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Gaussian Pulse

The Gaussian pulse of width (second central moment) $ \sigma $ centered on time 0 may be defined by

$\displaystyle g_\sigma(t) \frac{1}{\sigma\sqrt{2\pi}}\isdef e^{-\frac{t^2}{\sigma^2}}$ (B.29)

where the normalization scale factor is chosen to give unit area under the pulse. Its Fourier transform is derived in Appendix D to be

$\displaystyle G_\sigma(\omega) = e^{-\frac{\omega^2}{2(1/\sigma)^2}}.$ (B.30)


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA