Ambiguity Domain

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Moeness G. Amin - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - Sparse and cross-term free time-frequency distribution based on Hermite functions
    2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015
    Co-Authors: Branka Jokanovic, Moeness G. Amin
    Abstract:

    Hermite functions are an effective tool for improving the resolution of the single-window spectrogram. In this paper, we analyze the Hermite functions in the Ambiguity Domain and show that the higher order terms can introduce undesirable cross-terms in the multiwindow spectrogram. The optimal number of Hermite functions depends on the location and spread of signal auto-terms in the Ambiguity Domain. We apply and compare several sparsity measures, namely l 1 norm, the Gini index and the time-frequency concentration measure, for determining the optimal number of Hermite functions, leading to the most desirable time-frequency representation. Among the employed measures, the Gini index provides the sparsest solution. This solution corresponds to a well-concentrated and cross-term reduced time-frequency signature.

  • Reduced Interference Sparse Time-Frequency Distributions for Compressed Observations
    IEEE Transactions on Signal Processing, 2015
    Co-Authors: Branka Jokanovic, Moeness G. Amin
    Abstract:

    Traditional quadratic time-frequency distributions are not designed to deal with randomly undersampled signals or data with missing samples. The compressed data measurements introduce noise-like artifacts in the Ambiguity Domain, compounding the problem of separating the signal auto-terms and cross-terms. In this paper, we propose a multi-task kernel design for suppressing both the artifacts and the cross-terms, while preserving the signal desirable auto-terms. The proposed approach results in highly concentrated time-frequency signature. We evaluate our approach using various polynomial phase signals and show its benefits, especially in the case of strong artifacts.

  • Time-Frequency Signal Representations Using Interpolations in Joint-Variable Domains
    IEEE Geoscience and Remote Sensing Letters, 2015
    Co-Authors: Branka Jokanovic, Moeness G. Amin, Traian Dogaru
    Abstract:

    Time-frequency (TF) representations are a powerful tool for analyzing Doppler and micro-Doppler signals. These signals are frequently encountered in various radar applications. Data interpolators play a unique role in TF signal representations under missing samples. When applied in the instantaneous autocorrelation Domain over the time variable, the low-pass filter characteristic underlying linear interpolators lends itself to cross-terms reduction in the Ambiguity Domain. This is in contrast to interpolation performed over the lag variable or a direct interpolation of the raw data. We demonstrate the interpolator performance in both the time Domain and the time-lag Domain and compare it with sparse signal reconstruction, which exploits the local sparsity property assumed by most Doppler radar signals.

  • EUSIPCO - Time-Frequency Kernel Design for Sparse Joint-Variable Signal Representations
    2014
    Co-Authors: Branka Jokanovic, Moeness G. Amin, Yimin Zhang, Fauzia Ahmad
    Abstract:

    Highly localized quadratic time-frequency distributions cast nonstationary signals as sparse in the joint-variable representations. The linear model relating the Ambiguity Domain and time-frequency Domain permits the application of sparse signal reconstruction techniques to yield highresolution time-frequency representations. In this paper, we design signal-dependent kernels that enable the resulting time-frequency distribution to meet the two objectives of reduced cross-term interference and increased sparsity. It is shown that, for random undersampling schemes, the new adaptive kernel is superior to traditional reduced interference distribution kernels.

  • Reducing noise in the time-frequency representation using sparsity promoting kernel design
    Compressive Sensing III, 2014
    Co-Authors: Branka Jokanovic, Moeness G. Amin, Yimin Zhang
    Abstract:

    Missing samples in the time Domain introduce noise-like artifacts in the Ambiguity Domain due to their de facto zero values assumed by the bilinear transform. These artifacts clutter the dual Domain of the time-frequency signal representation and obscures the time-frequency signature of single and multicomponent signals. In order to suppress the artifacts influence, we formulate a problem based on the sparsity aware kernel. The proposed kernel design is more robust to the artifacts caused by the missing samples.

Maria Hansson-sandsten - One of the best experts on this subject based on the ideXlab platform.

  • Optimal stochastic discrete time-frequency analysis in the Ambiguity and time-lag Domain
    Signal Processing, 2010
    Co-Authors: J. Sandberg, Maria Hansson-sandsten
    Abstract:

    In stochastic time-frequency analysis, the covariance function is often estimated from only one observed realization with the use of a kernel function. For processes in continuous time, this can equivalently be done in the Ambiguity Domain, with the advantage that the mean square error optimal Ambiguity kernel can be computed. For processes in discrete time, several Ambiguity Domain definitions have been proposed. It has previously been reported that in the Jeong-Williams Ambiguity Domain, in contrast to the Nutall and the Claasen-Mecklenbrauker Ambiguity Domain, any smoothing covariance function estimator can be represented as an Ambiguity kernel function. In this paper, we show that the Jeong-Williams Ambiguity Domain cannot be used to compute the mean square error (MSE) optimal covariance function estimate for processes in discrete time. We also prove that the MSE optimal estimator can be computed without the use of the Ambiguity Domain, as the solution to a system of linear equations. Some properties of the optimal estimator are derived.

  • A Comparison Between Different Discrete Ambiguity Domain Definitions in Stochastic Time-Frequency Analysis
    IEEE Transactions on Signal Processing, 2009
    Co-Authors: J. Sandberg, Maria Hansson-sandsten
    Abstract:

    The Ambiguity Domain plays a central role in estimating the time-varying spectrum and in estimating the covariance function of nonstationary random processes in continuous time. For processes in discrete time, there exist different definitions of the Ambiguity Domain, but it is well known that neither of these definitions perfectly resembles the usefulness of the continuous Ambiguity Domain. In this paper, we present some of the most frequently used definitions of the Ambiguity Domain in discrete time: the Claasen-Mecklenbrauker, the Jeong-Williams, and the Nuttall definitions. For the first time, we prove their equivalence within some necessary conditions and we present theorems that justify their usage.

Branka Jokanovic - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - Sparse and cross-term free time-frequency distribution based on Hermite functions
    2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015
    Co-Authors: Branka Jokanovic, Moeness G. Amin
    Abstract:

    Hermite functions are an effective tool for improving the resolution of the single-window spectrogram. In this paper, we analyze the Hermite functions in the Ambiguity Domain and show that the higher order terms can introduce undesirable cross-terms in the multiwindow spectrogram. The optimal number of Hermite functions depends on the location and spread of signal auto-terms in the Ambiguity Domain. We apply and compare several sparsity measures, namely l 1 norm, the Gini index and the time-frequency concentration measure, for determining the optimal number of Hermite functions, leading to the most desirable time-frequency representation. Among the employed measures, the Gini index provides the sparsest solution. This solution corresponds to a well-concentrated and cross-term reduced time-frequency signature.

  • Reduced Interference Sparse Time-Frequency Distributions for Compressed Observations
    IEEE Transactions on Signal Processing, 2015
    Co-Authors: Branka Jokanovic, Moeness G. Amin
    Abstract:

    Traditional quadratic time-frequency distributions are not designed to deal with randomly undersampled signals or data with missing samples. The compressed data measurements introduce noise-like artifacts in the Ambiguity Domain, compounding the problem of separating the signal auto-terms and cross-terms. In this paper, we propose a multi-task kernel design for suppressing both the artifacts and the cross-terms, while preserving the signal desirable auto-terms. The proposed approach results in highly concentrated time-frequency signature. We evaluate our approach using various polynomial phase signals and show its benefits, especially in the case of strong artifacts.

  • Time-Frequency Signal Representations Using Interpolations in Joint-Variable Domains
    IEEE Geoscience and Remote Sensing Letters, 2015
    Co-Authors: Branka Jokanovic, Moeness G. Amin, Traian Dogaru
    Abstract:

    Time-frequency (TF) representations are a powerful tool for analyzing Doppler and micro-Doppler signals. These signals are frequently encountered in various radar applications. Data interpolators play a unique role in TF signal representations under missing samples. When applied in the instantaneous autocorrelation Domain over the time variable, the low-pass filter characteristic underlying linear interpolators lends itself to cross-terms reduction in the Ambiguity Domain. This is in contrast to interpolation performed over the lag variable or a direct interpolation of the raw data. We demonstrate the interpolator performance in both the time Domain and the time-lag Domain and compare it with sparse signal reconstruction, which exploits the local sparsity property assumed by most Doppler radar signals.

  • EUSIPCO - Time-Frequency Kernel Design for Sparse Joint-Variable Signal Representations
    2014
    Co-Authors: Branka Jokanovic, Moeness G. Amin, Yimin Zhang, Fauzia Ahmad
    Abstract:

    Highly localized quadratic time-frequency distributions cast nonstationary signals as sparse in the joint-variable representations. The linear model relating the Ambiguity Domain and time-frequency Domain permits the application of sparse signal reconstruction techniques to yield highresolution time-frequency representations. In this paper, we design signal-dependent kernels that enable the resulting time-frequency distribution to meet the two objectives of reduced cross-term interference and increased sparsity. It is shown that, for random undersampling schemes, the new adaptive kernel is superior to traditional reduced interference distribution kernels.

  • Reducing noise in the time-frequency representation using sparsity promoting kernel design
    Compressive Sensing III, 2014
    Co-Authors: Branka Jokanovic, Moeness G. Amin, Yimin Zhang
    Abstract:

    Missing samples in the time Domain introduce noise-like artifacts in the Ambiguity Domain due to their de facto zero values assumed by the bilinear transform. These artifacts clutter the dual Domain of the time-frequency signal representation and obscures the time-frequency signature of single and multicomponent signals. In order to suppress the artifacts influence, we formulate a problem based on the sparsity aware kernel. The proposed kernel design is more robust to the artifacts caused by the missing samples.

Patrick J. Loughlin - One of the best experts on this subject based on the ideXlab platform.

  • A time-frequency training-based approach for robust classification of unknown transients with unknown arrival time and doppler shift
    Journal of the Franklin Institute, 2001
    Co-Authors: B. Tacer, Patrick J. Loughlin
    Abstract:

    Abstract We present a training-based approach for the classification of noisy unknown transient signals with arbitrary range and Doppler shift (time and frequency shifts). The Ambiguity function, which is the 2-D inverse Fourier transform of the Wigner time-frequency distribution of the signal, is utilized to remove the unknown time and frequency shifts. An Ambiguity Domain template is then generated from labeled training data (tens of observations), and classification is performed using an inner product. The method is tested on synthetic transient signals in Gaussian noise and performs as well as or better than another recently proposed time-frequency based method, and an energy detector, particularly when limited training data are available.

J. Sandberg - One of the best experts on this subject based on the ideXlab platform.

  • Optimal stochastic discrete time-frequency analysis in the Ambiguity and time-lag Domain
    Signal Processing, 2010
    Co-Authors: J. Sandberg, Maria Hansson-sandsten
    Abstract:

    In stochastic time-frequency analysis, the covariance function is often estimated from only one observed realization with the use of a kernel function. For processes in continuous time, this can equivalently be done in the Ambiguity Domain, with the advantage that the mean square error optimal Ambiguity kernel can be computed. For processes in discrete time, several Ambiguity Domain definitions have been proposed. It has previously been reported that in the Jeong-Williams Ambiguity Domain, in contrast to the Nutall and the Claasen-Mecklenbrauker Ambiguity Domain, any smoothing covariance function estimator can be represented as an Ambiguity kernel function. In this paper, we show that the Jeong-Williams Ambiguity Domain cannot be used to compute the mean square error (MSE) optimal covariance function estimate for processes in discrete time. We also prove that the MSE optimal estimator can be computed without the use of the Ambiguity Domain, as the solution to a system of linear equations. Some properties of the optimal estimator are derived.

  • Discrete Stochastic Time-Frequency Analysis and Cepstrum Estimation
    2010
    Co-Authors: J. Sandberg
    Abstract:

    The theory of stochastic time-frequency analysis of non-stationary random processes has mostly been developed for processes in continuous time. In practice however, random processes are observed, processed, and interpreted at a finite set of time points. For processes in continuous time, the Ambiguity Domain has interesting properties which makes it particularly useful. One such property is that there exists a certain relationship between scaling in the Ambiguity Domain and convolution in the time-lag Domain. For processes in discrete time, several different definitions of the Ambiguity Domain have been proposed. Paper A and B of this thesis contributes to the discretization of time-frequency theory, where we in Paper A compare three of the most common definitions: the Claasen-Mecklenbrauker, the Nuttall, and the Jeong-Williams Ambiguity Domain. We prove that amongst these three, only the Jeong-Williams Ambiguity Domain has the property that there exists a bijection between scaling in this Domain and convolution in the time-lag Domain. For processes in continuous time, there is also a certain mapping between the mean square error (MSE) optimal smoothing covariance function estimator and the MSE optimal Ambiguity function estimator. This mapping allows us to compute the MSE optimal smoothing estimator in a convenient way. In Paper B, we prove that a similar relationship is not valid between the scaling estimators in the Jeong-Williams Ambiguity Domain and the smoothing covariance function estimators for processes in discrete time. However, we show that the MSE optimal smoothing covariance function estimator for a non-stationary random process in discrete time can be found as the solution to a linear system of equations. It allows us to find the lower MSE bound of this family of estimators. In Paper C, we show that it is possible to compute a covariance function estimator which is MSE optimal to a set of processes in order to increase the robustness. The cepstrum of a stationary random process has a lot of interesting applications. It is usually estimated as the Fourier transform of the log-periodogram. In Paper D, we propose a multitaper based estimator and we derive approximations of its bias and variance. We demonstrate the performance of the multitaper based estimator in a speaker verification task. In Paper E we discuss four different families of cepstrum estimators based on smoothing. We find the MSE optimal smoother in each family and the lower MSE bound of each family of estimators. The robustness of the optimal estimators within each family is also considered.

  • A Comparison Between Different Discrete Ambiguity Domain Definitions in Stochastic Time-Frequency Analysis
    IEEE Transactions on Signal Processing, 2009
    Co-Authors: J. Sandberg, Maria Hansson-sandsten
    Abstract:

    The Ambiguity Domain plays a central role in estimating the time-varying spectrum and in estimating the covariance function of nonstationary random processes in continuous time. For processes in discrete time, there exist different definitions of the Ambiguity Domain, but it is well known that neither of these definitions perfectly resembles the usefulness of the continuous Ambiguity Domain. In this paper, we present some of the most frequently used definitions of the Ambiguity Domain in discrete time: the Claasen-Mecklenbrauker, the Jeong-Williams, and the Nuttall definitions. For the first time, we prove their equivalence within some necessary conditions and we present theorems that justify their usage.

  • Ambiguity Domain Definitions and Covariance Function Estimation for Non-Stationary Random Processes in Discrete Time
    2008
    Co-Authors: J. Sandberg
    Abstract:

    The Ambiguity Domain plays a central role in estimating the time-varying spectrum of a non-stationary random process in continuous time, since multiplication in this Domain is equivalent with estimating the covariance function of the random process using an intuitively appealing estimator. For processes in discrete time there exists a corresponding covariance function estimator. The Ambiguity Domain was originally defined for processes in continuous time and by its construction it is not trivial to define a similar concept for processes in discrete time. Several different definitions have been proposed. In Paper A we examine three of the most frequently used definitions and prove that only one of them has the important property that multiplication is equivalent with the mentioned covariance function estimator. Another useful property of the continuous Ambiguity Domain is that the mean square error optimal covariance function estimator has an attractive formulation in this Domain. In Paper B we prove that none of the three examined Ambiguity Domain definitions for discrete processes has this property. However, we prove that the optimal estimator can be computed without the use of the Ambiguity Domain for processes in discrete time. In Paper C we prove that the mean square error optimal covariance function estimator of the form discussed in this thesis, can be computed for any parameterized family of random processes as the solution to a system of linear equations. Examples of families and their corresponding optimal estimators are given. (Less)