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from Part II - Constructive Approximation Theory
Published online by Cambridge University Press: 29 September 2022
This chapter begins with the study of trigonometric interpolation and the discrete Fourier transform. As a first application, the numerical integration of periodic functions is discussed. More detailed topics, like existence and uniqueness of trigonometric interpolants, as well as alias as convergence of trigonometric interpolation are discussed. An important practical tool, the fast Fourier transform (FFT) is then introduced. With this at hand the most rudimentary ideas of signal processing are presented.
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