DocumentCode :
905045
Title :
An estimate of the variation of a band-limited process
Author :
Papoulis, A.
Volume :
10
Issue :
1
fYear :
1964
fDate :
1/1/1964 12:00:00 AM
Firstpage :
72
Lastpage :
74
Abstract :
Upper and lower bounds are established for the mean-square variation of a stationary process X(t) whose power spectrum is bounded by \\omega _{c} , in terms of its average power P_{0} and the average power P_{1} of its derivative. It is shown that \\left( frac{2}{\\pi} \\right)^{2} P_{1} \\tau ^{2} \\leq E {|X(t+\\tau )-X(t)|^{2}} \\leq P_{1} \\tau ^{2} \\leq \\omega _{c}^{2}P_{0}\\tau ^{2} where the upper bounds are valid for any \\tau and the lower bound for \\tau < \\pi / \\omega _{c} . These estimates are applied to the mean-square variation of the envelope of a quasi-monochromatic process.
Keywords :
Bandlimited stochastic processes; Estimation; Autocorrelation; Diodes; Frequency modulation; Gaussian noise; Low pass filters; Oscillators; Power engineering and energy; Shape; Tuning; Upper bound;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1964.1053646
Filename :
1053646
Link To Document :
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