Digital computer simulation is widely used to design and develop wireless transmission systems and the components of wireless transmission systems. System performance such as coverage and outage are also frequently assessed by computer simulation. The fading caused by multipath propagation in wireless systems is accurately modeled in some practical cases by the Rayleigh distribution function. This paper presents a modification of the algorithm of Smith (1971) for the generation of correlated Rayleigh random variates by inverse discrete Fourier transform (IDFT) on a digital computer. The new method requires exactly one-half the number of IDFT operations and roughly two-thirds the computer memory of Smith's method. This paper also provides an analysis of the statistical properties of IDFT-based methods and comparisons between the IDFT approach and other approaches to correlated Rayleigh sample generation.