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Spectrum Analysis of a Sinusoid:
Windowing, Zero-Padding, and 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. They are written in matlab, and Python versions are available.



Subsections
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``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 © 2021-02-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA