Karim Maouche - Academia.edu (original) (raw)
Papers by Karim Maouche
The FNTF algorithm starts from the RLS algorithm for adapting FIR lters. The FNTF algorithm appro... more The FNTF algorithm starts from the RLS algorithm for adapting FIR lters. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix ARM assumption for the input signal. The approximate Kalman gain can still be c omputed using an exact recursion that involves the prediction parts of two Fast Transversal Filter FTF algorithms of order M. Here we introduce the Subsampled U p dating SU approach in which the FNTF lter estimate and Kalman gain are p r ovided at a subsampled r ate, say every L samples. The low-complexity prediction part is kept and a Schur type algorithm is used t o c ompute a priori ltering errors at the intermediate time instants, while some convolutions are c arried out with the FFT. This leads to the FSU FNTF algorithm which has a low computational complexity for relatively long lters.
In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS GSW RLS algorith... more In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS GSW RLS algorithm that has a better tracking ability than the SWC RLS algorithm. This algorithm uses a generalized window which consists of an exponential window for the L 0 most recent data and the same but attenuatedexponential window for the rest of the data. We give a theoritical proof that the use of this window leads to a better compromise between the Excess Mean Squared Errors due to estimation noise and lag noise. Furthermore, after providing a fast version of the GSW RLS algorithm, namely the GSW FTF algorithm, we apply the Subsampled-Upadating technique to derive the FSU GSW FTF algorithm, a doubly-fast version of the GSW RLS algorithm.
The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorit... more The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorithm for adapting an FIR lter of length N. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix of total bandwidth 2M+1 ARM assumption for the input signal. In this algorithm, the approximate Kalman gain can still be computed using an exact recursion that involves the prediction parts of two F ast Transversal Filter FTF algorithms of order M. We i n troduce the Subsampled Updating SU approach in which the FNTF lter estimate and Kalman gain are provided at a subsampled rate, say e v ery L samples. Because of its low computational complexity, the prediction part of the FNTF algorithm is kept. A Schur type algorithm is used to compute various lter outputs at the intermediate time instants, while some products of vectors with Toeplitz matrices are carried out with the FFT. This leads to the Fast Subsampled-Updating FNTF FSU FNTF algorithm which has a relatively low computational complexity for large N while presenting good convergence and tracking performances. This renders the FSU FNTF algorithm very interesting for applications such as acoustic echo cancellation.
A method of reducing noise in a noisy acoustic signal y (t) from a microphone, comprising the fol... more A method of reducing noise in a noisy acoustic signal y (t) from a microphone, comprising the following steps: a) conversion of the noisy acoustic signal y (t) in the time domain in a noisy signal Y in the frequency domain; b) estimating a noise component contained in the noisy signal Y by a method of recursive averaging minimum controlled called "MCRA"; c) cutting the frequency band into multiple frequency sub-bands SB; 2 d) estimation of the square modulus of a denoised component of own sub-band to each subband SB of a noise-suppressed signal by a spectral subtraction algorithm multiband from subband square modules | Y | and sub-band noise components; e) determining an output denoised signal SD; f) converting the SD output denoised signal into a voice signal output denoised sd (t) in the time domain.
Publication in the conference proceedings of EUSIPCO, Rhodes, Greece, 1998
Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181)
We derive a new adaptive filtering algorithm called the Instrumental Variable Affine Projection (... more We derive a new adaptive filtering algorithm called the Instrumental Variable Affine Projection (IVAP) algorithm and give its fast version (FIVAP algorithm). The IVAP algorithm departs from the AP algorithm and uses an IV. The IV process is generated in a way such that the new algorithm combines between the AP and the Fast Newton Transversal Filter (FNTF) algorithms. Simulations show that the IVAP algorithm is more robust to noise than the AP algorithm. With the IV, the sample covariance matrix loses its Hermitian property and its displacement structure is different from the one of the AP algorithm. Consequently, the derivation of a fast version is done by deriving the IV Sliding Window Covariance Fast Transversal Filter (IV SWC FTF) algorithm. Using this and other ingredients, we derive the FIVAP algorithm whose computational complexity is nearly the same as the one of the FAP algorithm.
Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers
We derive a new RLS algorithm: the generalized sliding window RLS (GSWRLS) algorithm and its fast... more We derive a new RLS algorithm: the generalized sliding window RLS (GSWRLS) algorithm and its fast numerically stabilized version: the GSW SFTF algorithm. The generalised window used consists of an exponential decay with base /spl lambda/ for the first L lags, a decrease by a factor 1-/spl alpha/ at lag L, and a further exponential decay with base /spl lambda/ beyond lag L. The exponential and rectangular windows are special cases of the generalized window. We analyze the steady-state excess mean squared error components due to the estimation noise and lag noise with different models for the time-varying optimal filter coefficients. This analysis shows that the exponential window performs better than the rectangular window, but also that the optimal generalized windows performs even better.
Signal Processing, 1994
In this paper, we derive a new fast algorithm for Recursive Least-Squares RLS adaptive ltering. T... more In this paper, we derive a new fast algorithm for Recursive Least-Squares RLS adaptive ltering. This algorithm is especially suited for adapting very long lters such as in the acoustic echo cancellation problem. The starting point is to introduce subsampled updating SU in the RLS algorithm. In the SU RLS algorithm, the Kalman gain and the likelihood variable are matrices. Due to the shift invariance of the adaptive FIR ltering problem, these matrices exhibit a low displacement rank. This leads to a representation of these quantities in terms of sums of products of triangular Toeplitz matrices. Finally, the product of these Toeplitz matrices with a vector can be computed e ciently by using the Fast Fourier Transform FFT. Zusammenfassung Dieser Artikel beschreibt die Herleitung eines neuen Algorithmus zur schnellen adaptiven Recursive Least Square RLS Filterung. Dieser Algorithmus eignet sich besonders f uer aufwendige Filter, wie sie zum Beispiel zur akkustischen Echounterdr ueckung benutzt werden. Im Zentrum dieses Algorithmus steht die Einf uehrung von unterabgetastetem Updating SU. Der Kalman Gewinn und die Likelihood Variable treten im SU RLS Algorithmus als Matrizen auf. Aufgrund der Verschiebungsinvarianz in der adaptiven FIR Filterung zeigen diese Matrizen einen niedrigen Verschiebungsrang. Dies f uehrt zu einer Darstellung dieser Gr oessen als Summe von Produkten von triangul aeren Toeplitz Matrizen. Das Produkt dieser Matrizen mit einem Vektor k ann auf sehr e ziente Weise mit der Fast Fourier Transform FFT berechnet werden. R esum e Dans ce papier, nous pr esentons un nouvel algorithme des moindres carr es r ecursif rapide. Cet algorithme pr esente un int erêt certain pour l'adaptation de ltres tr es longs comme ceux utilis es dans les probl emes d'annulation d' echo acoustique. L'id ee de d epart est d'utiliser l'algorithme RLS avec une mise a jour sous-echantillonn ee" du ltre. Dans cet algorithme le SU RLS le gain de Kalman et la variable de vraisemblance sont des matrices qui ont des rangs de d eplacement faibles. Ces quantit es sont alors repr esent ees et mises a jour par le biais de leurs g en erateurs, sous forme de sommes de produits de matrices de Toeplitz triangulaires. Le produit de l'une de ces quantit es avec un vecteur peut alorsêtre calcul e en utilisant la transform ee de Fourier rapide FFT.
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 2000
The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorit... more The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorithm for adapting an FIR lter of length N. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix of total bandwidth 2M+1 ARM assumption for the input signal. In this algorithm, the approximate Kalman gain can still be computed using an exact recursion that involves the prediction parts of two F ast Transversal Filter FTF algorithms of order M. We i n troduce the Subsampled Updating SU approach in which the FNTF lter estimate and Kalman gain are provided at a subsampled rate, say e v ery L samples. Because of its low computational complexity, the prediction part of the FNTF algorithm is kept. A Schur type algorithm is used to compute various lter outputs at the intermediate time instants, while some products of vectors with Toeplitz matrices are carried out with the FFT. This leads to the Fast Subsampled-Updating FNTF FSU FNTF algorithm which has a relatively low computational complexity for large N while presenting good convergence and tracking performances. This renders the FSU FNTF algorithm very interesting for applications such as acoustic echo cancellation.
In this paper, we derive a new normalisation technique for Frequency Domain Adaptive Filtering FD... more In this paper, we derive a new normalisation technique for Frequency Domain Adaptive Filtering FDAF algorithms. FDAF algorithms are well-known for their low computational complexity and for their decorrelating property that allows the use of di erent step sizes for each adaptive w eight, yielding a uniform convergence of all the modes of the input signal. In these algorithms, normalisation is done by recursively estimating the power of each frequency bin. By introducing a normalisation based on an orthogonal projection as is the case for the A ne Projection algorithm, we derive new frequency domain adaptive ltering algorithms and show b y means of simulation that the convergence speed is improved.
In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS (GSW RLS) algori... more In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS (GSW RLS) algorithm that has a better tracking ability than the SWC RLS algorithm. This algorithm uses a generalized window which consists of an exponential window for theL0 most recent data and the same but attenuatedexponential window for the rest of the data. We give a theoritical proof that the use of this window leads to a better compromise between the Excess Mean Squared Errors due to estimation noise and lag noise. Furthermore, after providing a fast version of the GSW RLS algorithm, namely the GSW FTF algorithm, we apply the Subsampled-Upadating technique to derive the FSU GSW FTF algorithm, a doubly-fast version of the GSW RLS algorithm.
The FNTF algorithm starts from the RLS algorithm for adapting FIR lters. The FNTF algorithm appro... more The FNTF algorithm starts from the RLS algorithm for adapting FIR lters. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix ARM assumption for the input signal. The approximate Kalman gain can still be c omputed using an exact recursion that involves the prediction parts of two Fast Transversal Filter FTF algorithms of order M. Here we introduce the Subsampled U p dating SU approach in which the FNTF lter estimate and Kalman gain are p r ovided at a subsampled r ate, say every L samples. The low-complexity prediction part is kept and a Schur type algorithm is used t o c ompute a priori ltering errors at the intermediate time instants, while some convolutions are c arried out with the FFT. This leads to the FSU FNTF algorithm which has a low computational complexity for relatively long lters.
In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS GSW RLS algorith... more In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS GSW RLS algorithm that has a better tracking ability than the SWC RLS algorithm. This algorithm uses a generalized window which consists of an exponential window for the L 0 most recent data and the same but attenuatedexponential window for the rest of the data. We give a theoritical proof that the use of this window leads to a better compromise between the Excess Mean Squared Errors due to estimation noise and lag noise. Furthermore, after providing a fast version of the GSW RLS algorithm, namely the GSW FTF algorithm, we apply the Subsampled-Upadating technique to derive the FSU GSW FTF algorithm, a doubly-fast version of the GSW RLS algorithm.
The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorit... more The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorithm for adapting an FIR lter of length N. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix of total bandwidth 2M+1 ARM assumption for the input signal. In this algorithm, the approximate Kalman gain can still be computed using an exact recursion that involves the prediction parts of two F ast Transversal Filter FTF algorithms of order M. We i n troduce the Subsampled Updating SU approach in which the FNTF lter estimate and Kalman gain are provided at a subsampled rate, say e v ery L samples. Because of its low computational complexity, the prediction part of the FNTF algorithm is kept. A Schur type algorithm is used to compute various lter outputs at the intermediate time instants, while some products of vectors with Toeplitz matrices are carried out with the FFT. This leads to the Fast Subsampled-Updating FNTF FSU FNTF algorithm which has a relatively low computational complexity for large N while presenting good convergence and tracking performances. This renders the FSU FNTF algorithm very interesting for applications such as acoustic echo cancellation.
A method of reducing noise in a noisy acoustic signal y (t) from a microphone, comprising the fol... more A method of reducing noise in a noisy acoustic signal y (t) from a microphone, comprising the following steps: a) conversion of the noisy acoustic signal y (t) in the time domain in a noisy signal Y in the frequency domain; b) estimating a noise component contained in the noisy signal Y by a method of recursive averaging minimum controlled called "MCRA"; c) cutting the frequency band into multiple frequency sub-bands SB; 2 d) estimation of the square modulus of a denoised component of own sub-band to each subband SB of a noise-suppressed signal by a spectral subtraction algorithm multiband from subband square modules | Y | and sub-band noise components; e) determining an output denoised signal SD; f) converting the SD output denoised signal into a voice signal output denoised sd (t) in the time domain.
Publication in the conference proceedings of EUSIPCO, Rhodes, Greece, 1998
Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181)
We derive a new adaptive filtering algorithm called the Instrumental Variable Affine Projection (... more We derive a new adaptive filtering algorithm called the Instrumental Variable Affine Projection (IVAP) algorithm and give its fast version (FIVAP algorithm). The IVAP algorithm departs from the AP algorithm and uses an IV. The IV process is generated in a way such that the new algorithm combines between the AP and the Fast Newton Transversal Filter (FNTF) algorithms. Simulations show that the IVAP algorithm is more robust to noise than the AP algorithm. With the IV, the sample covariance matrix loses its Hermitian property and its displacement structure is different from the one of the AP algorithm. Consequently, the derivation of a fast version is done by deriving the IV Sliding Window Covariance Fast Transversal Filter (IV SWC FTF) algorithm. Using this and other ingredients, we derive the FIVAP algorithm whose computational complexity is nearly the same as the one of the FAP algorithm.
Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers
We derive a new RLS algorithm: the generalized sliding window RLS (GSWRLS) algorithm and its fast... more We derive a new RLS algorithm: the generalized sliding window RLS (GSWRLS) algorithm and its fast numerically stabilized version: the GSW SFTF algorithm. The generalised window used consists of an exponential decay with base /spl lambda/ for the first L lags, a decrease by a factor 1-/spl alpha/ at lag L, and a further exponential decay with base /spl lambda/ beyond lag L. The exponential and rectangular windows are special cases of the generalized window. We analyze the steady-state excess mean squared error components due to the estimation noise and lag noise with different models for the time-varying optimal filter coefficients. This analysis shows that the exponential window performs better than the rectangular window, but also that the optimal generalized windows performs even better.
Signal Processing, 1994
In this paper, we derive a new fast algorithm for Recursive Least-Squares RLS adaptive ltering. T... more In this paper, we derive a new fast algorithm for Recursive Least-Squares RLS adaptive ltering. This algorithm is especially suited for adapting very long lters such as in the acoustic echo cancellation problem. The starting point is to introduce subsampled updating SU in the RLS algorithm. In the SU RLS algorithm, the Kalman gain and the likelihood variable are matrices. Due to the shift invariance of the adaptive FIR ltering problem, these matrices exhibit a low displacement rank. This leads to a representation of these quantities in terms of sums of products of triangular Toeplitz matrices. Finally, the product of these Toeplitz matrices with a vector can be computed e ciently by using the Fast Fourier Transform FFT. Zusammenfassung Dieser Artikel beschreibt die Herleitung eines neuen Algorithmus zur schnellen adaptiven Recursive Least Square RLS Filterung. Dieser Algorithmus eignet sich besonders f uer aufwendige Filter, wie sie zum Beispiel zur akkustischen Echounterdr ueckung benutzt werden. Im Zentrum dieses Algorithmus steht die Einf uehrung von unterabgetastetem Updating SU. Der Kalman Gewinn und die Likelihood Variable treten im SU RLS Algorithmus als Matrizen auf. Aufgrund der Verschiebungsinvarianz in der adaptiven FIR Filterung zeigen diese Matrizen einen niedrigen Verschiebungsrang. Dies f uehrt zu einer Darstellung dieser Gr oessen als Summe von Produkten von triangul aeren Toeplitz Matrizen. Das Produkt dieser Matrizen mit einem Vektor k ann auf sehr e ziente Weise mit der Fast Fourier Transform FFT berechnet werden. R esum e Dans ce papier, nous pr esentons un nouvel algorithme des moindres carr es r ecursif rapide. Cet algorithme pr esente un int erêt certain pour l'adaptation de ltres tr es longs comme ceux utilis es dans les probl emes d'annulation d' echo acoustique. L'id ee de d epart est d'utiliser l'algorithme RLS avec une mise a jour sous-echantillonn ee" du ltre. Dans cet algorithme le SU RLS le gain de Kalman et la variable de vraisemblance sont des matrices qui ont des rangs de d eplacement faibles. Ces quantit es sont alors repr esent ees et mises a jour par le biais de leurs g en erateurs, sous forme de sommes de produits de matrices de Toeplitz triangulaires. Le produit de l'une de ces quantit es avec un vecteur peut alorsêtre calcul e en utilisant la transform ee de Fourier rapide FFT.
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 2000
The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorit... more The Fast Newton Transversal Filter FNTF algorithm starts from the Recursive Least-Squares algorithm for adapting an FIR lter of length N. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix of total bandwidth 2M+1 ARM assumption for the input signal. In this algorithm, the approximate Kalman gain can still be computed using an exact recursion that involves the prediction parts of two F ast Transversal Filter FTF algorithms of order M. We i n troduce the Subsampled Updating SU approach in which the FNTF lter estimate and Kalman gain are provided at a subsampled rate, say e v ery L samples. Because of its low computational complexity, the prediction part of the FNTF algorithm is kept. A Schur type algorithm is used to compute various lter outputs at the intermediate time instants, while some products of vectors with Toeplitz matrices are carried out with the FFT. This leads to the Fast Subsampled-Updating FNTF FSU FNTF algorithm which has a relatively low computational complexity for large N while presenting good convergence and tracking performances. This renders the FSU FNTF algorithm very interesting for applications such as acoustic echo cancellation.
In this paper, we derive a new normalisation technique for Frequency Domain Adaptive Filtering FD... more In this paper, we derive a new normalisation technique for Frequency Domain Adaptive Filtering FDAF algorithms. FDAF algorithms are well-known for their low computational complexity and for their decorrelating property that allows the use of di erent step sizes for each adaptive w eight, yielding a uniform convergence of all the modes of the input signal. In these algorithms, normalisation is done by recursively estimating the power of each frequency bin. By introducing a normalisation based on an orthogonal projection as is the case for the A ne Projection algorithm, we derive new frequency domain adaptive ltering algorithms and show b y means of simulation that the convergence speed is improved.
In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS (GSW RLS) algori... more In this paper, we derive a new RLS algorithm: the Generalized Sliding Window RLS (GSW RLS) algorithm that has a better tracking ability than the SWC RLS algorithm. This algorithm uses a generalized window which consists of an exponential window for theL0 most recent data and the same but attenuatedexponential window for the rest of the data. We give a theoritical proof that the use of this window leads to a better compromise between the Excess Mean Squared Errors due to estimation noise and lag noise. Furthermore, after providing a fast version of the GSW RLS algorithm, namely the GSW FTF algorithm, we apply the Subsampled-Upadating technique to derive the FSU GSW FTF algorithm, a doubly-fast version of the GSW RLS algorithm.