# Time-Frequency Concepts

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 Title: Time-Frequency Concepts Author: Boashash, B Abstract: Time-frequency signal analysis and processing (TFSAP) concerns the analysis and processing of signals with time-varying frequency content. Such signals are best represented by a time-frequency distribution (TFD), which is intended to show how the energy of the signal is distributed over the two-dimensional time-frequency space. Processing of the signal may then exploit the features produced by the concentration of signal energy in two dimensions (time and frequency) instead of only one (time or frequency). The first chapter begins the introductory tutorial which constitutes Part I of the book. This tutorial updates the one given in [1] by including recent advances, refining terminology, and simplifying both the presentations of concepts and for- mulations of methodologies. Reading the three chapters of Part I will facilitate the understanding of the later chapters. The three sections of Chapter 1 present the key concepts needed to formu- late time-frequency methods. The first (Section 1.1) explains why time-frequency methods are preferred for a wide range of applications in which the signals have time-varying characteristics or multiple components. Section 1.2 provides the signal models and formulations needed to describe temporal and spectral characteristics of signals in the time-frequency domain. It defines such basic concepts as analytic signals, the Hilbert transform, the bandwidth-duration product and asymptotic signals. Section 1.3 defines the key quantities related to time-frequency methods, including the instantaneous frequency (IF), time-delay (TD) and group delay (GD). Description: This manuscript is a basic introduction to the time-frequency field; it presents clear rationales for justifying the need to use joint time-frequency representations for non-stationary signals such as FM signals; and it introduces all the basic signal concepts needed to understand the field in depth. (Additional details can be found in the other chapters of the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated). URI: http://hdl.handle.net/10576/10787 Date: 2003

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