G: The Fourier Transform of a Periodic Function
Barbara Burke Hubbard
Abstract
Barbara Burke Hubbard
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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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