EURASIP Journal on Advances in Signal Processing, Jan 14, 2002
A conceptually new approximation method to study the time-frequency properties of dynamical syste... more A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exact Wigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in time and frequency. We then show how it lends itself to effective approximation methods because in the time frequency plane there is a high degree of localization of the signal. Numerical examples are given and compared to exact solutions.
We investigate M-indeterminate probability densities by way of the characteristic function and se... more We investigate M-indeterminate probability densities by way of the characteristic function and self adjoint operators. The approach leads to new methods to construct M-indeterminate probability densities of the Stieltjes class as well as new non-Stieltjes classes of densities.
The Journal of the Acoustical Society of America, 1999
For two-dimensional classical densities it is very often the case that the general properties of ... more For two-dimensional classical densities it is very often the case that the general properties of a density can be characterized by low-order joint moments and conditional moments. The advantage of this is that moments and conditional moments are constants and one-dimensional functions, respectively, and hence can be more effectively used for characterization, classification, and detection than the full density. In the time-frequency case unique problems arise. First, the definition of conditional moments is problematic and has not been fully investigated. Second, since a time-frequency density may go negative the methods of probability theory may not be taken over directly. We investigate these issues and show that time-frequency conditional moments can be defined in such a way that they appropriately characterize the general features of a time-frequency density. [Work supported by ONR.]
* Available as a photocopy reprint only. Allow two weeks reprinting time plus standard delivery t... more * Available as a photocopy reprint only. Allow two weeks reprinting time plus standard delivery time. No discounts or returns apply. ... Standard delivery in the US is 7 to 10 business days and outside the US delivery is 4 to 6 weeks or longer. For further details, please see shipping policy. ... Listed below are the papers found in this volume. Click the paper title to view an abstract or to order an individual paper. ... Author(s): Julia A. Olkin; Paul J. Titterton, Jr.
Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 2007
We discuss the application of time-frequency analysis to biomechanical-type signals, and in parti... more We discuss the application of time-frequency analysis to biomechanical-type signals, and in particular to signals that would be encountered in the study of rotation rates of bicycle pedaling. We simulate a number of such signals and study how well they are represented by various time-frequency methods. We show that time-frequency representations track very well the instantaneous frequency even when there
Wavelet Applications in Signal and Image Processing III, 1995
ABSTRACT We argue that an important aspect of the human speech signal is scaling in the frequency... more ABSTRACT We argue that an important aspect of the human speech signal is scaling in the frequency domain. We discuss the two physical mechanisms responsible for the scaling. The first mechanism is that when we have a harmonic signal whose fundamental is frequency modulated then the spectrum is the sum of scaled functions. The second comes about from the consideration that while different speakers have very different size vocal tracts (for example an adult and a child), we none the less produce speech which is similar in some sense. We will argue and present evidence to show that the speaker differences result in scaling in the frequency domain. We further discuss how one can handle scale processing.
Wavelet Applications in Signal and Image Processing II, 1994
We show that signals which are harmonically related to a fundamental frequency which has a finite... more We show that signals which are harmonically related to a fundamental frequency which has a finite bandwidth is modeled by the sum of scaled functions. We present a method to study such signals and give an example which illustrates the method.
ABSTRACT In this paper, we present improvements over the original scale-cepstrum proposed. The sc... more ABSTRACT In this paper, we present improvements over the original scale-cepstrum proposed. The scale-cepstrum was proposed as an acoustic feature for speech analysis and was motivated by a desire to normalize the first-order effects of differences in vocal-tract lengths for a given vowel. Our subsequent work has shown that a more appropriate frequency-warping than the log-warping used is necessary to account for the frequency dependency of the scale-factor. Using this more appropriate frequency-warping and a modified method of computing the scale-cepstrum we have obtained improved features that provide better separability between vowels than before, and are also robust to noise. We have used the generalized F-ratio test as a measure of separability and have compared the proposed improved features with the melcepstral features. The data used in the comparison consist of ten vowels extracted from sentences spoken by different speakers in the TIMIT database.
Proceedings of SPIE - The International Society for Optical Engineering, 2004
We address the issue of cloud removal from images. Typically a cloud on an image is not uniform a... more We address the issue of cloud removal from images. Typically a cloud on an image is not uniform and we develop methods that do denoising on a local level. In this paper we present preliminary studies of such methods and also a method for image fusion. The procedure is based on ...
Applications of Digital Image Processing XXVII, 2004
Image fusion methods provide an enhanced image from a set of source images which present regions ... more Image fusion methods provide an enhanced image from a set of source images which present regions with different spatial degradation patterns. Here within a fusion procedure is presented, based on the use of a new defocusing pixel-level measure. Such measure is ...
We obtain the exact Wigner spectrum for non-white Gaussian noise. As a special case the Wigner sp... more We obtain the exact Wigner spectrum for non-white Gaussian noise. As a special case the Wigner spectrum for the Wiener process is obtained.
We present an explicit procedure for obtaining the equation of motion for the Wigner distribution... more We present an explicit procedure for obtaining the equation of motion for the Wigner distribution when the underlying governing equation is a linear ordinary or partial differential equation. The cases of constant and variable coefficients are considered.
The Journal of the Acoustical Society of America, 2009
If noise is generated at a particular region, it will generally propagate and be nonstationary in... more If noise is generated at a particular region, it will generally propagate and be nonstationary in position and time. We present a phase space approach to understand the propagation of noise in a dispersive medium and to present methods to ascertain when the noise is stationary or quasi‐stationary. The damping case is also discussed. In addition, we present approximate methods that allow one to study the statistical properties of the evolution of the noise field in space and time in a relatively simple way. A number of examples will be presented. [Work supported by ONR.]
We obtain an explicit equation for the time-frequency Wigner spectrum of momentum governed by the... more We obtain an explicit equation for the time-frequency Wigner spectrum of momentum governed by the Langevin equation when the random driving term is quantum noise. The equation is solved exactly and includes both the transient and the stationary part. The time-dependent Wigner spectrum generalizes the result of Wang and Uhlenbeck wherein they showed that for the white noise driving force the power spectrum in the stationary state regime is Lorenzian. We show that our solution reduces to the classical solution when the parameters of the quantum noise are such that the white noise limit is approached and when the long time limit is taken.
EURASIP Journal on Advances in Signal Processing, Jan 14, 2002
A conceptually new approximation method to study the time-frequency properties of dynamical syste... more A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exact Wigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in time and frequency. We then show how it lends itself to effective approximation methods because in the time frequency plane there is a high degree of localization of the signal. Numerical examples are given and compared to exact solutions.
We investigate M-indeterminate probability densities by way of the characteristic function and se... more We investigate M-indeterminate probability densities by way of the characteristic function and self adjoint operators. The approach leads to new methods to construct M-indeterminate probability densities of the Stieltjes class as well as new non-Stieltjes classes of densities.
The Journal of the Acoustical Society of America, 1999
For two-dimensional classical densities it is very often the case that the general properties of ... more For two-dimensional classical densities it is very often the case that the general properties of a density can be characterized by low-order joint moments and conditional moments. The advantage of this is that moments and conditional moments are constants and one-dimensional functions, respectively, and hence can be more effectively used for characterization, classification, and detection than the full density. In the time-frequency case unique problems arise. First, the definition of conditional moments is problematic and has not been fully investigated. Second, since a time-frequency density may go negative the methods of probability theory may not be taken over directly. We investigate these issues and show that time-frequency conditional moments can be defined in such a way that they appropriately characterize the general features of a time-frequency density. [Work supported by ONR.]
* Available as a photocopy reprint only. Allow two weeks reprinting time plus standard delivery t... more * Available as a photocopy reprint only. Allow two weeks reprinting time plus standard delivery time. No discounts or returns apply. ... Standard delivery in the US is 7 to 10 business days and outside the US delivery is 4 to 6 weeks or longer. For further details, please see shipping policy. ... Listed below are the papers found in this volume. Click the paper title to view an abstract or to order an individual paper. ... Author(s): Julia A. Olkin; Paul J. Titterton, Jr.
Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 2007
We discuss the application of time-frequency analysis to biomechanical-type signals, and in parti... more We discuss the application of time-frequency analysis to biomechanical-type signals, and in particular to signals that would be encountered in the study of rotation rates of bicycle pedaling. We simulate a number of such signals and study how well they are represented by various time-frequency methods. We show that time-frequency representations track very well the instantaneous frequency even when there
Wavelet Applications in Signal and Image Processing III, 1995
ABSTRACT We argue that an important aspect of the human speech signal is scaling in the frequency... more ABSTRACT We argue that an important aspect of the human speech signal is scaling in the frequency domain. We discuss the two physical mechanisms responsible for the scaling. The first mechanism is that when we have a harmonic signal whose fundamental is frequency modulated then the spectrum is the sum of scaled functions. The second comes about from the consideration that while different speakers have very different size vocal tracts (for example an adult and a child), we none the less produce speech which is similar in some sense. We will argue and present evidence to show that the speaker differences result in scaling in the frequency domain. We further discuss how one can handle scale processing.
Wavelet Applications in Signal and Image Processing II, 1994
We show that signals which are harmonically related to a fundamental frequency which has a finite... more We show that signals which are harmonically related to a fundamental frequency which has a finite bandwidth is modeled by the sum of scaled functions. We present a method to study such signals and give an example which illustrates the method.
ABSTRACT In this paper, we present improvements over the original scale-cepstrum proposed. The sc... more ABSTRACT In this paper, we present improvements over the original scale-cepstrum proposed. The scale-cepstrum was proposed as an acoustic feature for speech analysis and was motivated by a desire to normalize the first-order effects of differences in vocal-tract lengths for a given vowel. Our subsequent work has shown that a more appropriate frequency-warping than the log-warping used is necessary to account for the frequency dependency of the scale-factor. Using this more appropriate frequency-warping and a modified method of computing the scale-cepstrum we have obtained improved features that provide better separability between vowels than before, and are also robust to noise. We have used the generalized F-ratio test as a measure of separability and have compared the proposed improved features with the melcepstral features. The data used in the comparison consist of ten vowels extracted from sentences spoken by different speakers in the TIMIT database.
Proceedings of SPIE - The International Society for Optical Engineering, 2004
We address the issue of cloud removal from images. Typically a cloud on an image is not uniform a... more We address the issue of cloud removal from images. Typically a cloud on an image is not uniform and we develop methods that do denoising on a local level. In this paper we present preliminary studies of such methods and also a method for image fusion. The procedure is based on ...
Applications of Digital Image Processing XXVII, 2004
Image fusion methods provide an enhanced image from a set of source images which present regions ... more Image fusion methods provide an enhanced image from a set of source images which present regions with different spatial degradation patterns. Here within a fusion procedure is presented, based on the use of a new defocusing pixel-level measure. Such measure is ...
We obtain the exact Wigner spectrum for non-white Gaussian noise. As a special case the Wigner sp... more We obtain the exact Wigner spectrum for non-white Gaussian noise. As a special case the Wigner spectrum for the Wiener process is obtained.
We present an explicit procedure for obtaining the equation of motion for the Wigner distribution... more We present an explicit procedure for obtaining the equation of motion for the Wigner distribution when the underlying governing equation is a linear ordinary or partial differential equation. The cases of constant and variable coefficients are considered.
The Journal of the Acoustical Society of America, 2009
If noise is generated at a particular region, it will generally propagate and be nonstationary in... more If noise is generated at a particular region, it will generally propagate and be nonstationary in position and time. We present a phase space approach to understand the propagation of noise in a dispersive medium and to present methods to ascertain when the noise is stationary or quasi‐stationary. The damping case is also discussed. In addition, we present approximate methods that allow one to study the statistical properties of the evolution of the noise field in space and time in a relatively simple way. A number of examples will be presented. [Work supported by ONR.]
We obtain an explicit equation for the time-frequency Wigner spectrum of momentum governed by the... more We obtain an explicit equation for the time-frequency Wigner spectrum of momentum governed by the Langevin equation when the random driving term is quantum noise. The equation is solved exactly and includes both the transient and the stationary part. The time-dependent Wigner spectrum generalizes the result of Wang and Uhlenbeck wherein they showed that for the white noise driving force the power spectrum in the stationary state regime is Lorenzian. We show that our solution reduces to the classical solution when the parameters of the quantum noise are such that the white noise limit is approached and when the long time limit is taken.
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Papers by Leon Cohen