Time–frequency analysis of signals using support adaptive Hermite–Gaussian expansions

doi:10.1016/j.dsp.2012.05.005

Digital Signal Processing

Volume 22, Issue 6, December 2012, Pages 1010-1023

https://doi.org/10.1016/j.dsp.2012.05.005 Get rights and content

Abstract

Since Hermite–Gaussian (HG) functions provide an orthonormal basis with the most compact time–frequency supports (TFSs), they are ideally suited for time–frequency component analysis of finite energy signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components whose TFS has a non-circular shape away from the origin, straight forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot provide reliable estimates to the individual signal components. To alleviate these problems, by using expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which identifies and transforms TFSs of individual signal components to circular regions centered around the origin so that reliable signal estimates for the signal components can be obtained. The HG expansion order for each signal component is determined by using a robust estimation technique. Then, the estimated components are post-processed to transform their TFSs back to their original positions. The proposed technique can be used to analyze signals with overlapping components as long as the overlapped supports of the components have an area smaller than the effective support of a Gaussian atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap region is larger than this threshold, the components cannot be uniquely identified. Obtained results on the synthetic and real signals demonstrate the effectiveness for the proposed time–frequency analysis technique under severe noise cases.

Section snippets

Yaşar Kemal Alp was born in Konya, Turkey, in 1985. He received his B.Sc. degree in electrical and electronics engineering from Bilkent University, Ankara, Turkey. He worked as a Research Scientist in Schlumberger Cambridge Research between June–August 2009 and July–September 2010. He is currently pursuing his Ph.D. in Department of Electrical and Electronics Engineering, Bilkent University. His research interests are time–frequency signals analysis, inverse problems and their applications to

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Orhan Arıkan was born in 1964 in Manisa, Turkey. He received the B.Sc. degree in electrical and electronics engineering from the Middle East Technical University, Ankara, Turkey in 1986 and both the M.S. and Ph.D. degrees in electrical and computer engineering from the University of Illinois, Urbana-Champaign, in 1988 and 1990, respectively. Following his graduate studies, he worked for three years as a Research Scientist at Schlumberger – Doll Research, Ridgefield, CT. He joined Bilkent University in 1993, where he is presently Professor of Electrical Engineering since 2006 and chair of the Electrical Engineering Department since 2011. His current research interests are in statistical signal processing, time–frequency analysis, and array signal processing.

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Time–frequency analysis of signals using support adaptive Hermite–Gaussian expansions

Abstract

Section snippets

J. Neurosci. Methods

The Hermite transform: a survey

EURASIP J. Appl. Signal Process.

Accurate image rotation using Hermite expansions

IEEE Trans. Image Process.

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EURASIP J. Adv. Signal Process.

Spectrally efficient UWB pulse shaping with application in orthogonal PSM

IEEE Trans. Commun.

Ballistocardiogram artifact removal in EEG-fMRI signals using discrete Hermite transforms

IEEE J. Sel. Top. Signal Process.

Block-based neural networks for personalized ECG signal classification

IEEE Trans. Neural Netw.

Time–frequency analysis and Hermite projection method applied to swallowing accelerometry signals

EURASIP J. Adv. Signal Process.

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IEEE Trans. Antennas Propag.

Ultrawide-band antenna distortion characterization using Hermite–Gauss signal subspaces

IEEE Antennas Wirel. Propag. Lett.

Multiwindow s-method for instantaneous frequency estimation and its application in radar signal analysis

IET Signal Process.

Multitaper time–frequency reassignment for nonstationary spectrum estimation and chirp enhancement

IEEE Trans. Signal Process.

Multiple Window Time-Varying Spectrum Estimation in Nonlinear and Nonstationary Signal Processing

Multiple window time-varying spectral analysis

IEEE Trans. Signal Process.

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IEEE Signal Process. Mag.

Hybrid linear/quadratic time–frequency attributes

IEEE Trans. Signal Process.

Blind separation of speech mixtures via time–frequency masking

IEEE Trans. Signal Process.