Báo cáo hóa học: Review Article Techniques to Obtain Good Resolution and Concentrated Time-Frequency Distributions: A Review

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Báo cáo hóa học: "Review Article Techniques to Obtain Good Resolution and Concentrated Time-Frequency Distributions: A Review"Hindawi Publishing CorporationEURASIP Journal on Advances in Signal ProcessingVolume 2009, Article ID 673539, 43 pagesdoi:10.1155/2009/673539Review ArticleTechniques to Obtain Good Resolution and ConcentratedTime-Frequency Distributions: A Review Imran Shafi,1, 2 Jamil Ahmad,1, 2 Syed Ismail Shah,1, 2 and F. M. Kashif1, 2, 3 1 Centrefor Advanced Studies in Engineering (CASE), G-5/2 Islamabad, Pakistan 2 IqraUniversity, H-9 Islamabad, Pakistan 3 Laboratory for Electromagnetic and Electronic Systems (LEES), MIT, Cambridge, MA 02139, USA Correspondence should be addressed to Imran Shafi, imran.shafi@gmail.com Received 12 July 2008; Revised 13 December 2008; Accepted 23 April 2009 Recommended by Ulrich Heute We present a review of the diversity of concepts and motivations for improving the concentration and resolution of time- frequency distributions (TFDs) along the individual components of the multi-component signals. The central idea has been to obtain a distribution that represents the signal’s energy concentration simultaneously in time and frequency without blur and crosscomponents so that closely spaced components can be easily distinguished. The objective is the precise description of spectral content of a signal with respect to time, so that first, necessary mathematical and physical principles may be developed, and second, accurate understanding of a time-varying spectrum may become possible. The fundamentals in this area of research have been found developing steadily, with significant advances in the recent past. Copyright © 2009 Imran Shafi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.1. Introduction and Historical Perspective The introduction of time-frequency (t-f) signal process- ing has led to represent and characterize the STSC’ time- varying contents using TFDs [7, 8]. The TFDs are two-The signals with time-dependant spectral content (STSC) dimensional (2D) functions which provide simultaneously,are commonly found in nature or are self-generated for the temporal and spectral information and thus are usedmany reasons. The processing of such signals forms the to analyze the STSC. By distributing the signal energybasis of many applications including analysis, synthesis, over the t-f plane, the TFDs provide the analyst withfiltering, characterization or modeling, suppression, can- information unavailable from the STSC’ time or frequencycellation, equalization, modulation, detection, estimation, domain representation alone. This includes the number ofcoding, and synchronization [1]. For a practical application, components present in the signal, the time durations, andthe STSC can be processed in various ways, other than frequency bands over which these components are defined,time-domain, to extract useful information. A classicaltool is the Fourier transform (FT) which offers perfect the components’ relative amplitudes, phase information, and the IF laws that components follow in the t-f plane. Therespectral resolution of a signal. However FT possesses intrinsic has been a great surge of activity in the past few yearslimitations that depend on the signal to be processed. The in t-f signal processing domain. The pioneering work isinstantaneous frequency (IF) [2, 3], generally defined asthe first conditional moment in frequency ω t , is a useful performed by Claasen and Mecklenbrauker [9–11], Janse and Kaizer [12], and Bouachache [1 ...