Local-frequency description of optical signals and systems

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Part A. Introduction 1 1.Two candidates for a local frequency spectrum: the Wigner distribution function and the sliding-window spectrum 3 1.1.Definition of the Wigner distribution fun,otion and the sliding-window spectrum 1.2.Relatives of the Wigner distribution function 1.3.Wigner distribution function versus slidi:og-window spectrum 1.4.Gabor's signal expansion: a relative of t:oe sliding-window spectrum 1.5.Part A. INTRODUCTION It is sometimes convenient to describe a space signal ~(x), say, not in the space domain, but in the frequency domain by means of its frequency speccrum, i.e., the Fourier cransform ~(u) of the function ~(x), which is defined by ~(u) -J~(x)eXp[-iUXldx ; a bar on top of a symbol will mean throughout that we are dealing with a function in the frequency domain.(Unless otherwise stated, all integrations and summations in this report extend from _00 to +00.)The frequency spectrum shows us the global distribution of the energy of the signal as a function of freque

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