A constrained weighted least squares approach for time-frequency distribution kernel design

Amin, Moeness G.; Venkatesan, G.T.; Carroll, Joel

doi:10.1109/78.502325

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…Choi and Williams [17] introduced a distribution that uses an exponential kernel for reducing cross-terms suffer from smearing in the representation. This distribution was still found to be less efficient with ref- Costa et al [20], Amin et al [21] and Jemili et al [22] proposed certain TF representations using exponential kernels, modified comb filters and wavelet function respectively. These schemes aimed at obtaining better signal localization.…”

Section: Review Of the State-of-the-art In Tfd Designmentioning

confidence: 96%

Signal Analysis In The Ambiguity Domain

Sugavaneswaran¹

2021

Preprint

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Time-Frequency Distributions (TFDs) are accounted to be one of the powerful tools for analysis of time-varying signals. Although a variety of TFDs have been proposed, most of their designs were targeted towards obtaining good visualization and limited work is available for characterization applications. In this work, the characteristics of the ambiguity domain (AD) is suitably exploited to obtain a novel automated analysis scheme that preserves the inherent TF connection during Non-Stationary (NS) signal processing. Following this, an energy-based discriminative set of feature vectors for facilitating efficient characterization of the given time-varying input has been proposed. This scheme is motivated by the fact that, although, the interfering (or cross-) terms plague the representation, they carry important signal interaction information, which could be investigated for usability for time-varying signal analysis. Once having assessed the suitability of this domain for NS signal analysis, a new formulation for obtaining AD transformation is introduced. The number theory concepts, specifically the even-ordered Ramanujan Sums (RS) are used to obtain the proposed transform function. A detailed investigation and comparison to the classical approach, on this novel class of functions reveals the many benefits of the RS-modified AD functions: inherent sparsity in representation, dimensionality reduction, and robustness to noise. The next contribution in this work, is the proposal of kernel modifications in AD for obtaining high resolution (and good time localization) distribution. This is motivated by the existing trade-off between TF resolution and interfering term reduction in TF distributions. Here, certain variants of TF kernels are proposed in the AD. In addition, kernels that are derived from the concept of learning machines are introduced for discriminative characterization of NS signals. Following this, two novel AD-based schemes for neurological disorder discrimination using gait and pathological speech detection are introduced. The performance evaluation of these AD-based schemes, using a linear classifier, resulted in a maximum overall classification accuracy of 93.1% and 97.5% for gait and pathological speech applications respectively. The accuracies were obtained after a rigorous leave-one-out technique validation strategy.These results further confirm the potential of the proposed schemes for efficient information extraction for real-life signals.

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Section: Review Of the State-of-the-art In Tfd Designmentioning

confidence: 96%

Signal Analysis In The Ambiguity Domain

Sugavaneswaran¹

2021

Preprint

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“…(11) Since E and E, which respectively span the signal subspace and the noise subspace, are fixed and independent of the timefrequency point (t-f), relation (10) The BJD criterion allows the structural information contained in each STFD matrix to be jointly integrated in a single unitary matrix. In appendix A, we propose an efficient algorithm for solving (13).…”

Section: IImentioning

confidence: 99%

<title>Time-frequency MUSIC: an array signal processing method based on time-frequency signal representations</title>

Amin¹,

Belouchrani²

1998

SPIE Proceedings

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The concept of spatial time-frequency distribution (STFD) has been recently introduced and applied to solve the problem of blind source separation for nonstationary 2, 3 In this paper, we propose to apply this same concept to solve the problem of the direction of arriva' (DOA) estimation. A new method for the estimation of the signal subspace and noise subspace based on time-frequency signal representations is introduced. The proposed approach consists of the join blockdiagonalization (JBD) of a combined set of spatial time frequency distribution matrices. Once the signal and the noise subspaces are estimated, any subspace based approach can be applied for DOA estimation. Herein, we propose to use the MUSIC algorithm.Performance comparison of the proposed approach with the classical MUSIC method is provided. The influence of the timefrequency kernels on the performance of the newly proposed Time-Frequency MUSIC (TF-MUSIC) is evaluated numerically.

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“…Use of TFDs for signal classification [8] and detection [9][10] (a similar problem) has been researched previously, but from the point of view of discovering which, if any, of the existing TFDs might succeed with certain signal types. The idea of custom designing kernels has been explored [11], but not with an eye to classification.…”

Section: Introductionmentioning

confidence: 99%

Class-dependent, discrete time-frequency distributions via operator theory

McLaughlin

Droppo

Atlas

1997 IEEE International Conference on Acoustics, Speech, and Signal Processing

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We propose a property for kernel design which results in distributions for each of two classes of signals which maximally separates their energies in the time-frequency plane. Such maximally separated distributions may result in improved classification because the signal representation is optimized to accentuate the differences in signal classes. This is not the case with other time-frequency kernels which are optimized based upon some criteria unrelated to the classification task. Using our operator theory formulation for time-frequency representations, our "maximal separation" criteria takes on a very easily solved form. Analysis of the solution in both the time-frequency and ambiguity planes is given along with an example on discrete signals.

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A constrained weighted least squares approach for time-frequency distribution kernel design

Cited by 8 publications

References 16 publications

Signal Analysis In The Ambiguity Domain

Signal Analysis In The Ambiguity Domain

<title>Time-frequency MUSIC: an array signal processing method based on time-frequency signal representations</title>

Class-dependent, discrete time-frequency distributions via operator theory

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