Orthogonalization of correlated gaussian signals for volterra system identification

Journal ArticleThis letter presents a simple method for orthogonalizing correlated Gaussian input signals for identification of truncated Volterra systems of arbitrary order of nonlinearity P and memory length N. The procedure requires a Gram-Schmidt orthogonalizer for a vector containing N elements and some nonlinear processing of the output elements of the Gram-Schmidt processor. However, the nonlinear processors do not depend on the statistics of the input signals and, consequently, are easy to design and implement

Adaptive polynomial filters

Journal ArticleWhile linear filter are useful in a large number of applications and relatively simple from conceptual and implementational view points. there are many practical situations that require nonlinear processing of the signals involved. This article explains adaptive nonlinear filters equipped with polynomial models of nonlinearity. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion, or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. followed by adaptive algorithms using system models involving recursive nonlinear difference equations. Such systems are attractive because they may be able to approximate many nonlinear systems with great parsimony in the use pf coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is also described

Vector quantization of images using the L∞ distortion measure

Journal ArticleThis paper considers vector quantization of signals using the Loo distortion measure. The key contribution is a result that allows one to characterize the centroid of a set of vectors for the Loo distortion measure. A method similar to the LBG algorithm for designing codebooks has been developed and tested. The paper also discusses the design of vector quantizers employing the Loo distortion measure in an application in which the occurances of quantization errors with larger magnitudes than a pre-selected threshold must be minimized

Multiplication free vector quantization using the L 1 distortion measure and its variants

Journal ArticleVector quantization is a very powerful technique for data compression and consequently, it has attracted a lot for attention lately. One major drawback associated with this approach is its extreme computational complexity. This paper fist considers vector quantization that uses the L1 distortion measure for its implementation. The L1 distortion measure is very attractive from an implementational point of view, since no multiplication is required for computing the distortion measure. Unfortunately, the traditional Linde-Buzo-Gray (LBG) method for designing the code book for the L1 distortion measure involves several computations of medians of very large arrays and can become very complex. We propose a gradient-based approach for codebook design that does not require any multiplications or median computations. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparting the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appro[riate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. Finally, we apply our techniques in predicitve vector quantization of images and demonstrate the viability of multiplication free predicitve vector quantization of image data

Performance analysis of adaptive filters equipped with the dual sign algorithm

Journal ArticleAdaptive filters equipped with the sign algorithm are attractive in many applications because of their computational simplicity. Unfortunately, their slow speed of convergence is a major limitation. The dual sign algorithm (DSA) is a means by which the convergence speed can be increased without overly degrading the steady-state performance and with a minimal amount of additional computational complexity. This paper presents a convergence analysis for adaptive filters equipped with the dual sign algorithm. Previous analyses of the dual sign algorithm were based on two assumptions: 1) the input sequence to the adaptive filter is white; 2) the behavior for the DSA is such that it switches from an adaptive filter equipped with the sign algorithm with a relatively large convergence constant to another one with a smaller convergence constant a certain amount of the after the filter is initialized. Both these restrictions are removed for Gaussian input signals in our analysis. A simulation example that shows good match between theoretical and empirical results is also presented in this paper

Adaptive volterra filters using orthogonal structures

Journal ArticleAbstract-This paper presents an adaptive Volterra filter that empolys a recently developed orthogonalization procedure of Gaussian signals for Volterra system identification. The algorithm is capable of handling arbitrary orders of nonlinearity P as well as arbitrary lengths of memory N for the system model. The adaptive filter consists of a linear lattice predictor of order N, a set of GramSchmidt orthogonalizers for N vectors of size P+1 elements each, and a joint process estimator in which each coefficient is adapted individually. The complexity of implementing this adaptive filter is comparable to the complexity of the system model when N is much larger than P, a condition that is true in many practical situations. Experimental results demonstrating the capabilities of the algorithm are also presented in the paper

A fast recursive least-squares adaptive nonlinear filter

Journal ArticleThis paper presents a fast, recursive least-squares (RLS) adaptive nonlinear filter. The nonlinearity in the system is modeled using the Hammerstein model, which consists of a memoryless polynomial nonlinearity followed by a finite impulse response linear system. The complexity of our method is about 3NP2+7NP+N+10P2+6P multiplications per iteration and is substantially lower than the computational complexities of fast RLS algorithms that are direct extensions of RLS adaptive linear filters to the nonlinear case

Computationally efficient multiuser detection for coded CDMA

Journal ArticleAbstract: Computationally efficient multiuser detection for coded asynchronous CDMA systems is investigated. The particular receiver studied is a near-far resistant multi-user detector known as the projection receiver (PR) [originally developed in [1, 2]]. The PR perfoms multiple access interference resolution for CDMA with error control coding. The output of the front-end of the projection receiver yields a metric for decoding of the coded sequences. This metric allows the use of a standard sequence decoder (e.g., Viterbi algorithm, M-algorithm) for the error control code. The metric computation can be performed adaptively by an extension of the familiar recursive least-squares (RLS) algorithm. The adaptive PR operates on a single sample per chip. In chis paper it is shown that for random spreading codes this algorithm simplifies and can be executed an order of magnitude faster by exploiting the average cross-correlation of the spreading sequences. The performance of boll1 algorithms are studied for CDMA with random spreading sequences aid compared to theorctical performance bounds

Adaptive volterra filters using orthogonal structures

Journal ArticleAbstract- This paper presents an adaptive Volterra filter that employs a recently developed orthogonalization procedure of Gaussian signals for Volterra system identification. The algorithm is capable of handling arbitrary orders of nonlinearity P as well as arbitrary lengths of memory N for the system model. The adaptive filter consists of a linear lattice predictor or order N, a set of Gram-Schmidt orthogonalizers for N vectors of size P + 1 elements each, and a joint process estimator in which each coefficient is adaptive individually. The complexity of implementing this adaptive filter is comparable to the complexity of the system model when N is much larger than P, a condition that is true in many practical situations. Experimental results demonstrating the capabilities of the algorithm are also presented in the paper

Adaptive filters requiring zero multiplications

Journal ArticleThis paper introduces an adaptive filter structure that requires zero multiplications for its implementations. The primary input signals are quantized using DPCM and the DPCM outputs are processed by the adaptive filter. The sign algorithm. We show that if the parameters are chosen properly, hardware implementation of this filter structure requires no multipliers. Under the assumption that the signals are zero mean, wide-sense stationary, and Gaussian random processes, we derive theoretical results for the mean and mean-squared behavior of the filter. A simulation example is presented that shows very good match between theoretical and empirical results