  We compare several methods for the efficient generation of correlated random
sequences (colored noise) by filtering white noise to achieve a desired
correlation spectrum. We argue that a class of IIR filter-design techniques
developed in the 1970s, which obtain the global Chebyshev-optimum minimum-phase
filter with a desired magnitude and arbitrary phase, are uniquely suited for
this problem but have seldom been used. The short filters that result from such
techniques are crucial for applications of colored noise in physical
simulations involving random processes, for which many long random sequences
must be generated and computational time and memory are at a premium.
