An estimate of the variation of a band-limited process

Author

Papoulis, A.

Volume

Issue

fYear

1964

fDate

1/1/1964 12:00:00 AM

Firstpage

Lastpage

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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=905045