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Selected Continuous Fourier Theorems

This section presents continuous-time Fourier theorems that go beyond obvious analogs of the DTFT theorems proved in §2.3 above. The differentiation theorem comes up quite often, and its dual pertains as well to the DTFT. The scaling theorem provides an important basic insight into time-frequency duality. The Poisson Summation Formula (PSF) in continuous time extends the discrete-time version presented in §8.3.1. Finally, the extremely fundamental uncertainty principle is derived from the scaling theorem.



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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
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