2005
    Co-Authors: H Buchner, Robert Aichner, Walter Kellermann
    Abstract:

    We present a general broadband approach to blind source separation (BSS) for convolutive mixtures based on second-order statistics. This avoids several known limitations of the conventional narrowband approximation, such as the internal permutation problem. In contrast to traditional narrowband approaches, the new framework simultaneously exploits the nonwhiteness property and nonstationarity property of the source signals. Using a novel matrix formulation, we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms by generalizing a known cost-function which inherently allows joint optimization for several time-lags of the correlations. Based on the broadband approach time-domain, constraints are obtained which provide a deeper understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both the time-domain and the frequency-domain versions, we discuss links to well-known, and also, to novel algorithms that constitute special cases. Moreover, using the so-called generalized coherence, links between the time-domain and the frequency-domain algorithms can be established, showing that our cost function leads to an Update Equation with an inherent normalization ensuring a robust adaptation behavior. The concept is applicable to offline, online, and block-online algorithms by introducing a general weighting function allowing for tracking of time-varying real acoustic environments.

Jacob Benesty - One of the best experts on this subject based on the ideXlab platform.

  • robust frequency domain recursive least m estimate adaptive filter for acoustic system identification
    International Conference on Acoustics Speech and Signal Processing, 2020
    Co-Authors: Jingdong Chen, Jacob Benesty
    Abstract:

    To identify acoustic systems in non-Gaussian and Gaussian noises, a robust frequency-domain recursive least M-estimate (FRLM) adaptive filtering algorithm is proposed. The cost function of the adaptive filter is defined by using a robust time-domain M-estimator, while its Update Equation is derived from the normal Equation in the frequency domain. As compared to the frequency-domain recursive least-squares adaptive filter, the FRLM algorithm obtains the robustness to non-Gaussian and Gaussian noises. The performance of the proposed algorithm is validated in simulated acoustic environments.

H Buchner - One of the best experts on this subject based on the ideXlab platform.

  • on the causality problem in time domain blind source separation and deconvolution algorithms
    International Conference on Acoustics Speech and Signal Processing, 2005
    Co-Authors: Robert Aichner, H Buchner, Walter Kellermann
    Abstract:

    Using a recently presented generic framework for multichannel blind signal processing for convolutive mixtures, we investigate the problem of incorporating acausal delays which are necessary with certain geometric constellations. Starting from a generic Update Equation which is applicable to blind source separation (BSS), multichannel blind deconvolution (MCBD), and multichannel blind partial deconvolution (MCBPD) for dereverberation of speech signals, two formulations of the natural gradient are derived. It is shown that one expression is applicable to mere causal filters whereas the other also allows an implementation of noncausal filters. Moreover, proper initialization methods for both cases are given. For the implementation of these algorithms, cross-relation estimation techniques, known from linear prediction, are discussed. Based on these results, relationships between traditional MCBD algorithms can be established. Experimental results of different acoustic scenarios show the applicability of the presented algorithms.

  • a generalization of blind source separation algorithms for convolutive mixtures based on second order statistics
    IEEE Transactions on Speech and Audio Processing, 2005
    Co-Authors: H Buchner, Robert Aichner, Walter Kellermann
    Abstract:

    We present a general broadband approach to blind source separation (BSS) for convolutive mixtures based on second-order statistics. This avoids several known limitations of the conventional narrowband approximation, such as the internal permutation problem. In contrast to traditional narrowband approaches, the new framework simultaneously exploits the nonwhiteness property and nonstationarity property of the source signals. Using a novel matrix formulation, we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms by generalizing a known cost-function which inherently allows joint optimization for several time-lags of the correlations. Based on the broadband approach time-domain, constraints are obtained which provide a deeper understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both the time-domain and the frequency-domain versions, we discuss links to well-known, and also, to novel algorithms that constitute special cases. Moreover, using the so-called generalized coherence, links between the time-domain and the frequency-domain algorithms can be established, showing that our cost function leads to an Update Equation with an inherent normalization ensuring a robust adaptation behavior. The concept is applicable to offline, online, and block-online algorithms by introducing a general weighting function allowing for tracking of time-varying real acoustic environments.