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Signal Processing, IEEE Transactions on

Issue 6 • Date June 1993

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Displaying Results 1 - 25 of 27
  • Perfect reconstruction filter banks with rational sampling factors

    Page(s): 2047 - 2066
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    An open problem, namely, how to construct perfect reconstruction filter banks with rational sampling factors, is solved. Such filter banks have N branches, each one having a sampling factor of p i/qi, and their sum equals one. In this way, the well-known theory of filter banks with uniform band splitting is extended to allow for nonuniform divisions of the spectrum. This can be very useful in the analysis of speech and music. The theory relies on two transforms. The first transform leads to uniform filter banks having polyphase components as individual filters. The other results in a uniform filter bank containing shifted versions of same filters. This, in turn, introduces dependencies in design, and is left for future work. As an illustration, several design examples for the (2/3, 1/3) case are given. Filter banks are then classified according to the possible ways in which they can be built. It is shown that some cases cannot be solved even with ideal filters (with real coefficients) View full abstract»

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  • On the optimal weight vector of a perceptron with Gaussian data and arbitrary nonlinearity

    Page(s): 2257 - 2259
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    The authors investigate the solution to the following problem: find the optimal weighted sum of given signals when the optimality criterion is the expected value of a function of this sum and a given `training' signal. The optimality criterion can be a nonlinear function from a very large family of possible functions. A number of interesting cases fall under this general framework, such as a single layer perceptron with any of the commonly used nonlinearities, the least-mean-square (LMS), the LMF or higher moments, or the various sign algorithms. Assuming the signals to be jointly Gaussian, it is shown that the optimal solution, when it exits, is always collinear with the well-known Wiener solution, and only its scaling factor depends on the particular functions chosen. Necessary constructive conditions for the existence of the optimal solution are also presented View full abstract»

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  • Determination of the MA order of an ARMA process using sample correlations

    Page(s): 2277 - 2280
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    It is shown that autoregressive information and moving average information are implicitly contained in two different correlation matrices. An algorithm for MA order determination which adopts only autocorrelations and the AR order without requiring AR coefficients is proposed. Numerical simulations are presented to show the practical value of the proposed singular-value-decomposition (SVD)-based algorithm View full abstract»

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  • A note on the PQ theorem and the extrapolation of signals

    Page(s): 2259 - 2261
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    The problem of determining a bandlimited function from its values on a finite interval is ill-conditioned in the sense that although the pertinent inverse map exists, it is discontinuous at every point. Whenever certain closely related general problems are well conditioned in the sense that the inverse operator is continuous, they can be solved using a special case of a known algorithm. In particular, attention is directed to the relation between the PQ theorem, its Hilbert space projection-operator setting, and later work View full abstract»

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  • Blind convolution using signal reconstruction from partial higher order cepstral information

    Page(s): 2088 - 2095
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    A blind deconvolution scheme for the reconstruction of a signal that propagates in the presence of reverberation and additive noise is presented. The reconstruction employs data collected by two receivers placed well apart from each other. Each received sequence consists of the convolution of the transmitted signal with a channel. Applying the bicepstrum iterative reconstruction algorithm on the differences of the cepstra coefficients of the two received sequences, the cepstra coefficients of the transmission channels can be computed and used for the reconstruction of the transmitted signal. The deconvolution can be performed even if the data sequences are corrupted by additive noise. The computation of the cepstra coefficients is based on the cross-bispectrum if the noise processes present in the observation sequences are zero mean and uncorrelated, while the bicepstrum of each observation is used if the noise processes are zero mean correlated with a symmetric probability density function View full abstract»

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  • Linear interpolation lattice for nonstationary signals

    Page(s): 2262 - 2264
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    A ladder algorithm for linear interpolation of nonstationary signals is developed. The algorithm is based on the sliding-window least-squares method and can be implemented using a lattice structure. Furthermore, by assuming that the input signal is stationary, the number of parameters required to be calculated is reduced. The lattice structure in the case of stationary input is also presented View full abstract»

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  • Numerical stability properties of a QR-based fast least squares algorithm

    Page(s): 2096 - 2109
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    The numerical stability of a recent QR-based fast least-squares algorithm is established from a backward stability perspective. A stability domain approach applicable to any least-squares algorithm, constructed from the set of reachable states in exact arithmetic, is presented. The error propagation question is shown to be subordinate to a backward consistency constraint, which requires that the set of numerically reachable variables be contained within the stability domain associated to the algorithm. This leads to a conceptually lucid approach to the numerical stability question which frees the analysis of stationary assumptions on the filtered sequences and obviates the tedious linearization methods of previous approaches. Moreover, initialization phenomena and considerations related to poorly exciting inputs admit clear interpretations from this perspective. The algorithm under study is proved, in contrast to many fast algorithms, to be minimal View full abstract»

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  • Optimum weighted smoothing in finite data

    Page(s): 2265 - 2269
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    The authors consider a generalized smoothing problem and develop a procedure to obtain a set of optimum weights which gives minimum mean-squared error in the estimates of directions of arrival (DOAs) of signals in finite data when the signals are arbitrarily correlated. Using the optimum weights, they study the optimum tradeoff between the number of subarrays and the subarray size for a fixed total size of the array. The computation of optimum weights, however, requires full knowledge of the scenario. Since exact DOAs, powers, and correlations of signals are unknown a priori, a method for estimating these weights from the observed finite data is given. It is shown through empirical studies that the optimum weights can be approximated by Taylor weights, which serve as near-optimum weights. Simulation results are included to support the theoretical assertions View full abstract»

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  • Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain

    Page(s): 2110 - 2130
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    Convolution theorems for filter bank transformers are introduced. Both uniform and nonuniform decimation ratios are considered, and orthonormal as well as biorthonormal cases are addressed. All the theorems are such that the original convolution reduces to a sum of shorter, decoupled convolutions in the subbands. That is, there is no need to have cross convolution between subbands. For the orthonormal case, expressions for optimal bit allocation and the optimized coding gain are derived. The contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum. With one of the convolved sequences taken to be the unit pulse function,,e coding gain expressions reduce to those for traditional subband and transform coding. The filter-bank convolver has about the same computational complexity as a traditional convolver, if the analysis bank has small complexity compared to the convolution itself View full abstract»

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  • The achievable accuracy in estimating the instantaneous phase and frequency of a constant amplitude signal

    Page(s): 2216 - 2224
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    The approach is based on modeling the signal phase by a polynomial function of time on a finite interval. The phase polynomial is expressed as a linear combination of the Legendre basis polynomials. First, the Cramer-Rao bound (CRB) of the instantaneous phase and frequency of constant-amplitude polynomial-phase signals is derived. Then some properties of the CRBs are used to estimate the order of magnitude of the bounds. The analysis is extended to signals whose phase and frequency are continuous but not polynomial. The CRB can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood. The maximum-likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the CRB of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations View full abstract»

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  • Analysis of a sign algorithm with delayed data

    Page(s): 2253 - 2257
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    An adaptive filter whose weights are adapted using a sign algorithm with a delayed error signal is analyzed. For stationary environments it is proved that the excess average absolute estimation error is bounded for all values of the error signal delay and the algorithm step size. For the nonstationary case when the optimal filter weights are time varying, the optimum step size which minimizes the excess average absolute error is derived. It is shown that the optimum step size does not depend on the additive noise power. The analytical results are supported by computer simulations View full abstract»

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  • In the optimum design of the block adaptive FIR digital filter

    Page(s): 2131 - 2140
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    A general optimum block adaptive (GOBA) algorithm for adaptive FIR (finite impulse response) filtering is presented. In this algorithm, the correction terms for the filter coefficients in each block, instead of the convergence factors, are optimized in a least squares sense. There are no constraints on the block length L and the filter tap number N. It is shown that the GOBA algorithm is reduced to the normalized LMS algorithm when LN. The convergence of the GOBA algorithm can be assured if the correlation matrix of the input signal is positive definite. Computer simulations based on an efficient computing procedure confirm that the GOBA algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on L and N View full abstract»

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  • Quantification of the difference between detection and resolution thresholds for multiple closely spaced emitters

    Page(s): 2274 - 2277
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    The problem of estimating the parameters of multiple signals closely spaced in either space or frequency has been much researched because it is a difficult case for modern spectral analysis techniques. Based on empirical evidence, it has been noted by others that signal-to-noise ratio (SNR) detection thresholds typically are lower than resolution thresholds. That is, one can detect the occurrence of n closely spaced signals at SNRs lower than those at which one can resolve the signals and reliably estimate their parameters. The difference between detection and resolution thresholds is quantified for the direction-finding problem in which source locations are specified by a single angular coordinate (e.g., azimuth) View full abstract»

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  • A simple derivation of the constrained multiple parameter Cramer-Rao bound

    Page(s): 2247 - 2249
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    J.D. Gorman and A.O. Hero (1988) obtained a remarkable extension to the classical multiple parameter Cramer-Rao (CR) lower bound that accounts for deterministic nonlinear equality constraints on the parameters. The virtue of Gorman and Hero's result is that the constrained CR bound on all of the parameters is obtained by subtracting an easily computed nonnegative definite correction matrix from the unconstrained CR bound matrix. The author presents a new, simple derivation of the constrained CR bound and a new necessary condition for an estimator to satisfy the constrained CR bound with equality View full abstract»

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  • Scheduling of DSP programs onto multiprocessors for maximum throughput

    Page(s): 2225 - 2235
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    A flow graph scheduling algorithm that simultaneously considers pipelining, retiming, parallelism, and hierarchical node decomposition is presented. The ability to simultaneously consider the many types of concurrency allows the scheduler to find efficient multiprocessor solutions for a wide range of DSP applications. It has been implemented as part of a software environment for scheduling DSP programs onto fixed and configurable multiprocessor systems. The results on a set of benchmarks demonstrate that the algorithm achieves near ideal speedups even across programs with different types of concurrency View full abstract»

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  • Design of optimum signals for the simultaneous estimation of time delay and Doppler shift

    Page(s): 2141 - 2154
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    The problem of joint estimation of time delay and Doppler shift is considered from the point of view of the Wigner distribution of the signal. A very efficient method of obtaining the optimum signal with minimum estimation error based on the convexity of the design region is developed. Practical applications, however, require the signal to satisfy other constraints which present complications in acquiring the optimum signal. A design approach based on the method of simulated annealing is suggested to solve for the optimum signal under constraints. The performance of the signals so obtained is evaluated and compared with that of signals obtained by synthesis View full abstract»

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  • A stochastic gradient adaptive filter with gradient adaptive step size

    Page(s): 2075 - 2087
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    The step size of this adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error during each iteration. An approximate analysis of the performance of the adaptive filter when its inputs are zero mean, white, and Gaussian noise and the set of optimal coefficients are time varying according to a random-walk model is presented. The algorithm has very good convergence speed and low steady-state misadjustment. The tracking performance of these algorithms in nonstationary environments is relatively insensitive to the choice of the parameters of the adaptive filter and is very close to the best possible performance of the least mean square (LMS) algorithm for a large range of values of the step size of the adaptation algorithm. Several simulation examples demonstrating the good properties of the adaptive filters as well as verifying the analytical results are also presented View full abstract»

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  • Ambient noise statistics

    Page(s): 2249 - 2253
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    Signal processing algorithms optimized for Gaussian noise may degrade significantly in a non-Gaussian noise environment. Therefore it is important to characterize the noise accurately before including its structure in the formulation of algorithms. A generic distribution suitable for modeling non-Gaussian ambient noise in the kurtosis range 1.8⩽β2⩽4.2 is derived View full abstract»

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  • Observation noise and zero loci of the time series model

    Page(s): 2269 - 2273
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    The properties of zeros of time series models are examined in a linear stochastic system with white Gaussian observation noise. Each zero has a locus in the complex plane as the variance of observation noise changes from zero to infinity. An application of zero loci is presented for understanding the properties of the autoregressive model View full abstract»

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  • Modular VLSI architectures for computing the arithmetic Fourier transform

    Page(s): 2236 - 2246
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    Modular, area-efficient VLSI architectures for computing the arithmetic Fourier transform (AFT) are proposed. By suitable design of PEs and I/O sequencing, nonuniform data dependencies in the AFT computation which require nonequidistant inputs and assignment of Mobius function values are resolved. The proposed design employs 2N+1 PEs to compute 2N+1 Fourier coefficients. Each PE has an adder and a fixed amount of local storage, and one PE has a multiplier. I/O with the host is performed using a fixed number of channels. This results in simple PE organization, compared with those needed in known DFT/FFT architectures. The design achieves O(N) speedup. It uses significantly fewer PEs than designs in the literature and supports real-time applications by allowing continuous sequential input. It can be extended to achieve linear speedup in a fixed size array with 2p+1 PEs, 1⩽pN View full abstract»

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  • Gohberg-Semencul type formulas via embedding of Lyapunov equations [signal processing]

    Page(s): 2208 - 2215
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    The authors present a new way of deriving Gohberg-Semencul-type inversion formulas for Hermitian Toeplitz and quasi-Toeplitz matrices. The approach is based on a certain Σ-lossless embedding of Lyapunov equations. It has been shown that if a nonsingular matrix R has Toeplitz displacement inertia {p, q}, then R-1 does not have the same Toeplitz displacement inertia. However, a para-Hermitian conjugate of R-1 will have this property. It is also shown that the Gohberg-Semencul-type inversion formulas can be formed directly in terms of certain parameters of the embedding View full abstract»

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  • Wiener filter realization for target detection using group delay statistics

    Page(s): 2067 - 2074
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    Several techniques are demonstrated for Wiener filter realization based on group delay statistics. The theoretical analysis shows that an inverse relationship exists between the frequency-domain signal-to-noise ratio and the group delay moving standard deviation and/or group delay moving entropy. Therefore, an adaptive Wiener filter can be realized without a priori knowledge of the signal and noise spectra. Group delay statistics estimation algorithms are proposed and evaluated by simulation. Experimental data from ultrasonic flaw detection are presented to support the effectiveness of the techniques View full abstract»

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  • Two chi-square statistics for determining the orders p and q of an ARMA (p, q) process

    Page(s): 2165 - 2176
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    The θ, λ, and η functions have been previously proposed for use in choosing the autoregressive and moving-average orders of an ARMA (q, p) process visually. Two chi-square statistics associated with these three functions are presented and used here to determine the orders of an ARMA process statistically. It is shown that the two statistics are asymptotically equivalent to the Quenouille-Walker's goodness-of-fit test statistic, which is a Lagrange multiplier test statistic. Some numerical examples are presented to illustrate the usefulness of the two chi-square statistics as well as the three functions in ARMA modeling View full abstract»

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  • An adaptive ARMA four-line lattice filter for spectral estimation with frequency weighting

    Page(s): 2193 - 2207
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    A method for designing an adaptive four-line lattice filter which can perform frequency-weighting spectral estimation, which provides more accurate spectral estimation for some frequency bands than for others, is proposed. Using a suitable frequency-weighting function, denoted as an ARMA (autoregressive moving-average) model, an estimated spectrum is obtained by arbitrarily weighing some frequency bands more heavily than others. if the frequency-weighting function has the property of a low-pass filter, the spectrum of the reference model can be estimated accurately with a reduced ARMA order in the low-frequency band. Spectra of time-varying models can be estimated with an exponentially weighted sliding window, and the input signal of the reference model can be estimated by assumption. The order-update and the time-update recursive formulas and the frequency-weighting method for the filter are described. The algorithm is verified by experimental results View full abstract»

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  • Transient signal detection using prior information in the likelihood ratio test

    Page(s): 2177 - 2192
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    A uniform approach to the problem of detecting a deterministic transient signal of unknown waveshape in Gaussian noise that is applicable for a general class of signals is provided. It is assumed that the vector representation consists of a group of zero coefficients plus a group of unknown nonzero coefficients, starting at a certain index. Performance indices for a likelihood-ratio-test detector of such a generalized transient signal are derived for three cases: (a) both the starting index and the number of unknown nonzero signal coefficients are known; (b) only the number of unknown nonzero signal coefficients is known; and (c) neither of these is known. It is shown that the performance of detector (a) is always better than that of (b) and (c), and conditions under which the performance of detector (b) is better than that of (c) are derived. The theoretical results are demonstrated by considering signals of different assumed structures 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
Zhi-Quan (Tom) Luo
University of Minnesota