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Item An Adaptive Optimal-Kernel Time-Frequency Representation(1995-10-01) Jones, Douglas L.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Time-frequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signal- dependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are block-oriented techniques unsuitable for on-line implementation or for tracking signal components with characteristics that change with time. The time-frequency representation developed here, based on a signal-dependent radially Gaussian kernel that adapts over time, overcomes these limitations. The method employs a short-time ambiguity function both for kernel optimization and as an intermediate step in computing constant-time slices of the representation. Careful algorithm design provides reasonably efficient computation and allows on-line implementation. Certain enhancements, such as cone-kernel constraints and approximate retention of marginals, are easily incorporated with little additional computation. While somewhat more expensive than fixed-kernel representations, this new technique often provides much better performance. Several examples illustrate its behavior on synthetic and real-world signals.Show more Item Applications of Adaptive Time Frequency Representations to Underwater Acoustic Signal Processing(1991-11-01) Baraniuk, Richard G.; Jones, Douglas L.; Tom, Brotherton; Larry, Marple; Digital Signal Processing (http://dsp.rice.edu/)Show more The authors describe the application of an adaptive optimal kernel (AOK) time-frequency representation to the processing of underwater acoustic data. The optimal kernel is a signal-dependent radially Gaussian function. Examples are given which demonstrate the effectiveness of the approach for simulated and real sonar data. The simulations indicate that the technique should work well for a larger set of signal classes than any current fixed-kernel representation. The technique has excellent performance even in the presence of substantial additive noise; this property may be exploited for signal detection. The AOK technique appears to offer unique features that can be used to characterize and automatically classify signals of interest, particularly when compared to other processing techniques.Show more 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/)Show more 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.Show more Item 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/)Show more 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.Show more Item Community Driven Digital Signal Processing Laboratories in Connexions(2004-06-01) Baraniuk, Richard G.; Choi, Hyeokho; Jones, Douglas L.; Potter, Lee; Digital Signal Processing (http://dsp.rice.edu/)Show more The conventional textbook is largely inadequate for digital signal processing (DSP) laboratory education due to inherent factors such as a small and fragmented market and rapid hardware obsolescence. Freely available open-content materials that enable and promote both local customization and further development by a community of educators offers a fresh approach to lab text development that can surmount these barriers. In this paper, we overview a joint effort organized by the Connexions Project to develop a large pool of DSP lab modules sufficient to serve as the complete, stand-alone text for several types of DSP lab courses.Show more Item 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/)Show more 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.Show more Item Efficient Approximation of Continuous Wavelet Transforms(1991-04-01) Jones, Douglas L.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more An efficient method, based on the chirp-z transform, for computing equally spaced time samples of a continuous wavelet transform at arbitrary scale samples is developed. Applications include efficient computation of samples of the continuous wavelet transform and the broadband ambiguity function for time-frequency and time-scale signal analysis, and optimal detection of moving targets.Show more Item 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/)Show more 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.Show more Item Generalized Joint Signal Representations and Optimum Detection(1996-01-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Show more 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.Show more Item Improved Time-Frequency Filtering of Signal-Averaged Electrocardiograms(1995-01-15) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Show more 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.Show more Item 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/)Show more 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.Show more Item Multilingual Open-Content Signal Processing Laboratories in Connexions(2004-11-01) Frantz, Patrick; Baraniuk, Richard G.; Choi, Hyeokho; Jones, Douglas L.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)Show more Due to inherent factors like a small and fragmented market and rapid hardware obsolescence, the conventional textbook is inadequate for DSP laboratory education. Freely available open-content materials that enable and promote both local customization and further development by a community of educators offer a fresh approach to lab text development that can surmount these barriers. In this paper, we overview a joint effort under the aegis of the Connexions Project to develop a large pool of DSP lab modules sufficient to serve as a complete, stand-alone text for several types of DSP lab courses. In addition, we introduce a pilot project whose aim is to demonstrate the suitability of using Connexions for languages other than English, such as the Japanese, Chinese and Thai languages.Show more Item New Dimensions In Wavelet Analysis(1992-03-01) Baraniuk, Richard G.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Show more In this paper we propose a new class of signal analysis tools that generalizes the popular wavelet and short-time Fourier transforms. The class allows skews and rotations of the analyzing wavelet in the time-frequency plane, in addition to the time and frequency translations and scalings employed by conventional transforms. In addition to providing a unifying framework for studying existing time-frequency representations, the general class provides a systematic method for designing new representations with properties useful for certain types of signals.Show more Item New Signal-Space Orthonormal Bases via the Metaplectic Transform(1992-10-01) Baraniuk, Richard G.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Show more The discretization of the metaplectic transform (MT) is considered, and it is shown that it can lead to completely new orthonormal bases (ONBs) for the signal space of square integrable functions. Two new classes of bases, the scale-and-shear bases and the translation-and-shear bases, are derived to demonstrate the discretization process. Besides generalizing the current methods of generating time-frequency-concentrated ONBs, MT bases possess extra degrees of freedom that can be used to match a wider variety of signals.Show more Item An On-Line Signal-Dependent Time-Frequency Representation(1992-09-01) Jones, Douglas L.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more No Abstract.Show more Item 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/)Show more 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.Show more Item Optimal Kernels for Nonstationary Spectral Estimation(1995-02-20) Sayeed, Akbar M.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Show more 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.Show more Item 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/)Show more 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.Show more Item 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/)Show more 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.Show more Item A Radially-Gaussian, Signal-Dependent Time-Frequency Representation(1991-04-01) Baraniuk, Richard G.; Jones, Douglas L.; Digital Signal Processing (http://dsp.rice.edu/)Show more An optimization formulation for designing signal-dependent kernels that are based on radially Gaussian functions is presented. The method is based on optimality criteria and is not ad hoc. The procedure is automatic. The optimization criteria are formulated so that the resulting time-frequency distribution (TFD) is insensitive to the time scale and orientation of the signal in time-frequency. Examples demonstrate that the optimal-kernel TFD offers excellent performance for a larger class of signals than any current fixed-kernel representation. The technique performs well in the presence of substantial additive noise, which suggests that it may prove useful for automatic detection of unknown signals in noise. The cost of this technique is only a few times greater than that of the fixed-kernel methods and the 1/0 optimal kernel method.Show more