PROBABILITY DENSITY-FUNCTIONS OF AMPLITUDE-MODULATED RANDOM SIGNALS

The probability density function arising from multiplication of two in dependent random variables has been extensively treated by statisticia ns, yet some common signal processing product situations have not been analysed. An important example of this omission is the amplitude modu lation of a Gaussian process. Here, a little-known Hankel transform-ba sed procedure provides a ready solution for this problem and many othe r types of random modulation signals. Several new modulation results a re tabulated in graphical form and it is also shown that half-amplitud e sinusoidal processes added yield the same distribution as their (uni t-amplitude) product.