ZERO CROSSINGS OF A SINE WAVE PLUS RANDOM NOISE,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1956
- Accession Number
- AD0608019
Entities
People
- Julius S. Bendat
Organizations
- TRW Inc.