2140 - Notes, Syllabus Section V, lecture 32 (11/13/95)

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What do you do if you're given a function defined only on an interval? You can repeat it periodically, find the Fourier series, and then only look at it on the limited interval. This is an ambiguous procedure, as there are many ways to extend it and then repeat it.

Example of a simple step function on (0,1). Extended it to make a Fourier sin series, cos series (each with period 2), and a complex exponential series with period 1.

Discussed interpretation of Fourier coefficients in terms of what you hear (e.g.)

Introduction to Fourier transforms - needed if your function is not at all periodic, and/or if you need a continous spectrum of frequencies. (Same thing!)

Set up formalism - what happens in the limit that period goes to infinity?


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