Spectrum Analysis of a Sinusoid

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.

Subsections

FFT of a Simple Sinusoid
FFT of a Not-So-Simple Sinusoid
FFT of a Zero-Padded Sinusoid
Use of a Blackman Window
- Applying the Blackman Window
Hann-Windowed Complex Sinusoid
- Hann Window Spectrum Analysis Results
- Spectral Phase

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``Mathematics of the Discrete Fourier Transform (DFT), with Music and Audio Applications'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.
Copyright © 2007-02-02 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 FFT

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