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.