Distribution Functions for Outputs of Certain Linear Filters for Random Square-Wave Inputs
Abstract
This thesis considers the problem 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 in- dependent.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.
Degree
Ph.D.
Subject Area
Electrical engineering
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