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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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