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73
Optimal Detection Using Bilinear TimeFrequency And TimeScale Representations
 IEEE TRANS. SIGNAL PROCESSING
, 1995
"... Bilinear timefrequency representations (TFRs) and timescale 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 de ..."
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Cited by 33 (12 self)
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Bilinear timefrequency representations (TFRs) and timescale 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 timefrequency formulations of quadratic detection either implement classical optimal detectors equivalently in the timefrequency 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/TSRbased detectors provide a "natural" framework; that is, in which TFR/TSRbased 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 p...
An Adaptive OptimalKernel TimeFrequency Representation
, 1995
"... Timefrequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signaldependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are ..."
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Cited by 29 (2 self)
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Timefrequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signaldependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are blockoriented techniques unsuitable for online implementation or for tracking signal components with characteristics that change with time. The timefrequency representation developed here, based on a signaldependent radially Gaussian kernel that adapts over time, overcomes these limitations. The method employs a shorttime ambiguity function both for kernel optimization and as an intermediate step in computing constanttime slices of the representation. Careful algorithm design provides reasonably efficient computation and allows online implementation. Certain enhancements, such as conekernel constraints and approximate retention of marginals, are easily incorporated with little...
IPUS: An Architecture for the Integrated Processing and Understanding of Signals
, 1995
"... The Integrated Processing and Understanding of Signals (IPUS) architecture is presented as a framework that exploits formal signal processing models to structure the bidirectional interaction between frontend signal processing and signal understanding processes. This architecture is appropriate for ..."
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Cited by 23 (7 self)
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The Integrated Processing and Understanding of Signals (IPUS) architecture is presented as a framework that exploits formal signal processing models to structure the bidirectional interaction between frontend signal processing and signal understanding processes. This architecture is appropriate for complex environments, which are characterized by variable signal to noise ratios, unpredictable source behaviors, and the simultaneous occurrence of objects whose signal signatures can distort each other. A key aspect of this architecture is that frontend signal processing is dynamically modifiable in response to scenario changes and to the need to reanalyze ambiguous or distorted data. The architecture tightly integrates the search for the appropriate frontend signal processing configuration with the search for plausible interpretations. In our opinion, this dual search, informed by formal signal processing theory, is a necessary component of perceptual systems that must interact with c...
Shift Covariant TimeFrequency Distributions of Discrete Signals
 IEEE Trans. on Signal Processing
, 1997
"... Many commonly used timefrequency distributions are members of the Cohen class. This class is defined for continuous signals and since timefrequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the cla ..."
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Cited by 16 (5 self)
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Many commonly used timefrequency distributions are members of the Cohen class. This class is defined for continuous signals and since timefrequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic timefrequency distributions that are covariant to time shifts and frequency shifts. In this paper we extend this method to three types of discrete signals to derive what we will call the discrete Cohen classes. The properties of the discrete Cohen classes differ from those of the original Cohen class. To illustrate these properties we also provide explicit relationships between the classical Wigner distribution and the discrete Cohen classes. I. Introduction I N signal analysis there are four types of signals commonly used. These four types are based on whether the signal is continuous or discrete, and whether the signal is aperiodic or periodic. The four signal types ...
Application of the Wigner distribution function in optics
 in W. Mecklenbräuker and F. Hlawatsch, Eds., The Wigner Distribution – Theory and Applications in Signal Processing, Elsevier Science
, 1997
"... This contribution presents a review of the Wigner distribution function and of some of its applications to optical problems. The Wigner distribution function describes a signal in space and (spatial) frequency simultaneously and can be considered as the local frequency spectrum of the signal. Altho ..."
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Cited by 15 (3 self)
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This contribution presents a review of the Wigner distribution function and of some of its applications to optical problems. The Wigner distribution function describes a signal in space and (spatial) frequency simultaneously and can be considered as the local frequency spectrum of the signal. Although derived in terms of Fourier optics, the description of a signal by means of its Wigner distribution function closely resembles the ray concept in geometrical optics. It thus presents a link between Fourier optics and geometrical optics. The concept of the Wigner distribution function is not restricted to deterministic signals; it can be applied to stochastic signals, as well, thus presenting a link between partial coherence and radiometry. Some interesting properties of partially coherent light can thus be derived easily by means of the Wigner distribution function. Properties of the Wigner distribution function, for deterministic as well as for stochastic signals (i.e., for completely coherent as well as for partially coherent light, respectively), and its propagation through linear systems are considered; the corresponding description of signals and systems can directly be interpreted in geometricoptical terms. Some examples are included to show how the Wigner distribution function can be applied to problems that arise in the ®eld of optics. 1.
Topics In Harmonic Analysis With Applications To Radar And Sonar
 in RADAR and SONAR, Part 1, IMA Volumes in Mathematics and its Applications
, 1991
"... This minicourse is an introduction to basic concepts and tools in group representation theory, both commutative and noncommutative, that are fundamental for the analysis of radar and sonar imaging. Several symmetry groups of physical interest will be studied (circle, line, rotation, ax + b, Heisenbe ..."
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Cited by 15 (1 self)
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This minicourse is an introduction to basic concepts and tools in group representation theory, both commutative and noncommutative, that are fundamental for the analysis of radar and sonar imaging. Several symmetry groups of physical interest will be studied (circle, line, rotation, ax + b, Heisenberg, etc.) together with their associated transforms and representation theories (DFT, Fourier transform, expansions in spherical harmonics, wavelets, etc.). Through the unifying concepts of group representation theory, familiar tools for commutative groups, such as the Fourier transform on the line, extend to transforms for the noncommutative groups which arise in radarsonar. The insight and results obtained will be related directly to objects of interest in radarsonar, such as the ambiguity function. The material will be presented with many examples and should be easily comprehensible by engineers and physicists, as well as mathematicians. *School of Mathematics and IMA, University of Minnesota. The research contribution of this paper was supported in part by the National Science Foundation under grant DMS 8823054 Typeset by A M ST E X 1 2 WILLARD MILLER JR.* TABLE OF CONTENTS 1.
The IPUS Blackboard Architecture as a Framework for Computational Auditory Scene Analysis
 In Proc. IJCAI Workshop on CASA
, 1998
"... The Integrated Processing and Understanding of Signals (IPUS) architecture is designed for complex environments, which are characterized by variable signal to noise ratios, unpredictable source behaviors, and the simultaneous occurrence of objects whose signal signatures can distort each other. Beca ..."
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Cited by 13 (0 self)
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The Integrated Processing and Understanding of Signals (IPUS) architecture is designed for complex environments, which are characterized by variable signal to noise ratios, unpredictable source behaviors, and the simultaneous occurrence of objects whose signal signatures can distort each other. Because auditory scene analysis is replete with issues concerning the relationship between SPAappropriateness and multisound interactions in complex environments, much of our experimental work with IPUS has focused on applying the architecture to this problem. In this paper we present our workinprogress in scalingup our IPUS sound understanding testbed to accommodate a library of 50 sounds covering a range of types (e.g. impulsive, harmonic, periodic, chirps) and to analyze scenarios with three or four sounds. Introduction In previous articles [4, 5, 6] we have discussed the Integrated Processing and Understanding of Signals (IPUS) architecture as a general framework for structuring bidire...
Implications of Invariance and Uncertainty for Local Structure Analysis Filter Sets
, 2005
"... The paper discusses which properties of filter sets used in local structure estimation that are the most important. Answers are provided via the introduction of a number of fundamental invariances. Mathematical formulations corresponding to the required invariances leads up to the introduction of a ..."
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Cited by 11 (6 self)
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The paper discusses which properties of filter sets used in local structure estimation that are the most important. Answers are provided via the introduction of a number of fundamental invariances. Mathematical formulations corresponding to the required invariances leads up to the introduction of a new class of filter sets termed loglets. Loglets and are polar separable and have excellent uncertainty properties. The directional part uses a spherical harmonics basis. Using loglets it is shown how the concepts of quadrature and phase can be defined in ndimensions. It is also shown how a reliable measure of the certainty of the estimate can be obtained by finding the deviation from the signal model manifold. Local structure analysis algorithms are quite complex and involve a lot more than the filters used. This makes comparisons difficult to interpret from a filter point of view. To reduce the number ‘free’ parameters and target the filter design aspects a number of simple 2D experiments have been carried out. The evaluation supports the claim that loglets are preferable to other designs. In particular it is demonstrated that the loglet approach outperforms a Gaussian derivative approach in resolution and robustness.
Linear TimeFrequency Filters: Online Algorithms and Applications
, 2002
"... This chapter discusses practical discretetime methods for the timefrequency (TF) design of linear timevariant (LTV) filters. The filters are specified via a prescribed TF weight function (timevarying transfer function). We consider both explicit TF filter designs where a TF representation of the ..."
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Cited by 11 (3 self)
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This chapter discusses practical discretetime methods for the timefrequency (TF) design of linear timevariant (LTV) filters. The filters are specified via a prescribed TF weight function (timevarying transfer function). We consider both explicit TF filter designs where a TF representation of the LTV filter is matched to the specified TF weight function, and implicit TF filter designs that use an analysisweightingsynthesis procedure involving a linear TF signal representation. All filter designs allow for efficient online implementations and are thus suited to realtime applications. Our theoretical development is complemented by detailed descriptions of online algorithms, discussions of the choice of design parameters, and estimates of computational complexity and memory requirements. The performance and selected applications of the various TF filters are illustrated via numerical simulations.
Applications of Operator Theory to TimeFrequency Analysis and Classification
 IEEE Transactions on Signal Processing
, 1997
"... An entirely new set of criteria for the design of kernels (generating functions) for timefrequency representations (TFRs) is presented. These criteria aim only to produce kernels (and thus, TFRs) which will enable more accurate classification. We refer to these kernels, which are optimized to discr ..."
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Cited by 9 (1 self)
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An entirely new set of criteria for the design of kernels (generating functions) for timefrequency representations (TFRs) is presented. These criteria aim only to produce kernels (and thus, TFRs) which will enable more accurate classification. We refer to these kernels, which are optimized to discriminate among several classes of signals, as signal class dependent kernels, or simply class dependent kernels. The genesis of the class dependent kernel is to be found in the area of operator theory, which we use to establish a direct link between a discretetime, discretefrequency TFR and its corresponding discrete signal. We see that many similarities, but also some important differences, exist between the results of the continuoustime operator approach and our discrete one. The differences between the continuous representations and discrete ones may not be the simple sampling relationship which has often been assumed. From this work, we obtain a very concise, matrixbased expression ...