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They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis. Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. Folland, G. B. (2009). Fourier Analysis and its applications. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral A discrete inverse Fourier transform converts the comfort noise back to the time domain and overlapping windows eliminate artifacts that may have been produced during processing.

7 The Fourier Transform and Its Applications. 105. 7.1 The Fourier Integral Representation 105. 7.2 The Fourier Transform. 107. 7.3 The Fourier Transform

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