Theoretical analysis demonstrates energy concentration bounds in finite-energy signals, revealing waveforms that optimize simultaneous time and frequency localization.
The theory developed in the preceding paper 1 is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite-energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.
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Landau et al. (1961) studied this question.
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