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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.

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.