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Adaptive Filters
"... Introduction An adaptive filter is defined as a selfdesigning system that relies for its operation on a recursive algorithm, which makes it possible for the filter to perform satisfactorily in an environment where knowledge of the relevant statistics is not available. Adaptive filters are classif ..."
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Cited by 80 (1 self)
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Introduction An adaptive filter is defined as a selfdesigning system that relies for its operation on a recursive algorithm, which makes it possible for the filter to perform satisfactorily in an environment where knowledge of the relevant statistics is not available. Adaptive filters are classified into two main groups: linear, and non linear. Linear adaptive filters compute an estimate of a desired response by using a linear combination of the available set of observables applied to the input of the filter. Otherwise, the adaptive filter is said to be nonlinear. Adaptive filters may also be classified into: (i) Supervised adaptive filters, which require the availability of a training sequence that provides different realizations of a desired response for a specified input signal vector. The desired response is compared against the actual response of the filter due to the input signal vector, and the resulting error signal is
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
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Cited by 73 (0 self)
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Blind Source Separation of Real World Signals
 Proc. ICNN
, 1997
"... We present a method to separate and deconvolve sources which have been recorded in real environments. The use of noncausal FIR filters allows us to deal with nonminimum mixing systems. The learning rules can be derived from different viewpoints such as information maximization, maximum likelihood an ..."
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Cited by 55 (8 self)
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We present a method to separate and deconvolve sources which have been recorded in real environments. The use of noncausal FIR filters allows us to deal with nonminimum mixing systems. The learning rules can be derived from different viewpoints such as information maximization, maximum likelihood and negentropy which result in similar rules for the weight update. We transform the learning rule into the frequency domain where the convolution and deconvolution property becomes a multiplication and division operation. In particular, the FIR polynomial algebra techniques as used by Lambert present an efficient tool to solve true phase inverse systems allowing a simple implementation of noncausal filters. The significance of the methods is shown by the successful separation of two voices and separating a voice that has been recorded with loud music in the background. The recognition rate of an automatic speech recognition system is increased after separating the speech signals. 1 Introduct...
Combining timedelayed decorrelation and ICA: Towards solving the cocktail party problem
 In Proc. ICASSP98
, 1998
"... We present methods to separate blindly mixed signals recorded in a room. The learning algorithm is based on the information maximization in a single layer neural network. We focus on the implementation of the learning algorithm and on issues that arise when separating speakers in room recordings. We ..."
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Cited by 21 (4 self)
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We present methods to separate blindly mixed signals recorded in a room. The learning algorithm is based on the information maximization in a single layer neural network. We focus on the implementation of the learning algorithm and on issues that arise when separating speakers in room recordings. We used an infomax approach in a feedforward neural network implemented in the frequency domain using the polynomial filter matrix algebra technique. Fast convergence speed was achieved by using a timedelayed decorrelation method as a preprocessing step. Under minimumphasemixing conditions this preprocessing step was sufficient for the separation of signals. These methods successfully separated a recorded voice with music in the background(cocktail party problem). Finally, we discuss problems that arise in real world recordings and their potential solutions. 1.
Adaptive filtering in subbands using a weighted criterion
 IEEE Trans. Signal Processing
, 1998
"... Abstract — Transformdomain 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 ..."
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Cited by 5 (0 self)
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Abstract — Transformdomain 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 socalled “shortblock 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
Blind Source Separation and Independent Component Analysis: A Review
, 2004
"... Blind source separation (BSS) and independent component analysis (ICA) are generally based on a wide class of unsupervised learning algorithms and they found potential applications in many areas from engineering to neuroscience. A recent trend in BSS is to consider problems in the framework of matr ..."
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Cited by 5 (0 self)
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Blind source separation (BSS) and independent component analysis (ICA) are generally based on a wide class of unsupervised learning algorithms and they found potential applications in many areas from engineering to neuroscience. A recent trend in BSS is to consider problems in the framework of matrix factorization or more general signals decomposition with probabilistic generative and tree structured graphical models and exploit a priori knowledge about true nature and structure of latent (hidden) variables or sources such as spatiotemporal decorrelation, statistical independence, sparseness, smoothness or lowest complexity in the sense e.g., of best predictability. The possible goal of such decomposition can be considered as the estimation of sources not necessary statistically independent and parameters of a mixing system or more generally as finding a new reduced or hierarchical and structured representation for the observed (sensor) data that can be interpreted as physically meaningful coding or blind source estimation. The key issue is to find a such transformation or coding (linear or nonlinear) which has true physical meaning and interpretation. We present a review of BSS and ICA, including various algorithms for static and dynamic models and their applications. The paper mainly consists of three parts:
A general derivation of wavedomain adaptive filtering and application to acoustic echo cancellation
 in Asilomar Conference on Signals, Systems, and Computers
, 2008
"... WaveDomain Adaptive Filtering (WDAF) was introduced as an efficient spatiotemporal generalization of the popular FrequencyDomain Adaptive Filtering (FDAF). Through the incorporation of the mathematical foundations on wavefields, WDAF is suitable even for massive MIMO systems with highly crosscorr ..."
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Cited by 4 (4 self)
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WaveDomain Adaptive Filtering (WDAF) was introduced as an efficient spatiotemporal generalization of the popular FrequencyDomain Adaptive Filtering (FDAF). Through the incorporation of the mathematical foundations on wavefields, WDAF is suitable even for massive MIMO systems with highly crosscorrelated broadband input signals. In this paper, we present a new rigorous derivation of WDAF leading to a whole class of powerful MIMO adaptation algorithms within a compact matrix framework. We show efficient approximations which provide both new efficient WDAF realizations and interesting links to wellknown algorithms (including the various FDAF algorithms). Due to the rigorous approach, we obtain important practical design rules. 1
On FrequencyDomain Implementations of FilteredGradient Blind Deconvolution Algorithms
 in Proc. Asilomar Conf. Signals, Syst., Comput
, 2002
"... This paper describes an efficient realization of an adaptive singlechannel blind deconvolution algorithm. The algorithm uses fast convolution and correlation techniques, operates mainly in the frequency domain, and the adaptation of the deconvolution filter is based on the natural gradient learning ..."
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Cited by 4 (2 self)
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This paper describes an efficient realization of an adaptive singlechannel blind deconvolution algorithm. The algorithm uses fast convolution and correlation techniques, operates mainly in the frequency domain, and the adaptation of the deconvolution filter is based on the natural gradient learning algorithm. The proposed algorithm is compared to other methods via computational complexity analysis and simulations.
Practical Low Complexity Linear Equalization for MIMOCDMA Systems
 in Proc. Asilomar Conference on Signals, Systems and Computers
, 2003
"... Abstract—This article first reviews recently proposed techniques for adaptive and direct linear MIMO equalization in the context of MIMOCDMA systems and in particular with application to a MIMOextended UMTSFDD downlink. The focus is thereby mainly on the complexity of the algorithms. The second p ..."
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Cited by 3 (1 self)
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Abstract—This article first reviews recently proposed techniques for adaptive and direct linear MIMO equalization in the context of MIMOCDMA systems and in particular with application to a MIMOextended UMTSFDD downlink. The focus is thereby mainly on the complexity of the algorithms. The second part of the paper proposes frequency domain (FD) MIMO equalization using the overlap/add FFT method in conjunction with two different lowcomplexity FDdeconvolution techniques to obtain the equalizer coefficients based on explicit channel impulse response estimates. The effects of imperfect channel estimation are discussed. An architecture for the VLSI implementation of the proposed method is suggested and an estimate of the complexity of the proposed circuit is given in the conclusions. I.
Wideband Algorithms Versus Narrowband Algorithms for Adaptive Filtering in the DFT Domain
 IN ASILOMAR CONF
, 2003
"... Adaptive filtering in the DFT domain is popular for its computational efficiency and its attractive convergence properties resulting from the applicability of the FFT and separate adaptation of individual DFT bins. Narrowband algorithms assume a complete decoupling of different frequency bins, which ..."
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Cited by 3 (1 self)
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Adaptive filtering in the DFT domain is popular for its computational efficiency and its attractive convergence properties resulting from the applicability of the FFT and separate adaptation of individual DFT bins. Narrowband algorithms assume a complete decoupling of different frequency bins, which corresponds to assuming a circulant structure for the input data matrix. Wideband designs account for the difference between the actual Töplitz structure and the circulant structure by introducing additional constraints. In this contribution, we show that a wideband approach with rigorous implementation of appropriate constraints leads to highly efficient algorithms with excellent convergence properties. As examples we consider multichannel acoustic echo cancellation (MCAEC) and blind source separation (BSS) of convolutive mixtures.