Accession Number:

AD0608019

Title:

ZERO CROSSINGS OF A SINE WAVE PLUS RANDOM NOISE,

Descriptive Note:

Corporate Author:

THOMPSON RAMO WOOLDRIDGE INC LOS ANGELES CALIF

Personal Author(s):

Report Date:

1956-12-01

Pagination or Media Count:

42.0

Abstract:

New simple formulas are derived for the expected number of zeros per second of a sine wave process plus normal random noise. The variance in these mean estimates is investigated also. The main difference between this work and a previous study by Rice is that whereas Rice considers a single sine wave of fixed amplitude, phase and frequency, the present formulation allows the sine wave to be a representative member of a partially ergodic stationary random process, an ensemble of records varying in amplitude and phase, fixed in frequency only. This permits a closer agreement than before with many physical problems. The mean value result obtained in this paper agrees with Rice for normal random noise alone it coincides also with the required identity for sine wave alone. However, in combined situations, the formulas disagree. The variance for random noise by itself is shown to be expressible by a certain integral, and for the special case of normal random noise, the integral is reduced to a form amenable to numerical integration techniques. In cases of a combined sine wave process plus normal random noise, a formula is proposed for finding the variance, and applied to an example of a sine wave plus band limited white noise. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE