Probability density functions of amplitude-modulated random signals

The probability density function arising from multiplication of two independent random variables has been extensively treated by statisticians, yet some common signal processing product situations have not been analysed. An important example of this omission is the amplitude modulation of a Gaussian process. Here, a little-known Hankel transform-based procedure provides a ready solution for this problem and many other types of random modulation signals. Several new modulation results are tabulated in graphical form and it is also shown that half-amplitude sinusoidal processes added yield the same distribution as their (unit-amplitude) product