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Signal Processing, IEEE Transactions on

Issue 2 • Date Feb 1996

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Displaying Results 1 - 25 of 31
  • A VLSI-oriented parallel FFT algorithm

    Page(s): 445 - 448
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (264 KB)  

    Usually, parallel pipelined FFT processors are used to compute long FFTs due to high processing rate and easy implementation. The efficient VLSI implementation of each FFT processor at the pipelines is a critical problem to be considered. We propose a new parallel FFT algorithm that removes the complex multiplier between the two pipeline stages. The new algorithm also simplifies the address generation of twiddle factors and reduces the number of twiddle factors to a minimum. With the new algorithm, each FFT processor at the pipelines can be integrated easily onto a single chip View full abstract»

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  • Algorithm for mapping all-pole system parameters to wave-digital filter multiplier coefficients

    Page(s): 421 - 423
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB)  

    Based on the technique of wave-chain matrices and the digital equivalent of canonic polynomials, a recursive algorithm is derived to map the parameters of an all-pole system to the multiplier coefficients of a wave-digital filter consisting of two-port adaptor cascades. The algorithm will be useful in all-pole system modeling which adopts such a filter as a final form of realization View full abstract»

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  • On the uniform ADC bit precision and clip level computation for a Gaussian signal

    Page(s): 434 - 438
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    The problem of computing the required bit precision of analog-to-digital converters is revisited with emphasis on Gaussian signals. We present two methods of analysis. The first method fixes the probability of overload and sets the dynamic range of the quantizer to accommodate the worst-case signal-to-quantization noise ratio (SQNR). The second method sets the clipping level of the quantizer to meet a desired overload distortion level, using knowledge of the input probability density function. New closed-form expressions relating the distortion-minimizing clip level of the uniform quantizer and the input bit rate are derived and shown to give remarkably close results to the optimum ones obtained using numerical iterative procedures devised elsewhere View full abstract»

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  • Robust discrete-time minimum-variance filtering

    Page(s): 181 - 189
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (732 KB)  

    The bounded-variance filtered estimation of the state of an uncertain, linear, discrete-time system, with an unknown norm-bounded parameter matrix, is considered. An upper bound on the variance of the estimation error is found for all admissible systems, and estimators are derived that minimize the latter bound. We treat the finite-horizon, time-varying case and the infinite-time case, where the nominal system model is time invariant. In the special stationary case, where it is known that the uncertain system is time invariant, we provide a robust filter for all uncertainties that still keep the system asymptotically stable View full abstract»

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  • A broadband beam former with pole-zero unconstrained jammer rejection in linear arrays

    Page(s): 438 - 441
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (364 KB)  

    A new architecture is presented for broadband cancellation of jammer signals in a linear equally spaced array of sensors, where the jammers can be coherent or noncoherent with the target signal. Unique features lie in the ability of the preprocessor to cancel all poles in the ideal filters and simplify the remaining zeros. As a result, the adaptive process for jammer cancellation need only estimate these zeros with short-length digital filters and any generally available adaptive algorithm. The adaptive process is unconstrained and can use any least squares method including those with a lattice structure. The number of filters is equal to the maximum number of jammers and their length is unaffected by the number of array elements. The required lengths of the adapted filters are functions only of the jammer directions. The target signal may be weak or strong in comparison to the jammers, and there are no known deficiencies such as signal cancellation or look-direction bias View full abstract»

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  • H optimality of the LMS algorithm

    Page(s): 267 - 280
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    We show that the celebrated least-mean squares (LMS) adaptive algorithm is H optimal. The LMS algorithm has been long regarded as an approximate solution to either a stochastic or a deterministic least-squares problem, and it essentially amounts to updating the weight vector estimates along the direction of the instantaneous gradient of a quadratic cost function. We show that the LMS can be regarded as the exact solution to a minimization problem in its own right. Namely, we establish that it is a minimax filter: it minimizes the maximum energy gain from the disturbances to the predicted errors, whereas the closely related so-called normalized LMS algorithm minimizes the maximum energy gain from the disturbances to the filtered errors. Moreover, since these algorithms are central H filters, they minimize a certain exponential cost function and are thus also risk-sensitive optimal. We discuss the various implications of these results and show how they provide theoretical justification for the widely observed excellent robustness properties of the LMS filter View full abstract»

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  • Derived PDF of maximum likelihood signal estimator which employs an estimated noise covariance

    Page(s): 305 - 315
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1008 KB)  

    A probability density function (PDF) for the maximum likelihood (ML) signal vector estimator is derived when the estimator relies on a noise sample covariance matrix (SCM) for evaluation. By using a complex Wishart probabilistic model for the distribution of the SCM, it is shown that the PDF of the adaptive ML (AML) signal estimator (alias the SCM based minimum variance distortionless response (MVDR) beamformer output and, more generally, the SCM based linearly constrained minimum variance (LCMV) beamformer output) is, in general, the confluent hypergeometric function of a complex matrix argument known as Kummer's function. The AML signal estimator remains unbiased but only asymptotically efficient; moreover, the AML signal estimator converges in distribution to the ML signal estimator (known noise covariance). When the sample size of the estimated noise covariance matrix is fixed, it is demonstrated that there exists a dynamic tradeoff between signal-to-noise ratio (SNR) and noise adaptivity as the dimensionality of the array data (number of adaptive degrees of freedom) is varied, suggesting the existence of an optimal array data dimension that will yield the best performance View full abstract»

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  • Maximum likelihood estimation for array processing in colored noise

    Page(s): 169 - 180
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    Direction of arrival estimation of multiple sources, using a uniform linear array, in noise with unknown covariance is considered. The noise is modeled as a spatial autoregressive process with unknown parameters. Both stochastic and deterministic signal models are considered. For the random signal case, an approximate maximum likelihood estimator of the signal and noise parameters is derived. It requires numerical maximization of a compressed likelihood function over the unknown arrival angles. Analytical expressions for the MLEs of the signal covariance and the AR parameters are given. Similar results for the case of deterministic signals are also presented View full abstract»

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  • Efficient calculation of finite Gabor transforms

    Page(s): 190 - 200
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    The Gabor transform may be viewed as a collection of localized Fourier transforms and as such is useful for analysis of nonstationary signals and images. We present a new approach to analyzing the Gabor transform and use it to study the various critically sampled discretizations that form the infinite-discrete, periodic finite-discrete, and nonperiodic finite-discrete versions of the transform. In particular, we distinguish between the analysis and synthesis forms of the transform, and introduce an intermediate operation that decomposes both forms into collections of independent Toeplitz operators. In the continuous, the infinite-discrete, and the periodic finite-discrete cases, this decomposition allows us to show that, for appropriate windows, the analysis and synthesis transforms are inverses of each other. In the nonperiodic finite-discrete case this relation no longer holds, but we are still able to use the decomposition and results on Toeplitz matrices to show that both the transform and the inverse transform of P discrete samples are computable in O(P log P) operations (after a setup cost of O(Plog2P)). Furthermore, we use the decomposition to study in detail the differences between the periodic and nonperiodic versions of the transform and to compare their conditioning View full abstract»

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  • Spherical trigonometry, Yule's PARCOR identity, and FRLS fully normalized lattice

    Page(s): 427 - 430
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    Yule's PARCOR identity is recognized as the cosine law of spherical trigonometry. The six PARCORs propagated by the fully normalized FRLS lattice filter are the cosines of the six elements of a spherical triangle, and this lattice algorithm is one solution to a spherical triangle problem that arises naturally in navigation and astronomy. Exploiting this new geometric interpretation yields unnoticed (and potentially useful) recursions among FRLS quantities View full abstract»

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  • Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT

    Page(s): 316 - 328
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1236 KB)  

    The UCA-ESPRIT is a closed-form algorithm developed for use in conjunction with a uniform circular array (UCA) that provides automatically paired source azimuth and elevation angle estimates. The 2-D unitary ESPRIT is presented as an algorithm providing the same capabilities for a uniform rectangular array (URA). In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two major array axes. The 2-D unitary ESPRIT offers a number of advantages over other proposed ESPRIT based closed-form 2-D angle estimation techniques. First, except for the final eigenvalue decomposition of a dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to efficient beamspace implementations that are presented. Third, it is applicable to array configurations that do not exhibit identical subarrays, e.g., two orthogonal linear arrays. Finally, the 2-D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common. Simulation results are presented verifying the efficacy of the method View full abstract»

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  • Optimal filter banks for signal reconstruction from noisy subband components

    Page(s): 212 - 224
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    Conventional design techniques for analysis and synthesis filters in subband processing applications guarantee perfect reconstruction of the original signal from its subband components. The resulting filters, however, lose their optimality when additive noise due, for example, to signal quantization, disturbs the subband sequences. We propose filter design techniques that minimize the reconstruction mean squared error (MSE) taking into account the second order statistics of signals and noise in the case of either stochastic or deterministic signals. A novel recursive, pseudo-adaptive algorithm is proposed for efficient design of these filters. Analysis and derivations are extended to 2-D signals and filters using powerful Kronecker product notation. A prototype application of the proposed ideas in subband coding is presented. Simulations illustrate the superior performance of the proposed filter banks versus conventional perfect reconstruction filters in the presence of additive subband noise View full abstract»

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  • Nonparametric waveform estimation using filter banks

    Page(s): 239 - 247
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (804 KB)  

    This paper presents a nonparametric method for estimating waveforms of event-related signals embedded in additive noise. The signals have transient character with varying shapes and arrival times. The estimation method is based on a series expansion of the signal by a set of basis functions. Using a template that contains a priori information, two sets of basis functions are designed by means of one uniform and one nonuniform bandpass filter bank. Then, signal-dependent basis functions are obtained. When no a priori information about the signal is available, signal-independent basis functions are constituted by the impulse responses of the subfilters. Delayed copies are created for each basis function with which time jitter in arrival time of the signal can be handled. The method gives a robust estimate of the waveform of transient signals having unknown waveforms and arrival times since no model assumptions are needed. One application is discussed through examples and compared with the estimate, which is obtained by the Karhunen-Loeve expansion View full abstract»

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  • ARMA lattice identification: a new hereditary algorithm

    Page(s): 360 - 370
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    This paper derives an identification solution of the ARMA-type optimal linear predictor as a time varying-lattice of arbitrarily fixed dimension for a process whose output signal only is known. The projection technique introduced here leads to a hereditary algorithm that is the adaptive extension to raw data of the authors' previous results on lattice realization from given autocorrelation functions. It produces a minimum-phase linear model of the signal whose nth order “whiteness” of the associated innovation has the following restricted meaning: orthogonality to an n-dimensional subspace memory of the past in a suitable Hilbert sequence space. The L2 metric of that sequence space leads to a least-squares identification algorithm that possesses a “certainty equivalence principle” with respect to the corresponding realization algorithm (i.e., sample correlation products replace true correlation terms). Due to the detailed state-space time-varying computations, this is possible here while avoiding the well-known “side errors” from missing correlation products that usually occur in a blunt replacement of the output autocorrelation by averaged sample products. Application examples show the superiority of the hereditary algorithm over classical recursive and nonrecursive algorithms in terms of accuracy, adaptivity, and order reduction capabilities View full abstract»

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  • Direction of arrival estimation using parametric signal models

    Page(s): 339 - 350
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    We consider the problem of estimating the directions-of-arrival (DOAs) of narrowband sources with known center frequency. The paper evaluates the potential improvement in estimation accuracy by using spatial-temporal processing for signals obeying a deterministic parametric model. One would expect that prior information about the temporal structure of the signals will yield some gain in performance. By deriving the Cramer-Rao bound (CRB) on the DOA estimates, we quantify this gain and identify the cases for which the gain is significant. We show that for the single-source case, spatial-temporal processing does not yield any gain in performance relative to conventional spatial processing. For multiple noncoherent signals, incorporating temporal processing can achieve the single-source performance, yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array. However, spatial-temporal processing cannot yield any gain in performance for multiple coherent signals View full abstract»

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  • A CORDIC-based unified systolic architecture for sliding window applications of discrete transforms

    Page(s): 441 - 444
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    A CORDIC-based, unified systolic architecture for sliding window applications of the discrete Fourier transform (DFT), the discrete Hartley transform (DHT), the discrete cosine transform (DCT), and the discrete sine transform (DST) is proposed. Compared to earlier works, the proposed scheme offers significant reduction in hardware, particularly for DHT. For an N-point DHT, it requires only [N/2]+1 processing elements, each consisting of one CORDIC processor and two adders View full abstract»

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  • Mitigation of wing flexure induced errors for airborne direction-finding applications

    Page(s): 296 - 304
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (988 KB)  

    Errors in array calibration are the dominant error source for direction finding (DF) in airborne platforms. This problem arises since wings in large surveillance aircraft exhibit significant flexure, and their actual instantaneous positions during array calibration and operational flight is likely to be quite different. Scattering from time-varying wing structures onto the belly mounted antennas therefore causes the array responses to deviate from the array calibration and gives rise to DF errors. We present a simple model for array manifold perturbations due to wing flexure that captures their effect. The model is physically motivated and has been validated using experiments on a scale-model aircraft in an anechoic chamber. Our model can be exploited to derive new versions of the classical DF estimation schemes including weighted subspace fitting (WSF) View full abstract»

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  • Exploiting Walsh-based attributes to stereo vision

    Page(s): 409 - 420
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    This paper presents a new stereo feature matching method that extracts the disparity measure for the recovery of depth information in 2-D stereo images. In this method, a stereo pair of images are transformed row for row into strings carrying spatially varying Walsh coefficients as attributes. The significance of the information carried by the Walsh coefficients is expressed mathematically and through experimental evaluations. The choice of the Walsh coefficients in contrast to other orthogonal transform coefficients is a direct result of their computational simplicity and their interpretative meaning in terms of the information contained in the spatial domain. The string-to-string matching technique used to bring the two strings into correspondence integrates, into a unified process, both the feature detection and the feature matching processes. The uniqueness and the ordering constraints are explicitly integrated into this string-to-string matching technique. Both the issues of Gaussian filtering and the importance of enforcing the epipolar line constraint are addressed in view of the application of the proposed method. Experimental results are given and assessed in terms of both the accuracy in stereo matching and the ensuing computational requirements View full abstract»

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  • Efficient mixed-spectrum estimation with applications to target feature extraction

    Page(s): 281 - 295
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    We present a decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both 1-D and 2-D data sequences corrupted by autoregressive (AR) noise. In the first step of the DPE algorithm, we use a relaxation (RELAX) algorithm that requires simple fast Fourier transforms (FFTs) to obtain the estimates of the sinusoidal parameters. We describe how the RELAX algorithm may be used to extract radar target features from both 1-D and 2-D data sequences. In the second step of the DPE algorithm, a linear least-squares approach is used to estimate the AR noise parameters. The DPE algorithm is both conceptually and computationally simple. The algorithm not only provides excellent estimation performance under the model assumptions, in which case the estimates obtained with the DPE algorithm are asymptotically statistically efficient, but is also robust to mismodeling errors View full abstract»

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  • Complex fuzzy adaptive filter with LMS algorithm

    Page(s): 424 - 427
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (340 KB)  

    A fuzzy adaptive filter is constructed from a set of fuzzy IF-THEN rules that change adaptively to minimize some criterion function as new information becomes available. This paper generalizes the fuzzy adaptive filter based on least mean squares (LMS) to include complex parameters and complex signals. The fuzzy filter as adaptive equalizer is applied to quadrature amplitude modulation (QAM) digital communication with linear complex channel characteristics View full abstract»

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  • Eigenvalues of (↓2)H and convergence of the cascade algorithm

    Page(s): 233 - 238
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    This paper is about the eigenvalues and eigenvectors of (↓2)H. The ordinary FIR filter H is a convolution with a vector h=(h(O),...,h(N)), which is the impulse response. The operator (↓2) downsamples the output y=h*x, keeping the even-numbered components y(2n). Where H is represented by a constant-diagonal matrix, this is a Toeplitz matrix with h(k) on its kth diagonal, the odd-numbered rows are removed in (↓2)H. The result is a double shift between rows, yielding a block Toeplitz matrix with 1×2 blocks. Iteration of the filter is governed by the eigenvalues. If the transfer function H(z)=Σh(k)z-k has a zero of order p at z=-1, corresponding to ω=π, then (↓2)H has p special eigenvalues ½,¼...,(½)p. We show how each additional “zero at π” divides all eigenvalues by 2 and creates a new eigenvector for λ=½. This eigenvector solves the dilation equation φ(t)=2Σh(k)φ(2t-k) at the integers t=n. The left eigenvectors show how 1,t,...,tp-1 can be produced as combinations of φ(t-k). The dilation equation is solved by the cascade algorithm, which is an infinite iteration of M=(↓2)2H. Convergence in L2 is governed by the eigenvalues of T=(↓2)2HHT corresponding to the response 2H(z)H(z-1 ). We find a simple proof of the necessary and sufficient condition for convergence View full abstract»

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  • Signal modeling and detection using cone classes

    Page(s): 329 - 338
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    A new signal model-the cone classes-is presented. These models include classical models such as subspaces but are more general and potentially more useful than some existing signal models. Examples of cone classes include time-frequency concentrated classes and subspaces with bounded mismatch. The maximum likelihood detector for a cone class of signals in the presence of Gaussian noise is derived, and a simple algorithm is suggested as a possible detector implementation. The detector is examined in the specific case of subspaces with bounded mismatch. It is shown that there are conditions under which this detector has a higher detection probability for fixed false alarm than that of a comparable subspace detector and energy detector View full abstract»

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  • A quadratically convergent algorithm for convex-set constrained signal recovery

    Page(s): 248 - 266
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    This paper addresses the problem of recovering a signal that is constrained to lie in a convex set, from linear measurements. The current standard is the alternating projections paradigm (POCS), which has only first-order convergence in general. We present a quadratically convergent iterative algorithm (Newton algorithm) for signal recovery from linear measurements and convex-set constraints. A new result on the existence and construction of the derivative of the projection operator onto a convex set is obtained, which is used in the Newton algorithm. An interesting feature of the new algorithm is that each iteration requires the solution of a simpler subspace-constrained reconstruction problem. A computation- and memory-efficient version of the algorithm is also obtained by using the conjugate-gradient algorithm within each Newton iteration to avoid matrix inversion and storage. From a computational point of view, the computation per iteration of this algorithm is similar to the computation per iteration of the standard alternating projections algorithm. The faster rate of convergence (compared to alternating projections) enables us to obtain a high-resolution reconstruction with fewer computations. The algorithm is thus well suited for large-scale problems that typically arise in image recovery applications. The algorithm is demonstrated in several applications View full abstract»

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  • Cycle-static dataflow

    Page(s): 397 - 408
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1196 KB)  

    We present cycle-static dataflow (CSDF), which is a new model for the specification and implementation of digital signal processing algorithms. The CSDF paradigm is an extension of synchronous dataflow that still allows for static scheduling and, thus, a very efficient implementation of an application. In comparison with synchronous dataflow, it is more versatile because it also supports algorithms with a cyclically changing, but predefined, behavior. Our examples show that this capability results in a higher degree of parallelism and, hence, a higher throughput, shorter delays, and less buffer memory. Moreover, they indicate that CSDF is essential for modelling prescheduled components, like application-specific integrated circuits. Besides introducing the CSDF paradigm, we also derive necessary and sufficient conditions for the schedulability of a CSDF graph. We present and compare two methods for checking the liveness of a graph. The first one checks the liveness of loops, and the second one constructs a single-processor schedule for one iteration of the graph. Once the schedulability is tested, a makespan optimal schedule on a multiprocessor can be constructed. We also introduce the heuristic scheduling method of our graphical rapid prototyping environment (GRAPE) View full abstract»

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  • An extended Kalman filter frequency tracker for high-noise environments

    Page(s): 431 - 434
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    The problem of constructing a frequency tracker for weak, narrowband signals with slowly varying frequency is considered. An extended Kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal-to-noise ratios 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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Meet Our Editors

Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota