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Regularity and unitarity of bilinear timefrequency signal representations
 IEEE Trans. Inform. Theory
, 1992
"... AbstractTwo structural properties of bilinear timefrequency representations (BTFR’s) of signals are introduced and studied. The definition of these properties is based on a linearoperator description of BTFR’s. The first property, termed regularity, has important implications with respect to the r ..."
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Cited by 10 (2 self)
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AbstractTwo structural properties of bilinear timefrequency representations (BTFR’s) of signals are introduced and studied. The definition of these properties is based on a linearoperator description of BTFR’s. The first property, termed regularity, has important implications with respect to the recovery of signals from their BTFR outcome, the derivation of other bilinear signal representations from a BTFR, the BTFR’s reaction to linear signal transformations, and the construction of bases of induced BTFRdomain spaces. The second property, called uniturity, is equivalent to validity of Moyal’s formula. Unitarity is thus necessary and sufficient for a closedform solution of optimal signal synthesis and for a BTFR formulation of optimal detection/estimation methods. Besides, unitarity also allows the systematic construction of BTFR “product relations’’ like Wigner distribution’s interference formula and ambiguity
Optimum TimeFrequency Representations for the Classification and Detection of Signals
 Applied Signal Processing
, 1995
"... Timefrequency representations (TFRs) are powerful tools for signal analysis and thus widely used in signal processing. It is well known, however, that there is no single TFR which is "the best" for all problems. It is still an unsolved problem how to determine the optimum TFR for a given ..."
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Cited by 9 (2 self)
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Timefrequency representations (TFRs) are powerful tools for signal analysis and thus widely used in signal processing. It is well known, however, that there is no single TFR which is "the best" for all problems. It is still an unsolved problem how to determine the optimum TFR for a given signal class and analysis task. In this article we develop a new theory of optimum TFRs for classification and detection problems, where two (or more) classes are to be discriminated from one another. Usually this is performed by mapping the signals into some representation space (e.g. a feature space) where a distinction is easily possible. If we regard TFRs as representations in timefrequency space we have to look for TFRs where all signals of one class are similar to each other but dissimilar to all signals of other classes. After introducing a quantitative measure for similarity or, in contrast, for the distance, a measure for the quality of a given TFR for a given classification or detection pro...
Adaptive TimeVarying Cancellation of Wideband Interferences in SpreadSpectrum Communications Based on TimeFrequency Distributions
 IEEE Trans. Signal Processing
, 1999
"... The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the timefrequency representation of the received signal from which the parameters of an adaptive timevarying interference excision ..."
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Cited by 7 (0 self)
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The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the timefrequency representation of the received signal from which the parameters of an adaptive timevarying interference excision filter are estimated. The approach is based on the generalized WignerHough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise. The performance of the proposed approach is evaluated in the presence of linear and sinusoidal FM interferences plus white Gaussian noise in terms of SNR improvement factor and bit error rate (BER).
Multiple window timevarying spectrum estimation
 in Conf. Info. Sci. and Sys. (CISS
, 1996
"... We overview a new nonparametric method for estimating the timevarying spectrum of a nonstationary random process. Our method extends Thomson’s powerful multiple window spectrum estimation scheme to the timefrequency and timescale planes. Unlike previous extensions of Thomson’s method, we identi ..."
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Cited by 6 (0 self)
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We overview a new nonparametric method for estimating the timevarying spectrum of a nonstationary random process. Our method extends Thomson’s powerful multiple window spectrum estimation scheme to the timefrequency and timescale planes. Unlike previous extensions of Thomson’s method, we identify and utilize optimally concentrated Hermite window and Morse wavelet functions and develop a statistical test for extracting chirping line components. Examples on synthetic and realworld data illustrate the superior performance of the technique. 2
Radon–Wigner display: a compact optical implementation with a single varifocal lens
 Appl. Opt
"... lens ..."
Optimum TimeFrequency Distribution for Detecting a DiscreteTime Chirp Signal in White Gaussian Noise
"... In the continuoustime domain, MaximumLikelihood (ML) detection of a chirp signal in white Gaussian noise can be done via the lineintegral transform of the classical Wigner distribution. The lineintegral transform is known variously as the Hough transform and the Radon transform. For discretetim ..."
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In the continuoustime domain, MaximumLikelihood (ML) detection of a chirp signal in white Gaussian noise can be done via the lineintegral transform of the classical Wigner distribution. The lineintegral transform is known variously as the Hough transform and the Radon transform. For discretetime signals, the Wignertype distribution defined by Claasen and Mecklenbrauker has become popular as a signal analysis tool. Moreover, it is commonly believed that ML detection of a discretetime chirp signal in white Gaussian noise can be done via the lineintegral transform of the WignerClaasenMecklenbrauker distribution. This belief is false and results in loss of performance. We derive a Wignertype distribution for discretetime signals whose lineintegral transform can be used for ML detection of discretetime chirp signals in white Gaussian noise. We provide simulated Receiver Operating Curves for the WignerClaasenMecklenbrauker distribution based method and the new MLequivalent method and demonstrate the suboptimality of the former. I.
Some Underwater Acoustic Signals Using Time Frequency Analysis Techniques
"... AbstractSignal detection techniques based on timefrequency signal analysis with the WignerVille distribution (WVD) and the cross WignerVille distribution (XWVD) are presented. These techniques are shown to provide high resolution signal characterization in a timefrequency space, and good noise ..."
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AbstractSignal detection techniques based on timefrequency signal analysis with the WignerVille distribution (WVD) and the cross WignerVille distribution (XWVD) are presented. These techniques are shown to provide high resolution signal characterization in a timefrequency space, and good noise rejection performance. This type of detection is applied to the signaturing, detection, and classification of specific machine sounds: the individual cylinder firings of a marine engine. For this task, a four step procedure has been devised. 1) The autocorrelation function (ACF) is first employed for ascertaining the number of engine cylinders and the firing rate of the engine. 2) Further correlation techniques are then used to detect the time at which individual cylinder firing events occur. 3) WVD and XWVD based analyses follow to produce high resolution timefrequency signatures. 4) Finally, 2D correlations are employed for classification of the individual cylinders. The proposed methodology is tested on real data. XWVD based detection is also applied to detection of a transient with unknown waveshape (using real data). I.
L. Fridtjof WisurOlsen
"... We consider the design of kernels for timefrequency distributions through the phase, rather than amplitude, response. While phase kernels do not attenuate troublesome crosscomponents, they can translate them in the timefrequency plane. In contrast to previous work on phase kernels that concentrate ..."
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We consider the design of kernels for timefrequency distributions through the phase, rather than amplitude, response. While phase kernels do not attenuate troublesome crosscomponents, they can translate them in the timefrequency plane. In contrast to previous work on phase kernels that concentrated on placing the crosscomponents on top of the autocomponents, we set up a “don’t care ” region and place the crosscomponents there. The close connections between optimal allpass kernels and optimal lowpass kernels provide valuable insight into signaldependent timefrequency analysis. 1.
FREQUENCY ESTIMATION OF LINEAR FM SCATTEROMETER PULSES RECEIVED BY THE SEAWINDS CALIBRATION GROUND STATION
, 2004
"... The SeaWinds Calibration Ground Station (CGS) is a passive ground station used to receive and sample transmissions from the SeaWinds scatterometer. During post processing, the received transmissions are characterized in order to verify proper instrument operation and to eliminate error in satellite ..."
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The SeaWinds Calibration Ground Station (CGS) is a passive ground station used to receive and sample transmissions from the SeaWinds scatterometer. During post processing, the received transmissions are characterized in order to verify proper instrument operation and to eliminate error in satellite telemetry and in data products generated from processing SeaWinds data. Sources of instrument error include uncertainties in transmitted power, pulse timing, and carrier frequency drift. Identifying these errors prevents their propagation to data products. A key aspect of this analysis involves accurately estimating the parameters of the SeaWinds transmissions. As better parameter estimates are researched and developed, the scatterometer can be more finely calibrated and better characterized, allowing improved accuracy of environmental measurements. This work explores several methods to estimate SeaWinds frequency parameters by parametrically modeling the signal as a series of linear FM pulses. Improved frequency estimates are obtained by transforming the signal into appropriate signal spaces. These methods are compared and their tradeoffs revealed. SNR regions are assigned to each method to mark appropriate performance bounds, and improvements over previous SeaWinds data analysis methods are shown. Finally, recent estimates of SeaWinds parameters are disclosed. This analysis helps to advance the level to which future scatterometer instruments may be calibrated, providing the potential for more accurate scatterometer data products. ACKNOWLEDGMENTS And if any man think that he knoweth any thing, he knoweth nothing yet as he ought to know. 1