# Accession Number:

## AD0604083

# Title:

## APPLICATIONS OF THE KAC-SIEGERT METHOD FOR FINDING OUTPUT PROBABILITY DENSITIES FOR RECEIVERS WITH SQUARE LAW DETECTORS

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CA

# Personal Author(s):

# Report Date:

## 1952-04-14

# Pagination or Media Count:

## 32.0

# Abstract:

The method of Kac and Siegert for finding the output probability density characteristic function for receivers with square law envelope detections is discussed and a parallel development is given for the square law rectifier. Procedures are then outlined for determining the probability density functions directly, i.e., without solving the eigenvalue problem or inverting the characteristic function. The method depends on expanding the density function in an orthonormal series the coefficients of which are expressed in terms of cumulants which in turn are obtained from the system kernel by straightforward quadratures. As an example to illustrate the procedure, a receiver with Gaussian I. F. and Gaussian audio frequency pass characteristics is treated in detail, and the output probability density functions are found for various sinusoidal input signal strengths and I. F. vs. audio bandwidth ratios.

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Radiofrequency Wave Propagation