By Topic

Signal Processing, IEEE Transactions on

Issue 9 • Date Sept. 1996

Filter Results

Displaying Results 1 - 25 of 27
  • Comments on "Analysis of the properties of soft morphological filtering using threshold decomposition"

    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (119 KB)  

    Theorems 3 and 4 of the paper by Shih and Pu (see ibid., vol.43, no.2, p.539, 1995) are shown to be incorrect. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Digital computation of the fractional Fourier transform

    Page(s): 2141 - 2150
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1016 KB)  

    An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Wavelet transform based adaptive filters: analysis and new results

    Page(s): 2163 - 2171
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (720 KB)  

    In this paper the wavelet transform is used in an adaptive filtering structure. The coefficients of the adaptive filter are updated by the help of the least mean square (LMS) algorithm. First, the wavelet transform based adaptive filter (WTAF) is described and it is analyzed for its Wiener optimal solution. Then the performance of the WTAF is studied by the help of learning curves for three different convergence factors: (1) constant convergence factor, (2) time-varying convergence factor, and (3) exponentially weighted convergence factor. The exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation. It is shown for two different sets of data that the rate of convergence increases significantly for all three WTAF structures as compared to that of time-domain LMS. The high convergence rates of the WTAF give us reason to expect that it will perform well in tracking rapid changes in a signal View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to NMR spectroscopy data

    Page(s): 2245 - 2259
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1284 KB)  

    We present fast maximum likelihood (FML) estimation of parameters of multiple exponentially damped sinusoids. The FML algorithm was motivated by the desire to analyze data that have many closely spaced components, such as the NMR spectroscopy data of human blood plasma. The computational efficiency of FML lies in reducing the multidimensional search involved in ML estimation into multiple 1-D searches. This is achieved by using our knowledge of the shape of the compressed likelihood function (CLF) in the parameter space. The proposed FML algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the CLF. The other striking features of the proposed algorithm are that it provides procedures for initialization, has a fast converging iteration stage, and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal-to-noise ratio (SNR). The computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction, KiSS/IQML, alternating projections (AP), and expectation-maximization (EM) View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Reply to “Comments on `Analysis of the properties of soft morphological filtering using threshold decomposition' ”

    Page(s): 2350 - 2352
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB)  

    Constraints and proofs are provided by Shih and Pu (see ibid., vol.43, no.2, p.539, 1995) to justify their previous analysis of the idempotent soft morphological filters. It is shown that for a special case, the idempotency in Theorems 3 and 4 of a previous paper by the authors will not hold in the first stage, but the root signal will be produced in the second stage. The exact constraint is added to ensure the idempotency to be valid for the soft morphological closing and opening View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Co-channel interference mitigation in the time-scale domain: the CIMTS algorithm

    Page(s): 2151 - 2162
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (956 KB)  

    In many communication systems, the problem of co-channel interference is encountered when along with the signal of interest (SOI), and one or more interfering signals are present in a common receiver. The SOI and the interference are correlated, possess similar characteristics and power, and share the same region of support both in the time and frequency domains. In this paper, we present co-channel interference mitigation in the time-scale domain (CIMTS) algorithm (for MPSK signals) which estimates the SOI and the interfering signal from their superposition in the presence of additive noise. This method is inspired by the reconstruction of interference from the null space of the SOI in the time-scale domain. Once the null space of the SOI is determined, the interfering signal is reconstructed via a set of linear operations. Therefore, the SOI is estimated by a simple subtraction of the estimated interference from the observations View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Analysis of MUSIC and ESPRIT frequency estimates for sinusoidal signals with lowpass envelopes

    Page(s): 2359 - 2364
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (360 KB)  

    In this correspondence, the MUSIC and ESPRIT frequency estimates of sinusoidal signals with lowpass envelopes are analyzed. To achieve computational simplicity, the frequency estimation is conducted as if the signal had a constant amplitude. The aim of the correspondence is to analyze the degradation of performance induced by the aforementioned mismodeling. Unified expressions for the bias and variances of the MUSIC and ESPRIT frequency estimators are derived under the hypothesis of small bandwidth of the signal envelope. Numerical simulations illustrate the agreement between theoretical and empirical results and study the influence of the envelope bandwidth on the frequency estimation performance View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Design of two MUSIC-like estimators based on bias minimization

    Page(s): 2284 - 2299
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1196 KB)  

    Two classes of MUSIC-like estimators are considered. One class, called weighted norm MUSIC, possesses an optimizing functional, or null spectrum, which is the product of the MUSIC null spectrum and an angle-dependent weight. The second class, which is denoted the Dr estimator, has an optimizing functional that is dependent on a parameter r and is a generalized distance between two particular vectors in the signal subspace. It is shown that the asymptotic mean-square errors of these estimators are the same as MUSIC. By determining an appropriate weight, based on a derived large-sample expression for the estimator bias, a weighted norm MUSIC estimator is found that gives zero bias of order N-1, where N is the sample size. Using an approximate relation between the two types of estimators under consideration, a data-dependent parameter r(θ) is derived for the Dr estimator, which results in small bias over a wide range of signal-to-noise ratios (SNRs) for two closely spaced sources View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Minimum variance time-frequency distribution kernels for signals in additive noise

    Page(s): 2352 - 2356
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    We derive the minimum variance time-frequency distribution kernel for signals in additive circular complex Gaussian white noise processes. It is shown that the kernel that minimizes the average variance and simultaneously satisfies the time-frequency constraints for the noise-only ease remains optimum in the presence of frequency-modulated (FM) signals View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Modifications of the Euclidean algorithm for isolating periodicities from a sparse set of noisy measurements

    Page(s): 2260 - 2272
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1240 KB)  

    Modifications of the Euclidean algorithm are presented for determining the period from a sparse set of noisy measurements. The elements of the set are the noisy occurrence times of a periodic event with (perhaps very many) missing measurements. This problem arises in radar pulse repetition interval (PRI) analysis, in bit synchronization in communications, and in other scenarios. The proposed algorithms are computationally straightforward and converge quickly. A robust version is developed that is stable despite the presence of arbitrary outliers. The Euclidean algorithm approach is justified by a theorem that shows that, for a set of randomly chosen positive integers, the probability that they do not all share a common prime factor approaches one quickly as the cardinality of the set increases. In the noise-free case, this implies that the algorithm produces the correct answer with only 10 data samples, independent of the percentage of missing measurements. In the case of noisy data, simulation results show, for example, good estimation of the period from 100 data samples with 50% of the measurements missing and 25% of the data samples being arbitrary outliers View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A dynamic frequency grid allocation scheme for the efficient design of equiripple FIR filters

    Page(s): 2335 - 2339
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB)  

    In the design of a digital filter, the frequency response is often optimized to meet a given set of specifications on a dense grid of frequency points. The density of the frequency grid points must be sufficiently high so that the frequency response of the filter does not violate the specifications at frequencies in between the grid points. However, the computational complexity of the design process and the storage requirements of the computer increase with the number of frequency grid points. We propose a novel dynamic: grid point allocation technique for the design of minimax optimum FIR filter. It uses a sparse frequency grid but will produce a design that is the same as one designed on very dense frequency grid points. It requires significantly less computer time and memory resources compared with fixed grid point algorithms View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Impulse invariance and multiple-order poles

    Page(s): 2344 - 2347
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (340 KB)  

    The impulse-invariant method of IIR digital filter design from a given analog filter is useful both in filter design and especially in discrete-time simulation of continuous-time systems. The article clarifies aspects of impulse invariance and, in particular, the handling of multiple-order poles. The user is currently faced with incorrect formulas and Matlab software. The problems are discussed, and a method valid for any order poles is presented via a numerical example using original Matlab code View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Discarding data may help in system identification

    Page(s): 2300 - 2310
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (996 KB)  

    We present results concerning the parameter estimates obtained by prediction error methods in the case of input that are insufficiently rich. Such input signals are typical of industrial measurements where occasional stepwise reference changes occur. As is intuitively obvious, the data located around the input signal discontinuities carry most of the useful information. Using singular value decomposition (SVD) techniques, we show that in noise undermodeling situations, the remaining data may introduce large bias on the model parameters with a possible increase of their total mean square error. A data selection criterion is then proposed to discard such poorly informative data to increase the accuracy of the transfer function estimate. The system discussed in particular is a SISO ARMAX system View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Using the EM algorithm to increase the number of signals estimable by 2-D parametric techniques

    Page(s): 2365 - 2368
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    This paper provides an easy method for increasing the number of modes estimable by 2-D parameter estimation schemes which use a single snapshot of the data. For data of size M1×M2 few of these techniques allow the number of modes to exceed M1 and/or M2. As these restrictions are not inherent to the model but the algorithms themselves, this problem is circumvented by treating the observed data as an incomplete version of a larger data set. An existing 2-D parameter estimation scheme is then used for the maximization (M) step of the expectation-maximization (EM) algorithm. In this way, one can increase the number of modes the scheme can estimate without changing the scheme itself View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Full text access may be available. Click article title to sign in or learn about subscription options.
  • Phase-only blind deconvolution using bicepstrum iterative reconstruction algorithm (BIRA)

    Page(s): 2356 - 2359
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (528 KB)  

    In this correspondence, we propose a procedure based on the bicepstrum iterative reconstruction algorithm (BIRA) for the reconstruction of an input signal (unobservable) of a linear-phase or zero-phase linear time-invariant (LTI) system from its observed output. The desired input signal is reconstructed without the knowledge of the system transfer function View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The partitioned eigenvector method for towed array shape estimation

    Page(s): 2273 - 2283
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (988 KB)  

    The eigenvector method for estimating the positions of the receivers of a towed array is based on an eigendecomposition of the cross-spectral density matrix of the receiver outputs. The method assumes a signal scenario consisting of a single plane wave source in the presence of independent noise. This paper derives expressions for the bias and variance of the position estimates and shows that for acceptable performance, the array needs to be relatively linear and the source direction away from endfire. It also shows that the bias and variance is relatively independent of the number of receivers in the array. This observation led to the partitioned eigenvector method introduced in this paper. It is shown that the partitioning approach substantially reduces the computational cost of the array shape estimation algorithm without adversely affecting the quality of the position estimates. The theoretical work is substantiated with numerical simulations and compared to the Cramer-Rao lower bound (CRLB). Further-numerical simulations demonstrate the robustness of the technique against spatially correlated noise and an interference source View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Design of stable IIR filters in the complex domain by automatic delay selection

    Page(s): 2339 - 2344
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (644 KB)  

    A major problem encountered when designing infinite impulse response (IIR) filters in the complex domain is to ensure that the filter is stable. Instability occurs frequently when the IIR filter approximates the inverse of a nonminimum phase system. This is often the case for equalization filters. Addition of delay to the target frequency response can result in a stable filter. However, to date, delay selection has been a matter of trial and error. The article presents an automated method for finding the delay View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the identification of harmonic signal fields convergence method in an arbitrary noise field using the 1-D MV spectrum

    Page(s): 2311 - 2318
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (720 KB)  

    This paper considers the recovery of a multichannel harmonic signal field corrupted by a possibly unknown homogeneous noise field. An approach is presented using the convergence-based spectra developed by Foias et al. (1990) in the random process setting. This technique has the advantage of discerning between the point and narrowband noise spectrum based on the monotonically decreasing convergence properties of a sequence of minimum variance (MV) spectra. For the proposed technique, the random field is reduced to a sequence of random processes using a set of condensing functions. An additional advantage of the proposed technique is that these condensing functions can be used to reflect a priori information and, hence, improve the effective signal-to-noise ratio (SNR). This technique uses information from all dimensions. Traditional techniques would separately apply a spectral algorithm to each dimension of the random field and thereby lose joint information from other dimensions View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Asymptotic analysis of stochastic gradient-based adaptive filtering algorithms with general cost functions

    Page(s): 2186 - 2194
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (768 KB)  

    This paper presents an analysis of stochastic gradient-based adaptive algorithms with general cost functions. The analysis holds under mild assumptions on the inputs and the cost function. The method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates, whereas previous stochastic analyses typically considered mean and mean square behavior. The parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time. Furthermore, almost sure exponential bounds are given for the rate of convergence of the parameter estimates. The asymptotic distribution of the parameter estimates is shown to be Gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics. Specific adaptive algorithms that fall under the framework of this paper are signed error least mean square (LMS), dual sign LMS, quantized state LMS, least mean fourth, dead zone algorithms, momentum algorithms, and leaky LMS View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Gauss-Newton-like optimization algorithm for “weighted” nonlinear least-squares problems

    Page(s): 2222 - 2228
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (568 KB)  

    The Gauss-Newton algorithm is often used to minimize a nonlinear least-squares loss function instead of the original Newton-Raphson algorithm. The main reason is the fact that only first-order derivatives are needed to construct the Jacobian matrix. Some applications as, for instance multivariable system identification, give rise to “weighted” nonlinear least-squares problems for which it can become quite hard to obtain an analytical expression of the Jacobian matrix. To overcome that struggle, a pseudo-Jacobian matrix is introduced, which leaves the stationary points untouched and can be calculated analytically. Moreover, by slightly changing the pseudo-Jacobian matrix, a better approximation of the Hessian can be obtained resulting in faster convergence View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A modified block FTF adaptive algorithm with applications to underwater target detection

    Page(s): 2172 - 2185
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1064 KB)  

    In this paper, the problem of weighted block recursive least squares (RLS) adaptive filtering is formulated in the context of a block fast transversal filter (FTF) algorithm. This “modified block FTF algorithm” is derived by modifying the constrained block-LS cost function to guarantee global optimality. This new soft-constrained algorithm provides an efficient way of transferring weight information between blocks of data. The tracking ability of the algorithm can be controlled by varying the block length and/or a soft constrained parameter. This algorithm is computationally more efficient compared with other LS-based schemes. The effectiveness of this algorithm is tested on a real-life problem dealing with underwater target identification from acoustic backscatter. The process involves the identification of the presence of resonance in the acoustic backscatter from a target of unknown shape submerged in water View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Fast, rank adaptive subspace tracking and applications

    Page(s): 2229 - 2244
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1304 KB)  

    High computational complexity and inadequate parallelism have deterred the use of subspace-based algorithms in real-time systems. We proposed a new class of fast subspace tracking (FST) algorithms that overcome these problems by exploiting the matrix structure inherent in multisensor processing. These algorithms simultaneously track an orthonormal basis for the signal subspace and preserve signal eigenstructure information while requiring only O(Nr) operations per update (where N is the number of channels, and r is the effective rank). Because of their low computational complexity, these algorithms have applications in both recursive and block data processing. Because they preserve the signal eigenstructure as well as compute an orthonormal basis for the signal subspace, these algorithms may be used in a wide range of sensor array applications including bearing estimation, beamforming, and recursive least squares. We present a detailed description of the FST algorithm and its rank adaptive variation (RA-FST) as well as a number of enhancements. We also demonstrate the FST's rapid convergence properties in a number of application scenarios View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • IIR Volterra filtering with application to bilinear systems

    Page(s): 2209 - 2221
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1264 KB)  

    A new nonlinear filtering technique by means of infinite impulse response (IIR) Volterra functionals is developed. It yields the projection onto the closed class of finite Volterra series with separable kernels of arbitrary degree k. Such an optimal estimator is finitely realizable as a bilinear system with parameters that are computable off line. Moreover, if the original system model is itself bilinear, this computation is finitely recursive through higher moments of degree 2 k. Two simple illustrating examples are developed: (i) estimation of the covariance of the internal white noise driving a linear system and (ii) filtering of a non-Gaussian linear system (driven by a Poisson process). The robustness with respect to the observation noise distribution is finally examined View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A conjecture on iterated three-point median filter

    Page(s): 2347 - 2350
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    We prove the following conjecture: the N times iterated three-point median filter (1,1,1)N is equal to a weighted median filter; we also prove that the weighted median filter is unique in certain sense View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.

Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Sergios Theodoridis
University of Athens