DISTRIBUTION FUNCTIONS FOR OUTPUTS OF CERTAIN LINEAR FILTERS FOR RANDOM SQUARE-WAVE INPUTS
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1961
- Accession Number
- AD0262137
Entities
People
- A.r. Cohen
- J.a. Mcfadden
Organizations
- Purdue University