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Gaussians Closed under Convolution

In §D.8 we show that

Therefore, it follows from the convolution theorem for Fourier transforms (§B.7) that the convolution of any two Gaussians is Gaussian.


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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