Browsing by Author "Sayeed, Akbar M."
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Item Blind Quadratic and Time Frequency Based Detectors from Training Data(1995-01-20) Jones, Douglas L.; Sayeed, Akbar M.; Digital Signal Processing (http://dsp.rice.edu/)Time-frequency based methods, particularly quadratic (Cohen's-class) representations, are often considered for detection in applications ranging from sonar to machine monitoring. We propose a method of obtaining near-optimal quadratic detectors directly from training data using Fisher's optimal linear discriminant to design a quadratic detector. This detector is optimal in terms of Fisher's scatter criterion as applied to the quadratic outer product of the data vector, and in early simulations appears to closely approximate the true optimal quadratic detector. By relating this quadratic detector to an equivalent operation on the Wigner distribution of a signal, we derive near-optimal time-frequency detectors. A simple example demonstrates the excellent performance of the method.Item Unknown A Canonical Covariance Based Method for Generalized Joint Signal Representations(1996-04-20) Jones, Douglas L.; Sayeed, Akbar M.; Digital Signal Processing (http://dsp.rice.edu/)Generalized joint signal representations extend the scope of joint time-frequency representations to a richer class of nonstationary signals. Cohen's marginal-based generalized approach is canonical from a distributional viewpoint, whereas, in some other applications, for example, in a signal detection framework, a covariance-based formulation is needed and/or more attractive. In this note, we present a canonical covariance-based recipe for generating generalized joint signal representations. The method is highlighted by its simple characterization and interpretation, and naturally extends the concept of the corresponding linear representations.Item Unknown Data Driven Signal Detection and Classification(1997-01-20) Sayeed, Akbar M.; Digital Signal Processing (http://dsp.rice.edu/)In many practical detection and classification problems, the signals of interest exhibit some uncertain nuisance parameters, such as the unknown delay and Doppler in radar. For optimal performance, the form of such parameters must be known and exploited as is done in the generalized likelihood ratio test (GLRT). In practice, the statistics required for designing the GLRT processors are not available a priori and must be estimated from limited training data. Such design is virtually impossible in general due to two major difficulties: identifying the appropriate nuisance parameters, and estimating the corresponding GLRT statistics. We address this problem by using recent results that relate joint signal representations (JSRs), such as time-frequency and time-scale representations, to quadratic GLRT processors for a wide variety of nuisance parameters. We propose a general data-driven framework that: 1) identifies the appropriate nuisance parameters from an arbitrarily chosen finite set, and 2) estimates the second-order statistics that characterize the corresponding JSR-based GLRT processors.Item Unknown Design of Training Data Based Quadratic Detectors with Application to Mechanical Systems(1996-01-20) Rizzoni, Giorgio; Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Reliable detection of engine knock is an important issue in the design and maintenance of high performance internal combustion engines. Cost considerations dictate the use of vibration signals, measured at the engine block, for knock detection. Conventional techniques use the energy in a bandpass filtered version of the vibration signal as a measure. However, the low signal-to-noise ratio (SNR) in the vibration measurements significantly degrades the performance of such bandpass energy detectors. In this paper, we explore the design and application of more general quadratic detection procedures, including time-frequency methods, to this challenging problem. We use statistics estimated from labeled training data to design the detectors. Application of our techniques to real data shows that such detectors, by virtue of their flexible structure, improve the effective SNR, thereby substantially improving the detection performance relative to conventional methods.Item Unknown Equivalence of Generalized Joint Signal Representations of Arbitrary Variables(1996-12-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Joint signal representations (JSRs) of arbitrary variables generalize time-frequency representations (TFRs) to a much broader class of nonstationary signal characteristics. Two main distributional approaches to JSRs of arbitrary variables have been proposed by Cohen and Baraniuk. Cohen's method is a direct extension of his original formulation of TFRs, and Baraniuk's approach is based on a group theoretic formulation; both use the powerful concept of associating variables with operators. One of the main results of the paper is that despite their apparent differences, the two approaches to generalized JSRs are completely equivalent. Remarkably, the JSRs of the two methods are simply related via axis warping transformations, with the broad implication that JSRs with radically different covariance properties can be generated efficiently from JSRs of Cohen's method via simple pre- and post-processing. The development in this paper, illustrated with examples, also illuminates other related issues in the theory of generalized JSRs. In particular, we derive an explicit relationship between the Hermitian operators in Cohen's method and the unitary operators in Baraniuk's approach, thereby establishing the relationship between the two types of operator correspondences.Item Unknown Generalized Joint Signal Representations and Optimum Detection(1996-01-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Generalized joint signal representations (JSRs) extend the scope of joint time-frequency representations (TFRs) to a richer class of nonstationary signals, but their use, just as in the case of TFRs, has been primarily limited to qualitative, exploratory data analysis. To exploit their potential more fully, JSR-based statistical signal processing techniques need to be developed that can be successfully applied in real-world problems. In this paper, we present an optimal detection framework based on arbitrary generalized quadratic JSRs, thereby making it applicable in a wide variety of detection scenarios involving nonstationary stochastic signals, noise and interference. For any given class of generalized JSRs, we characterize the corresponding class of detection scenarios for which such JSRs constitute canonical detectors, and derive the corresponding JSR-based detectors. Our formulation also yields a very useful subspace-based interpretation in terms of corresponding linear JSRs that we exploit to design optimal detectors based on only partial signal information.Item Unknown Improved Time-Frequency Filtering of Signal-Averaged Electrocardiograms(1995-01-15) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)A recently proposed time-frequency filtering technique has shown promising results for the enhancement of signal-averaged electrocardiograms. This method weights the short-time Fourier transform (STFT) of the ensemble-averaged signal, analogous to the spectral domain Wiener filtering of stationary signals. In effect, it is a self-designing time-varying Wiener filter applied to the high resolution electrocardiogram (HRECG). In this paper, we empirically show that the performance of the proposed technique is about 2-3dB lower over the critical late-potential portion of the HRECG than the optimal fixed-window time-frequency filter based on ideal a priori knowledge of statistics. Although this ideal knowledge and performance is unattainable in practice, these results suggest that there remains potential for modest improvement. In order to narrow this gap in performance, we propose some improvements based on alternative structures for the time-frequency filter, including time-varying STFT windows. Simulation results show that an improved fixed-window technique can potentially yield an improvement of about 1-1.5 dB. By using properly chosen time-varying windows, the performance could potentially be improved even further. Thus, the improved techniques could produce a HRECG using fewer averages than the existing method, or could tolerate a lower signal-to-noise ratio.Item Unknown Improved Wavelet Denoising via Empirical Wiener Filtering(1997-07-01) Ghael, Sadeep; Sayeed, Akbar M.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Wavelet shrinkage is a signal estimation technique that exploits the remarkable abilities of the wavelet transform for signal compression. Wavelet shrinkage using thresholding is asymptotically optimal in a minimax mean-square error (MSE) sense over a variety of smoothness spaces. However, for any given signal, the MSE-optimal processing is achieved by the Wiener filter, which delivers substantially improved performance. In this paper, we develop a new algorithm for wavelet denoising that uses a wavelet shrinkage estimate as a means to design a wavelet-domain Wiener filter. The shrinkage estimate indirectly yields an estimate of the signal subspace that is leveraged into the design of the filter. A peculiar aspect of the algorithm is its use of two wavelet bases: one for the design of the empirical Wiener filter and one for its application. Simulation results show up to a factor of 2 improvement in MSE over wavelet shrinkage, with a corresponding improvement in visual quality of the estimate. Simulations also yield a remarkable observation: whereas shrinkage estimates typically improve performance by trading bias for variance or vice versa, the proposed scheme typically decreases both bias and variance compared to wavelet shrinkage.Item Unknown Integral Transforms Covariant to Unitary Operators and their Implications for Joint Signal Representations(1996-06-01) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Fundamental to the theory of joint signal representations is the idea of associating a variable, such as time or frequency, with an operator, a concept borrowed from quantum mechanics. Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parameterized unitary operator. It is well-known that the eigenfunctions of the unitary operator define a signal representation which is invariant to the effect of the unitary operator on the signal, and is hence useful when such changes in the signal are to be ignored. However, for detection or estimation of such changes, a signal representation covariant to them is needed. Using well-known results in functional analysis, we show that there always exists a translationally covariant representation; that is, an application of the operator produces a corresponding translation in the representation. This is a generalization of a recent result in which a transform covariant to dilations is presented. Using Stone's theorem, the "covariant" transform naturally leads to the definition of another, unique, dual parameterized unitary operator. This notion of duality, which we make precise, has important implications for joint distributions of arbitrary variables and their interpretation. In particular, joint distributions of dual variables are structurally equivalent to Cohen's class of time-frequency representations, and our development shows that, for two variables, the Hermitian and unitary operator correspondences can be used consistently and interchangeably if and only if the variables are dual.Item Unknown Joint multipath-Doppler diversity in fast fading channels(1998-11-20) Sayeed, Akbar M.; Aazhang, Behnaam; Center for Multimedia Communications (http://cmc.rice.edu/)We present a new framework for code-division multiple access (CDMA) communication over fast fading mobile wireless channels. The performance of the RAKE receiver, which is at the heart of existing CDMA systems, degrades substantially under fast fading encountered in many mobile scenarios. Due to the time-varying nature of the fast fading channel, we employ joint time-frequency processing, which is a powerful approach to time-varying signal processing. Whereas the RAKE receiver exploits multipath diversity to combat fading, our framework is based on joint multipath-Doppler diversity facilitated by a fundamental time-frequency decomposition of the channel into independent flat fading channels. Diversity processing is achieved by a time-frequency generalization of the RAKE receiver which can be leveraged into several important aspects of system design. Performance analysis shows that CDMA systems based on the time-frequency RAKE receiver, due to their inherently higher level of diversity, can potentially deliver significant performance gains over existing systems.Item Unknown Multiuser detection in fast-fading multipath environments(2001-10-20) Sayeed, Akbar M.; Aazhang, Behnaam; Center for Multimedia Communications (http://cmc.rice.edu/)We propose a new framework for multiuser detection in fast-fading channels that are encountered in many mobile communication scenarios. Existing multiuser RAKE receivers, developed to combat multipath fading and multiuser interference in slow fading, suffer substantial degradation in performance under fast fading due to errors in channel state estimation. The detectors proposed in this paper employ a novel receiver structure based on time-frequency (TF) processing that is dictated by a canonical representation of the wide-sense stationary uncorrelated scatterer (WSSUS) channel model. The workhorse of the framework is a TF generalization of the RAKE receiver that exploits joint multipath-Doppler diversity. Analytical and simulated results based on realistic fast-fading assumptions demonstrate that the proposed multiuser detectors promise substantially improved performance compared to existing systems due to the inherently higher level of diversity afforded by multipath-Doppler processing.Item Unknown Multiuser detection in fast-fading multipath environments(IEEE, 1998-12-20) Sayeed, Akbar M.; Sendonaris, Andrew; Aazhang, Behnaam; Center for Multimedia Communications (http://cmc.rice.edu/)We propose a new framework for multiuser detection in fast-fading channels that are encountered in many mobile communication scenarios. Existing multiuser RAKE receivers, developed to combat multipath fading and multiuser interference in slow fading, suffer substantial degradation in performance under fast fading due to errors in channel state estimation. The detectors proposed in this paper employ a novel receiver structure based on time-frequency (TF) processing that is dictated by a canonical representation of the wide-sense stationary uncorrelated scatterer (WSSUS) channel model. The workhorse of the framework is a TF generalization of the RAKE receiver that exploits joint multipath-Doppler diversity. Analytical and simulated results based on realistic fast-fading assumptions demonstrate that the proposed multiuser detectors promise substantially improved performance compared to existing systems due to the inherently higher level of diversity afforded by multipath-Doppler processing.Item Unknown Multiuser detectors for fast-fading multipath channels(1997-10-20) Sayeed, Akbar M.; Sendonaris, Andrew; Aazhang, Behnaam; Center for Multimedia Communications (http://cmc.rice.edu/)We propose a new framework for multiuser detection in fast fading channels that are encountered in many mobile communication scenarios. The detectors proposed in this paper employ a novel multiuser receiver structure based on time-frequency processing that exploits joint multipath-Doppler diversity. Performance analysis shows that the proposed time-frequency multiuser receivers, due to their inherently higher level of diversity, can potentially deliver substantial performance gains relative to conventional multiuser RAKE receivers.Item Unknown On the Equivalence of the Operator and Kernel Methods for Joint Distributions of Arbitrary Variables(1997-04-20) Sayeed, Akbar M.; Digital Signal Processing (http://dsp.rice.edu/)Generalizing the concept of time-frequency representations, Cohen has recently proposed a general method, based on operator correspondence rules, for generating joint distributions of arbitrary variables. As an alternative to considering all such rules, which is a practical impossibility in general, Cohen has proposed the kernel method in which different distributions are generated from a fixed rule via an arbitrary kernel. In this paper, we derive a simple but rather stringent necessary condition, on the underlying operators, for the kernel method (with the kernel functionally independent of the variables) to generate all bilinear distributions. Of the specific pairs of variables that have been studied, essentially only time and frequency satisfy the condition; in particular, the important variables of time and scale do not. The results warrant further study for a systematic characterization of bilinear distributions in Cohen's method.Item Unknown Optimal Detection Using Bilinear Time Frequency and Time Scale Representations(1995-12-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Bilinear time-frequency representations (TFRs) and time-scale representations (TSRs) are potentially very useful for detecting a nonstationary signal in the presence of nonstationary noise or interference. As quadratic signal representations, they are promising for situations in which the optimal detector is a quadratic function of the observations. All existing time-frequency formulations of quadratic detection either implement classical optimal detectors equivalently in the time-frequency domain, without fully exploiting the structure of the TFR, or attempt to exploit the nonstationary structure of the signal in an ad hoc manner. We identify several important nonstationary composite hypothesis testing scenarios for which TFR/TSR-based detectors provide a "natural" framework; that is, in which TFR/TSR-based detectors are both optimal and exploit the many degrees of freedom available in the TFR/TSR. We also derive explicit expressions for the corresponding optimal TFR/TSR kernels. As practical examples, we show that the proposed TFR/TSR detectors are directly applicable to many important radar/sonar detection problems. Finally, we also derive optimal TFR/TSR-based detectors which exploit only partial information available about the nonstationary structure of the signal.Item Unknown Optimal Kernels for Nonstationary Spectral Estimation(1995-02-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by difficulties in estimation, an assumption that the signal statistics vary slowly over time. This restrictive quasi-stationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's class of time-frequency representations (TFRs), for estimating the Wigner-Ville spectrum of a nonstationary process. We also solve the related problem of minimum mean-squared error estimation of an arbitrary bilinear TFR of a realization of a process from a correlated observation. Both optimal time-frequency invariant and time-frequency varying kernels are derived. It is proven that, in the presence of any additive noise, optimal performance requires a nontrivial kernel, and that optimal estimation may require smoothing filters very different from those based on a quasi-stationarity assumption. Examples confirm that the optimal estimators often yield tremendous improvements in performance over existing methods. In particular, the ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering.Item Unknown Optimal Reduced Rank Time-Frequency/Time Scale Quadratic Detectors(1996-01-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Optimal detectors based on time-frequency/time-scale representations (TFRs/TSRs) admit a representation in terms of a bank of spectrograms/scalograms that yields a large class of detectors. These range from the conventional matched filter to the more complex higher-rank detectors offering a superior performance in a wider variety of detection situations. In this paper, we optimize this complexity versus performance tradeoff by characterizing TFR/TSR detectors that optimize performance (based on the deflection criterion) for any given fixed rank. We also characterize the gain in performance as a function of increasing complexity thereby facilitating a judicious tradeoff. Our experience with real data shows that, in many cases, relatively low-rank optimal detectors can provide most of the gain in performance relative to matched-filter processors.Item Unknown Optimum Quadratic Detection and Estimation Using Generalized Joint Signal Representations(1996-12-01) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Time-frequency analysis has recently undergone significant advances in two main directions: statistically optimized methods that extend the scope of time-frequency-based techniques from merely exploratory data analysis to more quantitative application, and generalized joint signal representations that extend time-frequency-based methods to a richer class of nonstationary signals. This paper fuses the two advances by developing statistically optimal detection and estimation techniques based on generalized joint signal representations. By generalizing the statistical methods developed for time-frequency representations to arbitrary joint signal representations, this paper develops a unified theory applicable to a wide variety of problems in nonstationary statistical signal processing.Item Unknown A Simple Covariance Based Characterization of Joint Signal Representations of Arbitrary Variables(1996-01-20) Jones, Douglas L.; Sayeed, Akbar M.; Digital Signal Processing (http://dsp.rice.edu/)Joint signal representations of arbitrary variables extend the scope of joint time-frequency representations, and provide a useful description for a wide variety of nonstationary signal characteristics. Cohen's marginal-based theory for bilinear representations is canonical from a distributional viewpoint, whereas, from other perspectives, such as characterization of the effect of unitary signal transformations of interest, a covariance-based formulation is needed and more attractive. In this paper, we present a simple covariance-based characterization of bilinear joint signal representations of arbitrary variables. The formulation is highlighted by its simple structure and interpretation, and naturally extends the concept of the corresponding linear representations.Item Unknown Time Frequency Detectors(1996-01-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Time-frequency representations (TFRs) provide a powerful and flexible structure for designing optimal detectors in a variety of nonstationary scenarios. In this paper, we describe a TFR-based framework for optimal detection of arbitrary second-order stochastic signals, with certain unknown or random nuisance parameters, in the presence of Gaussian noise. The framework provides a useful model for many important applications including machine fault diagnostics and radar/sonar. We emphasize a subspace-based formulation of such TFR detectors which can be exploited in a variety of ways to design new techniques. In particular, we explore an extension based on multi-channel/sensor measurements that are often available in practice to facilitate improved signal processing. In addition to potentially improved performance, the subspace-based interpretation of such multi-channel detectors provides useful information about the physical mechanisms underlying the signals of interest.