Origin of Rice´s formula

Author

Rainal, A.J.

Author_Institution

AT&T Bell Lab., Whippany, NJ

Volume

34

Issue

6

fYear

1988

fDate

11/1/1988 12:00:00 AM

Firstpage

1383

Lastpage

1387

Abstract

The origin of S.O. Rice´s formula for the average rate of level crossings of a rather general random process is traced to his 1936 private notes entitled Singing Transmission Lines. The notes formulate an engineering problem in terms of the probability distribution of the absolute maximum of an envelope process in a closed interval. Rice showed that if the envelope of the reflected wave on a loaded transmission line were to equal or exceed the maximum value in the closed interval, then `singing´ or oscillation could be expected to occur and the analog transmission system would become unstable and useless for the transmission of information. The formula and its generalizations are now basic for the analysis of level crossings and first and second passage times of random processes

Keywords

information theory; probability; random processes; transmission line theory; Rice; closed interval; envelope process; level crossings; loaded transmission line; passage times; probability distribution; random process; singing transmission lines; Equations; Gaussian processes; Narrowband; Probability distribution; Radar; Random processes; Random variables; Retirement; Transmission lines;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.21276

Filename

21276