Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and the FFT

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and the FFT

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and the FFT

The examples below give a progression from the most simplistic analysis up to a proper practical treatment. Careful study of these examples will teach you a lot about how spectrum analysis is carried out on real data, and provide opportunities to see the Fourier theorems in action.



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