Accession Number : AD0262137

Title :   DISTRIBUTION FUNCTIONS FOR OUTPUTS OF CERTAIN LINEAR FILTERS FOR RANDOM SQUARE-WAVE INPUTS

Corporate Author : PURDUE UNIV LAFAYETTE IND

Personal Author(s) : MCFADDEN,J.A. ; COHEN,A.R.

Report Date : 01 AUG 1961

Pagination or Media Count : 1

Abstract : The problem is considered of the calculation of the distribution function of the output of a linear filter with a random square-wave input. The systems considered are the finite-time integrator, the RC low-pass filter, and certain restricted higher-order filters. The inputs are square-waves in which the lengths of axis-crossing intervals are random, but statistically independent. For the finite-time integrator with a coin-toss square-wave input, a difference equation for the characteristic function of the output is derived and solved. The continuity and differentiability properties of the distribution function of the output of an RC low-pass filter are discussed. Under specified conditions on an RC low-pass filter with a coin-toss square-wave input, the distribution function of the output is constructed. For the same problem, a functional equation is derived for the characteristic function of the output, and a recurrence relation is obtained for certain moments of the output. For a general square-wave input, an integral equation is derived for the characteristic function of the output of an RC low-pass filter at an axis-crossing of the input. From this equation a second recurrence relation for the moments of the output is obtained. For the coin-toss square-wave input, certain higher-order systems are also considered. (Author)

Descriptors :   *INTEGRATORS, *LOW PASS FILTERS, DIFFERENCE EQUATIONS, INTEGRAL EQUATIONS, LINEAR SYSTEMS, MATHEMATICAL ANALYSIS, STATISTICAL FUNCTIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE