Sequences with Minimal Time-Frequency Spreads

For a given time or frequency spread, one can always find continuous- time signals, which achieve the Heisenberg uncertainty principle bound. This is known, however, not to be the case for discrete-time sequences; only widely spread sequences asymptotically achieve this bound. We provide a constructive method for designing sequences that are maximally compact in time for a given frequency spread. By formulating the problem as a semidefinite program, we show that maximally compact sequences do not achieve the classic Heisenberg bound. We further provide analytic lower bounds on the time-frequency spread of such signals.


Presented at:
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, 2013
Year:
2013
Publisher:
New York, Ieee
Keywords:
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 Record created 2012-12-01, last modified 2018-03-17

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