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Signal Processing, IEEE Transactions on

Issue 12 • Date Dec. 2002

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Displaying Results 1 - 24 of 24
  • Comments on discrete chirp-Fourier transform and its application to chirp rate estimation [with reply]

    Page(s): 3115 - 3116
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (214 KB)  

    This comment points out that the sample rate of the discrete chirp-Fourier transform (DCFT) proposed by Xia (see ibid., vol.48, p. 3122-33, 2000) is not sufficient to avoid severe "picket-fence" effect and causes some restrictions for its practical applications. By increasing the sample rate and modifying the DCFT definition, a new robust DCFT is proposed. Xia (see ibid., vol.50, no.12, p.3116, 2002) replies by first correcting an error on the analog-to-discrete parameter conversions of a chirp signal. Xia also add that when the chirp rate detection resolution is increased, it is more robust to the chirp rate error. On the other- hand, what is sacrificed by doing so is that the magnitudes of the sidelobes of the transform are increased, which may limit its capability of detecting chirps in a multicomponent or low SNR signal. Therefore, which DCFT needs to be used has to depend on the practical application. View full abstract»

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  • List of reviewers

    Page(s): 3117 - 3121
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    Freely Available from IEEE
  • Author index

    Page(s): 3125 - 3133
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    Freely Available from IEEE
  • Subject index

    Page(s): 3133 - 3164
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    Freely Available from IEEE
  • Optimal design and placement of pilot symbols for channel estimation

    Page(s): 3055 - 3069
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1134 KB) |  | HTML iconHTML  

    The problem of designing and placing pilot symbols for the estimation of frequency-selective random channels is considered. The channel is assumed to be a block-fading model with finite impulse response (FIR). For both single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels, under the assumption of independent and identical distributed channel taps, the Cramer-Rao bound (CRB) on the mean square error (MSE) of semi-blind channel estimators is derived and minimized with respect to pilot symbols and their placement. It is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet. The results also indicate that the optimal pilot placements are independent of channel probability distribution. For constant modulus symbols, we show that the quasi-periodic placement and its generalization in the multiuser case turn out to be optimal. We further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences. View full abstract»

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  • Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

    Page(s): 3018 - 3027
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (852 KB) |  | HTML iconHTML  

    Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signal-processing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion known as omnidirectional balancing is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalar-signal expansion. It is shown that the straightforward implementation of a vector wavelet transform, namely, the application of a scalar transform to each vector component independently, is a special case of an omnidirectionally balanced vector wavelet transform in which filter-coefficient matrices are constrained to be diagonal. Additionally, a family of symmetric-antisymmetric multiwavelets is designed according to the omnidirectional-balancing criterion. In empirical results for a vector-field compression system, it is observed that the performance of vector wavelet transforms derived from these omnidirectionally-balanced symmetric-antisymmetric multiwavelets is far superior to that of transforms implemented via other multiwavelets and can exceed that of diagonal transforms derived from popular scalar wavelets. View full abstract»

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  • Interpolated Mth-band filters for image size conversion

    Page(s): 3028 - 3035
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1207 KB) |  | HTML iconHTML  

    Image/video size conversion at variable rates requires that a large set of interpolation filters should be stored in a table. We present the interpolated Mth-band filters as the interpolation filters, which are obtained from the cubic spline interpolation of a prototype Mpth-band eigenfilter. The proposed filter can be calculated in real time, eliminating the need for a large on-chip memory. Scaled images using the proposed filters show superb image quality. View full abstract»

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  • Adaptive MMSE receiver for multirate CDMA systems

    Page(s): 3098 - 3106
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (661 KB) |  | HTML iconHTML  

    We consider the adaptive receiver for multirate code division multiple access (CDMA) systems under a fading channel environment. The main difficulty that arises in the use of the adaptive receiver for multirate CDMA systems is that the adaptation should resume after the rate change. Hence, the adaptive receiver may not provide a reasonable performance during the transient after the rate change. In order to overcome this difficulty, we investigate an approach that allows updating the weight vectors for all rates simultaneously. For example, in a dual-rate system, the weight vector for the lower rate (the higher rate) can be updated during the period of the higher rate (resp., the lower rate) to avoid the transient after the rate change. The resulting adaptive receiver has multiple parallel adaptive filters. The adaptive filters for each rate can carry out the adaptation simultaneously, regardless of what the current rate is. As a result, the performance is not degraded by the rate change. View full abstract»

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  • DS/CDMA signature sequences based on PR-QMF banks

    Page(s): 3043 - 3054
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1067 KB) |  | HTML iconHTML  

    In this paper, we propose two classes of multivalued signature sequences for direct sequence code division multiple access (DS/CDMA) systems. The proposed classes are obtained from the coefficients of the subbands of perfect reconstruction quadrature mirror filterbanks (PR-QMF). The first and second classes are derived from the tree and lattice structure PR-QMF banks, respectively, and they both have perfect correlation properties for synchronous DS/CDMA systems. The second class, in addition, has generally better correlation properties than other well-known sequences in asynchronous DS/CDMA systems. Some numerical results for the performance of the asynchronous DS/CDMA systems with several sequences, including the second class of sequences, are obtained. View full abstract»

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  • Spectrogram segmentation by means of statistical features for non-stationary signal interpretation

    Page(s): 2915 - 2925
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2246 KB) |  | HTML iconHTML  

    Time-frequency representations (TFRs) are suitable tools for nonstationary signal analysis, but their reading is not straightforward for a signal interpretation task. This paper investigates the use of TFR statistical properties for classification or recognition purposes, focusing on a particular TFR: the spectrogram. From the properties of a stationary process periodogram, we derive the properties of a nonstationary process spectrogram. It leads to transform the TFR to a local statistical features space from which we propose a method of segmentation. We illustrate our matter with first- and second-order statistics and identify the information they, respectively, provide. The segmentation is operated by a region growing algorithm, which does not require any prior knowledge on the nonstationary signal. The result is an automatic extraction of informative subsets from the TFR, which is relevant for the signal understanding. Examples are presented concerning synthetic and real signals. View full abstract»

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  • Unsupervised frequency tracking beyond the Nyquist frequency using Markov chains

    Page(s): 2905 - 2914
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (627 KB)  

    This paper deals with the estimation of a sequence of frequencies from a corresponding sequence of signals. This problem arises in fields such as Doppler imaging, where its specificity is twofold. First, only short noisy data records are available (typically four sample long), and experimental constraints may cause spectral aliasing so that measurements provide unreliable, ambiguous information. Second, the frequency sequence is smooth. Here, this information is accounted for by a Markov model, and application of the Bayes rule yields the a posteriori density. The maximum a posteriori is computed by a combination of Viterbi and descent procedures. One of the major features of the method is that it is entirely unsupervised. Adjusting the hyperparameters that balance data-based and prior-based information is done automatically by maximum likelihood (ML) using an expectation-maximization (EM)-based gradient algorithm. We compared the proposed estimate to a reference one and found that it performed better: variance was greatly reduced, and tracking was correct, even beyond the Nyquist frequency. View full abstract»

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  • A fast convergence algorithm for sparse-tap adaptive FIR filters identifying an unknown number of dispersive regions

    Page(s): 3008 - 3017
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (668 KB) |  | HTML iconHTML  

    This paper proposes a fast convergence algorithm for sparse-tap adaptive finite impulse response (FIR) filters to identify an unknown number of multiple dispersive regions. Coefficient values and tap-positions of the adaptive filter are simultaneously controlled. A constrained region for new-tap positions is selected from equisize subgroups of all possible tap-positions, and it hops from one subgroup to another to cover multiple dispersive regions. The hopping order and the stay time for each subgroup are adaptively determined based on the absolute coefficient values. Simulation results with colored signals show that the proposed algorithm saves more than 80% in the convergence time over the full-tap NLMS and 50% over the STWQ. Tracking capability of the proposed algorithm exhibits its superior characteristics. These characteristics are confirmed by hardware evaluations with a telephone network simulator. View full abstract»

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  • Reduced-order H filtering for stochastic systems

    Page(s): 2998 - 3007
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (717 KB) |  | HTML iconHTML  

    This paper deals with the reduced-order H filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach. View full abstract»

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  • Linear time-variant transformations of generalized almost-cyclostationary signals .I. Theory and method

    Page(s): 2947 - 2961
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (922 KB) |  | HTML iconHTML  

    The problem of linear time-variant filtering is addressed in the fraction-of-time (FOT) probability framework. The adopted approach, which is an alternative to the classical stochastic one, provides a statistical characterization of the system in terms of time averages of functions of time rather than ensemble averages of stochastic processes. Thus, it is particularly useful when stochastic systems transform ergodic input signals into nonergodic output signals, as it happens with several channel models encountered in practice. The analysis is carried out with reference to the wide class of the generalized almost-cyclostationary signals, which includes, as,a special case, the class of almost-cyclostationary signals. In this paper, systems are classified as deterministic or random in the FOT probability framework. Moreover, the new concept of expectation in the FOT probability framework of the impulse-response function of a system is introduced. For the linear time-variant systems, the higher order system characterization in the time domain is provided in terms of the system temporal moment function, which is the kernel of the operator that transforms the additive sinewave components contained in the input lag product into the additive sinewave components contained in the output lag product. Moreover, the higher order characterization in the frequency domain is also provided, and input/output relationships are derived in terms of temporal and spectral moment and cumulant functions. Developments and examples of application of the theory introduced here are presented in part II of this two-part paper. View full abstract»

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  • L2-sensitivity analysis and minimization of 2-D separable-denominator state-space digital filters

    Page(s): 3107 - 3114
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (783 KB) |  | HTML iconHTML  

    For two-dimensional (2-D) state-space digital filters that are separable in the denominator, the coefficient sensitivity is analyzed by using a pure L2-norm, and then, the problem of minimizing the L2-sensitivity is considered. First, a novel expression is developed in closed form for the evaluation of the L2-sensitivity. Next, an iterative procedure is presented for synthesizing the optimal filter structures that minimize the L2-sensitivity. Finally, a numerical example is given to illustrate the utility of the proposed technique. View full abstract»

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  • Statistical performance analysis of the algebraic constant modulus algorithm

    Page(s): 3083 - 3097
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1050 KB)  

    This paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm (ACMA) method for blindly separating constant modulus sources. This can be used to predict the signal-to-interference plus noise ratio (SINR) performance of these beamformers, as well as their deviation from the (nonblind) Wiener receivers to which they asymptotically converge. The analysis is based on viewing ACMA as a subspace fitting optimization, where the subspace is spanned by the eigenvectors of a fourth-order covariance matrix. The theoretical performance is illustrated by numerical simulations and shows a good match. View full abstract»

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  • Maximum-SNR spatial-temporal formatting designs for MIMO channels

    Page(s): 3036 - 3042
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (467 KB) |  | HTML iconHTML  

    We consider a communication scenario involving an m × n multiple input multiple output (MIMO) flat fading channel whose input is a symbol stream multiplied prior to transmission by an n × n spatial-temporal formatting matrix X and whose output is fed into an m × n linear combiner Z. We show how to choose the matrices X and Z to maximize the signal-to-noise ratio (SNR) of the linear combiner output data that are used for detection, under the total power constraint (TPC), the elemental power constraint (EPC), or the total and elemental power constraint (TEPC). The TEPC design (considered here for the first time) is shown to include the TPC and EPC designs (previously considered by the authors) as special cases and, hence, to provide a theoretically and practically interesting unifying framework. We make use of this framework to discuss various tradeoffs of the three space-time formatting designs considered, such as transmission rate and requirements for channel state information at the transmission side. Additionally, we show that the EPC design, which is the only one of the aforementioned designs that does not require channel information at the transmission side, is also the maximum SNR design in the worst channel case under a TPC. View full abstract»

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  • Linear prediction error method for blind identification of periodically time-varying channels

    Page(s): 3070 - 3082
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (920 KB) |  | HTML iconHTML  

    Blind channel estimation for single-input multiple-output (SIMO) periodically time-varying channels is considered using only the second-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). The linear prediction error method for blind identification of time-invariant channels is extended to time-varying channels represented by a CE-BEM. Sufficient conditions for identifiability are investigated. The cyclostationary nature of the received signal is exploited to consistently estimate the time-varying correlation function of the data from a single observation record. The proposed method requires the knowledge of the active basis functions but not the channel length (an upper bound suffices). Several existing methods require precise knowledge of the channel length. Equalization of the time-varying channel, given the estimated channel, is investigated. Computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches. View full abstract»

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  • Particle filters for tracking an unknown number of sources

    Page(s): 2926 - 2937
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (775 KB) |  | HTML iconHTML  

    This paper addresses the application of sequential importance sampling (SIS) schemes to tracking directions of arrival (DOAs) of an unknown number of sources, using a passive array of sensors. This proposed technique has significant advantages in this application, including the ability to detect a changing number of signals at arbitrary times throughout the observation period and that the requirement for quasistationarity over a limited interval may be relaxed. We propose the use of a reversible jump Monte Carlo Markov chain (RJMCMC) step to enhance the statistical diversity of the particles. This step also enables us to introduce two novel moves that significantly enhance the performance of the algorithm when the DOA tracks cross. The superior performance of the method is demonstrated by examples of application of the particle filter to sequential tracking of the DOAs of an unknown and nonstationary number of sources and to a scenario where the targets cross. Our results are compared with the PASTd method. View full abstract»

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  • Blind adaptation of zero forcing projections and oblique pseudo-inverses for subspace detection and estimation when interference dominates noise

    Page(s): 2938 - 2946
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (606 KB) |  | HTML iconHTML  

    In much of modern radar, sonar, and wireless communication, it seems more reasonable to model "measurement noise" as subspace interference-plus-broadband noise than as colored noise. This observation leads naturally to a variety of detection and estimation problems in the linear statistical model. To solve these problems, one requires oblique pseudo-inverses, oblique projections, and zero-forcing orthogonal projections. The problem is that these operators depend on knowledge of signal and interference subspaces, and this information is often not at hand. More typically, the signal subspace is known, but the interference subspace is unknown. We prove a theorem that allows these operators to be estimated directly from experimental data, without knowledge of the interference subspace. As a byproduct, the theorem shows how signal subspace covariance may be estimated. When the strict identities of the theorem are approximated, then the detectors, estimators, and beamformers of this paper take on the form of adaptive subspace estimators, detectors, and Capon beamformers, all of which are reduced in rank. The fundamental operator turns out to be a certain reduced-rank Wiener filter, which we clarify in the course of our derivations. The results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation. They may be applied to detection and estimation in radar, sonar, and hyperspectral imaging and to data decoding in multiuser communication receivers. View full abstract»

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  • Double-dimensional distributions: another approach to "quartic" distributions

    Page(s): 2987 - 2997
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1113 KB) |  | HTML iconHTML  

    We present the definitions of double-dimensional time-frequency distributions, especially the Wigner distribution (WD) of the WD and the ambiguity function of the ambiguity function. The first coincides with the notion of the local ambiguity function presented in the papers of O'Neill and Williams (1999), and O'Neill and Flandrin (2000) and are classified as the "quartic time-frequency distribution." The second turned out to be the Fourier transform of the quartic ambiguous ambiguity function. Using the above notions, the double dimensional extension of the Cohen's class distributions is defined and illustrated by examples. View full abstract»

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  • Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets

    Page(s): 2976 - 2986
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (689 KB) |  | HTML iconHTML  

    It was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet tree to the log multitaper spectrum ordinates, thresholding the empirical wavelet packet coefficients, and then inverting the transform. For a small number of tapers, suitable transforms/partitions for the logarithm of the multitaper spectrum estimator are derived using a method matched to statistical thresholding properties. The partitions thus derived starting from different stationary time series are all similar and easily derived, and any differences between the wavelet packet and discrete wavelet transform (DWT) approaches are minimal. For a larger number of tapers, where the chosen parameters satisfy the conditions of a proven theorem, the simple DWT again emerges as appropriate. Hence, using our approach to thresholding and the method of partitioning, we conclude that the DWT approach is a very adequate wavelet-based approach and that the use of wavelet packets is unnecessary. View full abstract»

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  • Linear time-variant transformations of generalized almost-cyclostationary signals.II. Development and applications

    Page(s): 2962 - 2975
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1627 KB) |  | HTML iconHTML  

    For pt. I see ibid., vol.50, no.12, p.2947-61 (2000). In Part I, the problem of the linear time-variant (LTV) filtering is addressed in the fraction-of-time (FOT) probability framework. The adopted approach, which is an alternative to the classical stochastic one, provides a statistical characterization of the systems in terms of functions that can be estimated by a single time-series. The analysis is carried out with reference to the wide class of the generalized almost-cyclostationary (GACS) signals, which includes, as a special case, the class of the almost-cyclostationary (ACS) signals. Examples of applications and developments of the theory introduced in Part I are presented here in Part II. Specifically, the countability of the set of the output cycle frequencies is studied with reference to linear time-variant systems for both ACS and GACS not containing any ACS component input signals. Thus, the linear almost-periodically time-variant filtering and the product modulation are considered in detail. Moreover, several Doppler channel models are analyzed. In all these examples, it is shown that the FOT probability approach allows one to characterize the system and its output in terms of statistical functions that can be measured by a single time-series. Furthermore, the usefulness of considering the linear filtering problem within the class of the GACS signals is clarified, and several pitfalls arising from continuing to adopt for the observed time-series the ACS model when an increase in the data-record length makes the GACS model more appropriate are pointed out. View full abstract»

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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