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Chapter 6 FOURIER SERIES AND INTEGRALS..... Fourier series. Odd and even functions. Half range Fourier sine and cosine series. Complex form of Fourier series. Parseval's identity for Fourier series. Finite Fourier transforms. The Fourier integral. Complex form of Fourier integrals. Fourier transforms. Fourier sine and cosine transforms. FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST).

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It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A Chapter 2 Fourier Transform 2.1 A First Look at the Fourier Transform WeвЂ™re about to make the transition from Fourier series to the Fourier transform.

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