
Accession Number : AD0262137
Title : DISTRIBUTION FUNCTIONS FOR OUTPUTS OF CERTAIN LINEAR FILTERS FOR RANDOM SQUAREWAVE 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 squarewave input. The systems considered are the finitetime integrator, the RC lowpass filter, and certain restricted higherorder filters. The inputs are squarewaves in which the lengths of axiscrossing intervals are random, but statistically independent. For the finitetime integrator with a cointoss squarewave 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 lowpass filter are discussed. Under specified conditions on an RC lowpass filter with a cointoss squarewave 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 squarewave input, an integral equation is derived for the characteristic function of the output of an RC lowpass filter at an axiscrossing of the input. From this equation a second recurrence relation for the moments of the output is obtained. For the cointoss squarewave input, certain higherorder 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