1998Unpublished venueRequires access

G: The Fourier Transform of a Periodic Function

Barbara Burke Hubbard

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Abstract

As T becomes longer, the coefficients are spaced closer and closer together. When T = co, our periodic function has become nonperiodic, and the discrete Fourier series has become a continuous Fourier transform; we are looking at all possible frequencies. (Of course, in practice a Fourier transform is computed for some sampling of frequencies, as described in The Fast Fourier Transform, p. 141.)

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What this paper is about

As T becomes longer, the coefficients are spaced closer and closer together. When T = co, our periodic function has become nonperiodic, and the discrete Fourier series has become a continuous Fourier transform; we are looking at all possible frequencies. (Of course, in practice a Fourier transform is computed for some sampling of frequencies, as described in The Fast Fourier Transform, p. 141.)

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Available abstract

As T becomes longer, the coefficients are spaced closer and closer together. When T = co, our periodic function has become nonperiodic, and the discrete Fourier series has become a continuous Fourier transform; we are looking at all possible frequencies. (Of course, in practice a Fourier transform is computed for some sampling of frequencies, as described in The Fast Fourier Transform, p. 141.)

Key concepts: Fourier transform, Function (biology), Mathematics, Mathematical analysis, Biology, Evolutionary biology

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