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Time-Bandwidth Products Unbounded Above

We have considered two lower bounds for the time-bandwidth product based on two different definitions of duration in time. In the opposite direction, there is no upper bound on time-bandwidth product. To see this, imagine filtering an arbitrary signal with an allpass filter.B.3 The allpass filter cannot affect bandwidth $ \Delta\omega$ , but the duration $ \Delta t$ can be arbitrarily extended by successive applications of the allpass filter.


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2014-06-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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