  A method for simulating power law noise in clocks and oscillators is
presented based on modification of the spectrum of white phase noise, then
Fourier transforming to the time domain. Symmetric real matrices are introduced
whose traces--the sums of their eigenvalues--are equal to the Allan variances,
in overlapping or non-overlapping forms, as well as for the corresponding forms
of the modified Allan variance. Diagonalization of these matrices leads to
expressions for the probability distributions for observing a variance at an
arbitrary value of the sampling or averaging interval $\tau$, and hence for
estimating confidence in the measurements. A number of applications are
presented for the common power-law noises.
