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Signal Processing, IEEE Transactions on

Issue 5 • Date May 1991

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Displaying Results 1 - 25 of 26
  • A note on the Cramer-Rao bound for 2-D direction finding based on 2-D array

    Publication Year: 1991 , Page(s): 1215 - 1218
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (309 KB)  

    The authors present explicit expressions for the Cramer-Rao bound (CRB) for estimating the two-dimensional (2-D) direction of a single source based on 2-D arrays of identical omnidirectional sensors. Two commonly used models, random wave and unknown wave, are compared. It is shown that the CRBs for the two models have the same dependency on the array structure. A specialization of the CRB to two orthogonal uniform linear arrays (ULAs) is discussed. It is found that the joint CRBs of the direction angles based on the two orthogonal ULAs can be as low as one quarter (for a random waveform model with a large number of snapshots and low SNR) or one half (for both models with high SNR) of the CRBs based on each ULA.<> View full abstract»

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  • Comments on "An FPT algorithm with a modularized structure for computing 2-D cyclic convolutions" by T.K. Truong, et al

    Publication Year: 1991
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (91 KB)  

    The modularized FPT algorithm proposed by Truong et al. in the above-named work (see ibid. vol.36. p.1540-1542, Sept. 1988) is extended to the finite fields for computing 2-D cyclic convolutions. In this method, only FPTs and number theoretic transforms (NTTs) of the same length are required.<> View full abstract»

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  • The techniques of the generalized fast Fourier transform algorithm

    Publication Year: 1991 , Page(s): 1058 - 1069
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (908 KB)  

    A general method of deriving DFT (discrete Fourier transform) algorithms, generalised fast Fourier transform algorithms, is presented. It is shown that a special case of the method is equivalent to nesting of FFTs. The application of the method to the case where N has mutually prime factors results in a new interpretation of the permutations characteristic of this class of algorithms. It is shown that the equalization of FFTs leads to results which are different from the widely used intuitive ones. The high efficiency of split-radix FFTs is explained. It is shown that the formulae of the method can be easily adapted for deriving algorithms for the cosine/sine DFT. A set of FFTs that has smaller arithmetical and/or memory complexities than any algorithm known is presented. In particular, a method of deriving split-radix-2s FFTs requiring N log2 N-3N+4 real multiplications and 3N log2 N-3N+4 additions for any s>1 is presented View full abstract»

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  • Improved spatial smoothing techniques for DOA estimation of coherent signals

    Publication Year: 1991 , Page(s): 1208 - 1210
    Cited by:  Papers (24)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (264 KB)  

    In the context of coherent signal classification, spatial smoothing is necessary for the application of the eigen-based direction of arrival (DOA) estimation methods. However, the currently known spatial smoothing algorithms not only reduce the effective aperture of the array, but also do not consider the cross correlations of the subarray outputs. An improved spatial smoothing algorithm which can fully utilize the correlations of the array outputs and produce a more stable estimate of the covariance matrix is presented. Simulation results are provided to verify the theoretical prediction. The superiority of this method over the conventional methods is obvious, especially when the SOSR (subarray to overall size ratio) is small View full abstract»

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  • Cumulant-based approach to harmonic retrieval and related problems

    Publication Year: 1991 , Page(s): 1099 - 1109
    Cited by:  Papers (101)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (932 KB)  

    A frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored Gaussian noise. In practice, the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density. A cumulant-based approach to these problems is proposed. The cumulants of complex processes are defined, and it is shown that specific 1-D slices of the fourth-order cumulant of the noisy signal for the direction of arrival (DOA) and retrieval of harmonics in noise (RHN) problems are identical to the autocorrelation of a related noiseless signal. Hence correlation-based high-resolution methods may be used with fourth-order cumulants as well. The effectiveness of the proposed methods is demonstrated through standard simulation examples View full abstract»

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  • Multisource delay estimation: nonstationary signals [underwater acoustics]

    Publication Year: 1991 , Page(s): 1033 - 1048
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1196 KB)  

    The authors study delay estimation in a very general framework: multiple sources, correlated noises, nonstationary random signals, and varying delays. The optimal maximum likelihood (ML) delay estimator is derived; its performance via the Cramer-Rao inequality is analyzed; and it is tested by experimentation with synthetic data. The present time-varying delay estimator extends to the nonstationary/multisource environment the estimators of L.C. Ng and Y. Bar-Shalom (1986), L.R. Kirlin and L.A. Dewey (1985), and C.H. Knapp and G.C. Carter (1976). However, the present receiver significantly departs from the correlator structures of those authors View full abstract»

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  • An order-16 integer cosine transform

    Publication Year: 1991 , Page(s): 1205 - 1208
    Cited by:  Papers (11)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    It is shown that it is possible to replace the real-numbered elements of a discrete cosine transform (DCT) matrix with integers and still maintain the structure, i.e., relative magnitudes and orthogonality, among the matrix elements. The result is an integer cosine transform (ICT). Thirteen ICTs have been found, and some of them have performance comparable to the DCT. The main advantage of the ICT lies in having only integer values, which in two cases can be represented perfectly by 6-bit numbers, thus providing a potential reduction in the computational complexity View full abstract»

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  • On the convergence of the multichannel maximum likelihood point spectrum estimator

    Publication Year: 1991 , Page(s): 1210 - 1212
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (276 KB)  

    In 1948, Geronimus discovered that the inverse of the sum of the (modulus squared) orthogonal polynomials corresponding to a Toeplitz matrix converges to the point spectrum as the matrix order goes to infinity. In 1969, Capon independently generalized part of Geronimus' result to the random field setting as a fixed-order point spectrum estimator. Within signal processing, this Geronimus-Capon result is known as the maximum likelihood spectral estimator or alternatively, the minimum variance estimator. A simple proof that the Geronimus-Capon spectra estimator converges to the point spectrum in the multichannel setting is presented View full abstract»

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  • Detecting boundaries in a vector field

    Publication Year: 1991 , Page(s): 1181 - 1194
    Cited by:  Papers (51)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1216 KB)  

    A vector gradient approach is proposed to detect boundaries in multidimensional data with multiple attributes (a vector field). It is used to extend a gradient edge detector to color images. The statistical effects of noise on the distribution of the amplitudes and directions of the vector gradient are characterized. The noise behavior of the L 2 norm of the scalar gradients is also characterized for comparison. When the attribute components are highly correlated, as is often the case in color images, use of the vector gradient shows a small gain in signal-to-noise ratio over that of the L2 norm of the scalar gradients. This small gain may or may not be significant, depending on other measures an edge detector uses to deal with noise View full abstract»

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  • Effect of sampling rate on the conjugate gradient method applied to signal extrapolation

    Publication Year: 1991 , Page(s): 1235 - 1238
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    A different response to changes in sampling rate has been observed for conjugate gradients as opposed to SVD (singular-value decomposition) applied to signal extrapolation. The conjugate gradient solution is described in terms of the SVD, which leads to an explanation of the behavior of the conjugate gradient method in this context. Formulating the conjugate gradient method as a spectral filtering method and analyzing it in terms of the spectral filter functions generated as the iteration progresses have made it possible to explain the difference in the effect of sampling rate changes on the conjugate gradients approach to signal extrapolation as compared to the truncated SVD approach discussed by Sullivan and Liu (1984) View full abstract»

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  • Direction-of-arrival estimation using rank revealing QR factorization

    Publication Year: 1991 , Page(s): 1224 - 1229
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (484 KB)  

    The authors describe a novel technique for direction-of-arrival estimation based on computing a permutation matrix E and a QR factorization RE=HB of the permuted covariance matrix R, such that a possible rank deficiency of R is revealed in the triangular factor B having a minimum norm lower right block. A subset of the columns of the orthogonal matrix, H, is shown to be orthogonal to the direction vectors of sources and hence can be used to estimate their bearings. The cost of this algorithm is only slightly more than that of one QR factorization, but is much lower than that of an eigen-decomposition. Simulation results are included to show that the proposed method performs nearly as well as MUSIC in terms of signal resolution, bias, and variance of the estimated bearings View full abstract»

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  • Error-free solution to a Toeplitz system of equations

    Publication Year: 1991 , Page(s): 1212 - 1215
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB)  

    A numerical method which allows error-free computation of the solution to a Toeplitz system of equations is developed. The method requires that the system of equations have rational entries. To avoid error that is inherent in floating-point arithmetic, multiple-modulus residue arithmetic is applied to a modified version of the Levinson algorithm and to an algorithm presented by S.Y. Kung and Y.H. Hu (1983). The error-free method has a highly parallel structure and can be implemented with existing software and hardware. The exact method presented here serves as an outline for the general approach to the development of error-free solution methods View full abstract»

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  • The PDF of adaptive beamforming weights

    Publication Year: 1991 , Page(s): 1232 - 1235
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    The author derives a closed-form expression for the marginal probability density function (PDF) for the weight vector coefficients in a minimum-variance distortionless response (MVDR) adaptive beamformer, when the snapshots are independently identically distributed (IID) normal and the weights are computed via sample matrix inversion. The marginal PDF allows one to determine the dynamic range required to avoid saturation (with a specified degree of probability) in digital and/or analog implementation of beamforming weights View full abstract»

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  • An improved systolic architecture for 2-D digital filters

    Publication Year: 1991 , Page(s): 1195 - 1202
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    An improved systolic architecture for two-dimensional infinite-impulse response (IIR) and finite-impulse-response (FIR) digital filters is presented. Comparisons with recently published work are made. When compared with the architecture of M.A. Sid-Ahmed (1989), a substantial reduction in the number of delay elements is observed. This reduction is of the order of 102 for a 2-D IIR filter and equals N+1 for an Nth-order 2-D FIR filter. The clock period has been made independent of the order of the filter. The speed-up factor is the maximum achievable and is independent of the filter order. Comparison with the work of S. Sunder et al. (1990) shows an improvement in the latency of the systolic array, which has been reduced from 1 to 0. A reduction of N+1 delay elements has been achieved for the FIR filter. An error analysis for the architecture is made View full abstract»

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  • Threshold bounds in SVD and a new iterative algorithm for order selection in AR models

    Publication Year: 1991 , Page(s): 1218 - 1221
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    The problem of order determination of AR (autoregressive) models using singular value decomposition (SVD) is reexamined from a statistical point of view. Thresholds for distinguishing between significant and nonsignificant singular values are derived, and a novel iterative algorithm for order selection in AR models is presented. Simulation results show the technique to be very effective when a small number of samples is available View full abstract»

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  • The constrained total least squares technique and its applications to harmonic superresolution

    Publication Year: 1991 , Page(s): 1070 - 1087
    Cited by:  Papers (73)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1124 KB)  

    The constrained total least squares (CTLS) method is a natural extension of TLS to the case when the noise components of the coefficients are algebraically related. The CTLS technique is developed, and some of its applications to superresolution harmonic analysis are presented. The CTLS problem is reduced to an unconstrained minimization problem over a small set of variables. A perturbation analysis of the CTLS solution is derived, and from it the root mean-square error (RMSE) of the CTLS solution, which is valid for small noise levels, is obtained in closed form. The complex version of the Newton method is derived and applied to determine the CTLS solution. It is also shown that the CTLS problem is equivalent to a constrained parameter maximum-likelihood problem. The CTLS technique is applied to estimate the frequencies of sinusoids in white noise and the angle of arrival of narrowband wavefronts at a linear uniform array. In both cases the CTLS method shows superior or similar accuracy to other advanced techniques View full abstract»

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  • A polynomial approach to optimal and adaptive filtering with application to speech

    Publication Year: 1991 , Page(s): 1221 - 1224
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB)  

    Explicit polynomial solutions to the Wiener filtering problem are given. They rely on the identification of innovations models for the disturbance and for the noisy signal. The Wiener filter is found from the solution of a diophantine equation. Results illustrating the attenuation of background interference in a speech signal are presented. The explicit approach presented does not rely on minimizing a prediction error over a performance surface and can be applied where two input techniques are impracticable or impossible View full abstract»

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  • Sensor array processing based on subspace fitting

    Publication Year: 1991 , Page(s): 1110 - 1121
    Cited by:  Papers (252)  |  Patents (23)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1004 KB)  

    Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals View full abstract»

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  • Evaluation of the quantization error in denominator-separable 2-D recursive filters

    Publication Year: 1991 , Page(s): 1229 - 1232
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the computation of the infinite square sum Jm=φΣ ny2 (m, n). A simple method is presented for evaluating J based on partial fraction expansion and using the residue method provided the Z-transform Y(Z1, Z2) of the sequence y(m, n) having quadrant support is a causal bounded input, bounded output (BIBO) stable denominator-separable rational function. The value of J is expressed as a sum of simple integrals which can easily be evaluated. The simple integrals are tabulated for ready reference. The proposed method is suitable for analytical as well as numerical computation and can easily be programmed View full abstract»

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  • Detection of the number of signals: a predicted eigen-threshold approach

    Publication Year: 1991 , Page(s): 1088 - 1098
    Cited by:  Papers (59)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (824 KB)  

    A novel method for detecting the number of signals incident upon an array of sensors is described. The method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output. The asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds. Due to the fact that the detection error of the method can be controlled by a parameter t, the performance of the method is superior to the MDL (minimum description length) under low SNR (signal-to-noise ratio) and superior to an AIC (Akaike information criterion) under high SNR. The distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen. Simulation results are presented to confirm the analysis View full abstract»

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  • Multistage order statistic filters for image sequence processing

    Publication Year: 1991 , Page(s): 1146 - 1163
    Cited by:  Papers (48)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2552 KB)  

    The application of multistage order statistic filters (MOS) to the task of noise suppression in time-varying imagery is studied. It is shown that MOS filters efficiently preserve image structures under motion without motion compensation preprocessing. In particular, the families of multistage median and weighted median filters are considered. Motion preservation and statistical smoothing measures are derived. It is shown that spatiotemporal filtering allows for a significant improvement over both spatial and temporal filtering in terms of output image resolution and noise suppression View full abstract»

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  • On estimating the angle parameters of an exponential signal at high SNR

    Publication Year: 1991 , Page(s): 1203 - 1205
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB)  

    It is shown that at high signal-to-noise ratio, phase data alone constitute a sufficient statistic for the estimation of the angle parameters of a single exponential signal in Gaussian noise. The threshold effect, which occurs when estimating frequency based on phase only, can be deduced by examining the joint probability distribution function of the phase and amplitude View full abstract»

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  • Recursive updating the eigenvalue decomposition of a covariance matrix

    Publication Year: 1991 , Page(s): 1136 - 1145
    Cited by:  Papers (36)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (892 KB)  

    The author addresses the problem of computing the eigensystem of the modified Hermitian matrix, given the prior knowledge of the eigensystem of the original Hermitian matrix. Specifically, an additive rank-k modification corresponding to adding and deleting blocks of data to and from the covariance matrix is considered. An efficient and parallel algorithm which makes use of a generalized spectrum-slicing theorem is derived for computing the eigenvalues. The eigenvector can be computed explicitly in terms of the solution of a much-reduced (k ×k) homogeneous Hermitian system. The overall computational complexity is shown to be improved by an order of magnitude from O(N3) to O(N 2k), where N×N is the size of the covariance matrix. It is pointed out that these ideas can be applied to adaptive signal processing applications, such as eigen-based techniques for frequency or angle-of-arrival estimation and tracking. Specifically, adaptive versions of the principal eigenvector method and the total least squares method are derived View full abstract»

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  • The extended MENT algorithm: a maximum entropy type algorithm using prior knowledge for computerized tomography

    Publication Year: 1991 , Page(s): 1164 - 1180
    Cited by:  Papers (5)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2092 KB)  

    Unlike MENT (maximum entropy algorithm), the extended MENT algorithm can process prior information and deal with incomplete projections or limited angle data. The reconstruction problem is formulated for solving linear systems involving the Fredholm integral equation. To develop the extended MENT algorithm, maximum entropy is substituted by a more general optimization criterion, that of minimizing the discriminatory function. The a priori knowledge of the shape of the object is easily incorporated in the algorithm by using the discriminatory function. Useful mathematical properties that make the discriminatory function attractive are derived. The sensitivity of the minimum discriminatory solution is derived to determine the characteristics of the noise in the reconstructed images. The extended MENT algorithm is developed for a parallel geometry, and its convergence properties are given. Its image processing performance is better than that for other maximum entropy algorithms such as multiplicative algebraic reconstruction techniques (MART) or more standard methods such as ART and the convolution backprojection View full abstract»

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  • A low delay 16 kb/s speech coder

    Publication Year: 1991 , Page(s): 1049 - 1057
    Cited by:  Papers (17)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (848 KB)  

    A code tree generated by a stochastically populated innovations tree with a backward adaptive gain and backward adaptive synthesis filters is considered. The synthesis configuration uses a cascade of two all-pole filters: a pitch (long time delay) filter followed by a formant (short time delay) filter. Both filters are updated using backward adaptation. The formant predictor is updated using an adaptive lattice algorithm. The multipath (M, L) search algorithm is used to encode the speech. A frequency-weighted error measure is used to reduce the perceptual loudness of the quantization noise. The addition of the pitch filter gives 2-10-dB increase in segSNR (segmental signal-to-noise ratio) in the voiced segments. Subjective testing has shown that the coder attains a subjective quality equivalent to 7 b/sample log-PCM (pulse code modulation) with an encoding delay of eight samples (1 ms with an 8-kHz sampling rate) View full abstract»

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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

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Editor-in-Chief
Sergios Theodoridis
University of Athens