Showing papers in "IEEE Transactions on Signal Processing in 1995"

Subspace methods for the blind identification of multichannel FIR filters

Abstract: This paper addresses a problem arising in a context of digital communications. A digital source is transmitted through a continuous channel (the propagation medium), and several measurements are performed at the receiver, either by means of several sensors, or by oversampling the received signal compared to the emission rate. Given only these observations, the baseband equivalents of the corresponding channels have to be recovered. An orthogonality property between "signal" and "noise" subspaces is exploited to build some quadratic form whose minimization yields the desired estimates up to a scale factor. This is in the same spirit as recent works by Tong et al. (see Proc. 25th Asilomar Conf., p.856-860, 1991) but requires fewer computations. Numerical simulations demonstrate the performance of the proposed methods in a channel identification context. >

Projection approximation subspace tracking

Abstract: Subspace estimation plays an important role in a variety of modern signal processing applications. We present a new approach for tracking the signal subspace recursively. It is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem. We show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation. The resulting algorithms have a computational complexity of O(nr) where n is the input vector dimension and r is the number of desired eigencomponents. Simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition. Relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed. >

Improving the readability of time-frequency and time-scale representations by the reassignment method

Abstract: In this paper, the use of the reassignment method, first applied by Kodera, Gendrin, and de Villedary (1976) to the spectrogram, is generalized to any bilinear time-frequency or time-scale distribution. This method creates a modified version of a representation by moving its values away from where they are computed, so as to produce a better localization of the signal components. We first propose a new formulation of this method, followed by a thorough theoretical study of its characteristics. Its practical use for a large variety of known time-frequency and time-scale distributions is then addressed. Finally, some experimental results are reported to demonstrate the performance of this method. >

A least-squares approach to blind channel identification

Abstract: Conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates of certain statistics. In this paper, we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel FIR systems without requiring the knowledge of the input statistical model. A new blind identification algorithm based solely on the system outputs is proposed. Necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented.

Widely linear estimation with complex data

Abstract: Mean square estimation of complex and normal data is not linear as in the real case but widely linear. The purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties. The advantage with respect to the linear procedure is especially analyzed. >

Wavelet neural networks for function learning

Abstract: A wavelet-based neural network is described. The structure of this network is similar to that of the radial basis function (RBF) network, except that in the present paper the radial basis functions are replaced by orthonormal scaling functions that are not necessarily radial-symmetric. The efficacy of this type of network in function learning and estimation is demonstrated through theoretical analysis and experimental results. In particular, it has been shown that the wavelet network has universal and L/sup 2/ approximation properties and is a consistent function estimator. Convergence rates associated with these properties are obtained for certain function classes where the rates avoid the "curse of dimensionality". In the experiments, the wavelet network performed well and compared favorably to the MLP and RBF networks. >

Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden

Abstract: ESPRIT is a high-resolution signal parameter estimation technique based on the translational invariance structure of a sensor array. Previous ESPRIT algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary. The authors present a simple and efficient method to constrain the estimated phase factors to the unit circle, if centro-symmetric array configurations are used. Unitary ESPRIT, the resulting closed-form algorithm, has an ESPRIT-like structure except for the fact that it is formulated in terms of real-valued computations throughout. Since the dimension of the matrices is not increased, this completely real-valued algorithm achieves a substantial reduction of the computational complexity. Furthermore, Unitary ESPRIT incorporates forward-backward averaging, leading to an improved performance compared to the standard ESPRIT algorithm, especially for correlated source signals. Like standard ESPRIT, Unitary ESPRIT offers an inexpensive possibility to reconstruct the impinging wavefronts (signal copy). These signal estimates are more accurate, since Unitary ESPRIT improves the underlying signal subspace estimates. Simulations confirm that, even for uncorrelated signals, the standard ESPRIT algorithm needs twice the number of snapshots to achieve a precision comparable to that of Unitary ESPRIT. Thus, Unitary ESPRIT provides increased estimation accuracy with a reduced computational burden. >

The chirplet transform: physical considerations

Abstract: We consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis. We propose the use of quadratic chirp functions (which we will call q-chirps for short), giving rise to a parameter space that includes both the time-frequency plane and the time-scale plane as 2-D subspaces. The parameter space contains a "time-frequency-scale volume" and thus encompasses both the short-time Fourier transform (as a slice along the time and frequency axes) and the wavelet transform (as a slice along the time and scale axes). In addition to time, frequency, and scale, there are two other coordinate axes within this transform space: shear in time (obtained through convolution with a q-chirp) and shear in frequency (obtained through multiplication by a q-chirp). Signals in this multidimensional space can be obtained by a new transform, which we call the "q-chirplet transform" or simply the "chirplet transform". The proposed chirplets are generalizations of wavelets related to each other by 2-D affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets, which are related to each other by 1-D affine coordinate transformations (translations and dilations) in the time domain only.

A new class of two-channel biorthogonal filter banks and wavelet bases

Abstract: Proposes a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters. >

Analysis of multicomponent LFM signals by a combined Wigner-Hough transform

Abstract: The aim of the paper is the performance evaluation of a method for the analysis of mono- or multicomponent linear-frequency modulation (LFM) signals, based on the Hough transform of the Wigner-Ville distribution of the signals. A closed form expression is found for the signal-to-noise ratio and the parameter estimation accuracy. The overall method, as any nonlinear method, exhibits a threshold effect. Nevertheless, it is shown to be asymptotically efficient and offers a good rejection capability of the cross terms. >

The discrete polynomial-phase transform

Abstract: The discrete polynomial-phase transform (DPT) is a new tool for analyzing constant-amplitude polynomial-phase signals. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly-varying amplitude, additive noise and nonpolynomial phase. The authors define the DPT, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms. A statistical accuracy analysis of the estimated parameters is also presented. >

An adaptive optimal-kernel time-frequency representation

Abstract: Time-frequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signal-dependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are block-oriented techniques unsuitable for on-line implementation or for tracking signal components with characteristics that change with time. The time-frequency representation developed in the present paper, based on a signal-dependent radially Gaussian kernel that adapts over time, surmounts these difficulties. The method employs a short-time ambiguity function both for kernel optimization and as an intermediate step in computing constant-time slices of the representation. Careful algorithm design provides reasonably efficient computation and allows on-line implementation. Certain enhancements, such as cone-kernel constraints and approximate retention of marginals, are easily incorporated with little additional computation. While somewhat more expensive than fixed kernel representations, this new technique often provides much better performance. Several examples illustrate its behavior on synthetic and real-world signals. >

Parametric localization of distributed sources

Abstract: Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method. >

A delayless subband adaptive filter architecture

Abstract: Some adaptive signal processing applications, such as wideband active noise control and acoustic echo cancellation, involve adaptive filters with hundreds of taps. The computational burden associated with these long adaptive filters precludes their use for many low-cost applications. In addition, adaptive filters with many taps may also suffer from slow convergence, especially if the reference signal spectrum has a large dynamic range. Subband techniques have been previously developed for adaptive filters to solve these problems. However, the conventional approach is ruled out for many applications because delay is introduced into the signal path. The paper presents a new type of subband adaptive filter architecture in which the adaptive weights are computed in subbands, but collectively transformed into an equivalent set of wideband filter coefficients. In this manner, signal path delay is avoided while retaining the computational and convergence speed advantages of subband processing. An additional benefit accrues through a significant reduction of aliasing effects. An example of the general technique is presented for a 32-subband design using a polyphase FFT implementation. For this example, the number of multiplies required are only about one-third that of a conventional full band design with zero delay, and only slightly greater than that of a conventional subband design with 16 ms delay. >

Minimum bias multiple taper spectral estimation

Abstract: Two families of orthonormal tapers are proposed for multitaper spectral analysis: minimum bias tapers, and sinusoidal tapers {/spl upsisup (k/)}, where /spl upsisub nsup (k/)=/spl radic/(2/(N+1))sin(/spl pi/kn/N+1), and N is the number of points. The resulting sinusoidal multitaper spectral estimate is S/spl circ/(f)=(1/2K(N+1))/spl Sigmasub j=1sup K/|y(f+j/(2N+2))-y(f-j/(2N+2))|/sup 2/, where y(f) is the Fourier transform of the stationary time series, S(f) is the spectral density, and K is the number of tapers. For fixed j, the sinusoidal tapers converge to the minimum bias tapers like 1/N. Since the sinusoidal tapers have analytic expressions, no numerical eigenvalue decomposition is necessary. Both the minimum bias and sinusoidal tapers have no additional parameter for the spectral bandwidth. The bandwidth of the jth taper is simply 1/N centered about the frequencies (/spl plusmn/j)/(2N+2). Thus, the bandwidth of the multitaper spectral estimate can be adjusted locally by simply adding or deleting tapers. The band limited spectral concentration, /spl intsub -wsup w/|V(f)|/sup 2/df of both the minimum bias and sinusoidal tapers is very close to the optimal concentration achieved by the Slepian (1978) tapers. In contrast, the Slepian tapers can have the local bias, /spl intsub - 1/2 sup 1/2 /f/sup 2/|V(f)|/sup 2/df, much larger than of the minimum bias tapers and the sinusoidal tapers. >

Source number estimators using transformed Gerschgorin radii

Abstract: We introduce effective uses of Gerschgorin radii of the unitary transformed covariance matrix for source number estimation. There are two approaches, likelihood and heuristic, used for developing the detection criteria. The likelihood approach combines the Gerschgorin radii to the well-known source number detectors and improves their detection performances for Gaussian and white noise processes. It is verified that the Gerschgorin likelihood estimators (GLE) are consistent. The Gerschgorin AIC yields a consistent estimate and the Gerschgorin MDL criterion does not tend to underestimate for small or moderate data samples. The heuristic approach applying the Gerschgorin disk estimator (GDE) developed from the projection concept, overcomes the problem in cases of small data samples, an unknown noise model, and data dependency. Furthermore, the detection performances of both approaches through the suggested rotations and averaging can be further improved. Finally, the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data. >

Applications of cumulants to array processing .I. Aperture extension and array calibration

Abstract: An interpretation for the use of cumulants in narrowband array processing problems is proposed. It is shown how fourth-order cumulants of multichannel observations increase the directional information compared with second-order statistics. Based on the interpretation, it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array. The amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far-field sources is also investigated. It is proven that the presence of a doublet and use of fourth-order cumulants is sufficient to accomplish this task. The proposed approach is computationally efficient and more general than covariance-based algorithms that have addressed the calibration problem under constraints. A class of beamforming techniques is proposed to recover the source waveforms. Proposed estimation procedures are based on cumulants, which bring insensitivity to the spatial correlation structure of additive Gaussian measurement noise. Simulations are provided to illustrate the use of the proposed algorithms. >

Signal separation by symmetric adaptive decorrelation: stability, convergence, and uniqueness

Abstract: The performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference. In the LMS algorithm, signal leakage into the noise reference leads to signal distortion and poor noise cancellation. The origin of the problem lies in the fact that LMS decorrelates the signal estimate with the noise reference, which, in the case of signal leakage, makes little sense. An algorithm is proposed that decorrelates the signal estimate with a "signal-free" noise estimate, obtained by adding a symmetric filter to the classical structure. The symmetric adaptive decorrelation (SAD) algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler. Stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied. Apart from limitations on the adaptation constants, stability around the desired solution can only be guaranteed for a subclass of signal mixtures. Furthermore, the decorrelation criterion does not yield a unique solution, and expressions for the "phantom" solutions are derived. Simulations with short FIR filters confirm the predicted behavior. >

Efficient realizations of the discrete and continuous wavelet transforms: from single chip implementations to mappings on SIMD array computers

Abstract: This paper presents a wide range of algorithms and architectures for computing the 1D and 2D discrete wavelet transform (DWT) and the 1D and 2D continuous wavelet transform (CWT). The algorithms and architectures presented are independent of the size and nature of the wavelet function. New on-line algorithms are proposed for the DWT and the CWT that require significantly small storage. The proposed systolic array and the parallel filter architectures implement these on-line algorithms and are optimal both with respect to area and time (under the word-serial model). Moreover, these architectures are very regular and support single chip implementations in VLSI. The proposed SIMD architectures implement the existing pyramid and a'trous algorithms and are optimal with respect to time. >

Unitary equivalence: a new twist on signal processing

Abstract: Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature. >

Nonlinear adaptive prediction of nonstationary signals

Abstract: We describe a computationally efficient scheme for the nonlinear adaptive prediction of nonstationary signals whose generation is governed by a nonlinear dynamical mechanism. The complete predictor consists of two subsections. One performs a nonlinear mapping from the input space to an intermediate space with the aim of linearizing the input signal, and the other performs a linear mapping from the new space to the output space. The nonlinear subsection consists of a pipelined recurrent neural network (PRNN), and the linear section consists of a conventional tapped-delay-line (TDL) filter. The nonlinear adaptive predictor described is of general application. The dynamic behavior of the predictor is demonstrated for the case of a speech signal; for this application, it is shown that the nonlinear adaptive predictor outperforms the traditional linear adaptive scheme in a significant way. >

Simulation-based word-length optimization method for fixed-point digital signal processing systems

Abstract: Word-length optimization and scaling software that utilizes the fixed-point simulation results using realistic input signal samples is developed for the application to general, including nonlinear and time-varying, signal processing systems. Word-length optimization is conducted to minimize the hardware implementation cost while satisfying a fixed-point performance measure. In order to minimize the computing time, signal grouping and efficient search methods are developed. The search algorithms first determine the minimum bound of the word-length for an individual group of signals and then try to find out the cost-optimal solution by using either exhaustive or heuristic methods.

Short wavelets and matrix dilation equations

Abstract: Scaling functions and orthogonal wavelets are created from the coefficients of a lowpass and highpass filter (in a two-band orthogonal filter bank). For "multifilters" those coefficients are matrices. This gives a new block structure for the filter bank, and leads to multiple scaling functions and wavelets. Geronimo, Hardin, and Massopust (see J. Approx. Theory, vol.78, p.373-401, 1994) constructed two scaling functions that have extra properties not previously achieved. The functions /spl Phi//sub 1/ and /spl Phi//sub 2/ are symmetric (linear phase) and they have short support (two intervals or less), while their translates form an orthogonal family. For any single function /spl Phi/, apart from Haar's piecewise constants, those extra properties are known to be impossible. The novelty is to introduce 2/spl times/2 matrix coefficients while retaining orthogonality of the multiwavelets. This note derives the properties of /spl Phi//sub 1/ and /spl Phi//sub 2/ from the matrix dilation equation that they satisfy. Then our main step is to construct associated wavelets: two wavelets for two scaling functions. The properties were derived by Geronimo, Hardin, and Massopust from the iterated interpolation that led to /spl Phi/1 and /spl Phi//sub 2/. One pair of wavelets was found earlier by direct solution of the orthogonality conditions (using Mathematica). Our construction is in parallel with recent progress by Hardin and Geronimo, to develop the underlying algebra from the matrix coefficients in the dilation equation-in another language, to build the 4/spl times/4 paraunitary polyphase matrix in the filter bank. The short support opens new possibilities for applications of filters and wavelets near boundaries. >

Optimal weighted median filtering under structural constraints

Abstract: A new expression for the output moments of weighted median filtered data is derived. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filter's behavior. In certain special cases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters. >

Wideband array processing using a two-sided correlation transformation

Abstract: A new method for broadband array processing is proposed. The method is based on unitary transformation of the signal subspaces. We apply a two-sided transformation on the correlation matrices of the array. It is shown that the two-sided correlation transformation (TCT) has a smaller subspace fitting error than the coherent signal-subspace method (CSM). It is also shown that unlike CSM, the TCT algorithm can generate unbiased estimates of the directions-of-arrival, regardless of the bandwidth of the signals. The capability of the TCT and CSM methods for resolving two closely spaced sources is compared. The resolution threshold for the new technique is much smaller than that for CSM. >

EVAM: an eigenvector-based algorithm for multichannel blind deconvolution of input colored signals

Abstract: A new algorithm is proposed for the deconvolution of an unknown, possibly colored, Gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions. More specifically, not only the root (pole and zero) locations but also the orders of the channel transfer functions are unknown. It is assumed that the channel orders may be overestimated. The proposed algorithm estimates the orders and root locations of the channel transfer functions, therefore it can also be used in multichannel system identification problems. The input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal, hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones. Several experimental results indicate improvement compared to the existing methods in the literature. >

Computationally efficient angle estimation for signals with known waveforms

Abstract: This paper presents a large sample decoupled maximum likelihood (DEML) angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise. The DEML estimator decouples the multidimensional problem of the exact ML estimator to a set of 1-D problems and, hence, is computationally efficient. We shall derive the asymptotic statistical performance of the DEML estimator and compare the performance with its Cramer-Rao bound (CRB), i.e., the best possible performance for the class of asymptotically unbiased estimators. We will show that the DEML estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms. We will also show that for moderately correlated signals with known waveforms, the DEML estimator is no longer a large sample maximum likelihood (ML) estimator, but the DEML estimator may still be used for angle estimation, and the performance degradation relative to the CRB is small. We shall show that the DEML estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix. Finally, several numerical examples showing the performance of the DEML estimator are presented in this paper. >

Principal component filter banks for optimal multiresolution analysis

Abstract: An important issue in multiresolution analysis is that of optimal basis selection. An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version. The resulting PRFB decomposes the input signal into uncorrelated, low-resolution principal components with decreasing variance. Optimality issues are further analyzed in the special case of stationary and cyclostationary processes. By exploiting the connection between discrete-time filter banks and continuous wavelets, an optimal multiresolution decomposition of L/sub 2/(R) is obtained. Analogous results are also derived for deterministic signals. Some illustrative examples and simulations are presented. >

Parameter estimation and blind channel identification in impulsive signal environments

Abstract: New methods for parameter estimation and blind channel identification in impulsive signal environments are presented, where the signals/noise are modeled as symmetric /spl alpha/-stable (S/spl alpha/S) processes. First, we present methods for estimating the parameters (characteristic exponent /spl alpha/ and dispersion /spl gamma/) of a S/spl alpha/S distribution from a time series. The fractional lower order moments, with both positive and negative orders, and their applications to signal processing are introduced. Then we present a new algorithm for blind channel identification using the output fractional lower order moments, and the /spl alpha/-Spectrum, a new spectral representation for impulsive signals, is introduced. From the /spl alpha/-Spectrum, we establish the blind identifiability conditions of any FIR channel (mixed-phase, unknown order) with i.i.d. S/spl alpha/S (/spl alpha/>1) input. As a byproduct, a simple algorithm for recovering the phase of any type of a signal from the magnitude of its z-transform is presented. The novelty of our paper is in parameter estimation and blind identification of the FIR channel based on fractional lower order moments of its output data. Monte Carlo simulations clearly demonstrate the performance of the new methods.

Transform-domain adaptive filters: an analytical approach

Abstract: Transform-domain adaptive filters refer to LMS filters whose inputs are preprocessed with a unitary data-independent transformation followed by a power normalization stage. The transformation is typically chosen to be the discrete Fourier transform (DFT), although other transformations, such as the cosine transform (DCT), the Hartley transform (DHT), or the Walsh-Hadamard transform, have also been proposed in the literature. The resulting algorithms are generally called DFT-LMS, DCT-LMS, etc. This preprocessing improves the eigenvalue distribution of the input autocorrelation matrix of the LMS filter and, as a consequence, ameliorates its convergence speed. In this paper, we start with a brief intuitive explanation of transform-domain algorithms. We then analyze the effects of the preprocessing performed in DFT-LMS and DCT-LMS for first-order Markov inputs. In particular, we show that for Markov-1 inputs of correlation parameter /spl rho//spl isin/[0,1], the eigenvalue spread after DFT and power normalization tends to (1+/spl rho/)l(1-/spl rho/) as the size of the filter gets large, whereas after DCT and power normalization, it reduces to (1+/spl rho/). For comparison, the eigenvalue spread before transformation is asymptotically equal to (1+/spl rho/)/sup 2//(1-/spl rho/)/sup 2/. The analytical method used in the paper provides additional insight into how the algorithms work and is expected to extend to other input signal classes and other transformations. >