L02_fourier

L02_fourier - Intro to Fourier Series Function...

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1 6.02 Spring 2008 Intro to Fourier Series, Slide 1 Intro to Fourier Series Function decomposition Even and Odd functions Fourier Series definition and examples Copyright © 2007 by M.H. Perrott & C. G. Sodini All rights reserved. 6.02 Spring 2008 Intro to Fourier Series, Slide 2 Can We Decompose Functions ? Consider a periodic function such as a square wave Can we decompose the above waveform into a weighted sum of basis functions ? What is a good choice for such basis functions? How do we calculate the weights? t
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2 6.02 Spring 2008 Intro to Fourier Series, Slide 3 Consider Sine Wave Basis Functions Suppose we consider sine waves of progressively increasing frequencies as our basis functions t t t sin( ω o t) sin(2 ω o t) sin(3 ω o t) 6.02 Spring 2008 Intro to Fourier Series, Slide 4 Issue: Sine Waves Are Limited A sine wave corresponds to an odd function Odd function definition: Adding odd functions together can only produce an odd function t t sin( ω o t)
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3 6.02 Spring 2008
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L02_fourier - Intro to Fourier Series Function...

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