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Time, frequency, sequency, and their uncertainty relations (Corresp.)

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1 Author(s)

We study the form assumed by the classical time-frequency uncertainty relations in discrete as well as nontrigonometric spectral analysis. In particular we find that if an N -sample time signal is to contain a fraction \gamma of its energy in T consecutive samples, then the minimum number of frequency components containing that same energy fraction must be greater than N/T(2\gamma - 1)^2 . It is also found that the discrete Walsh transform permits greater energy concentration (less uncertainty) than the discrete Fourier transform.

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Information Theory, IEEE Transactions on  (Volume:19 ,  Issue: 2 )