This report addresses the requirements on the length and resolution of realizations of sampled Rayleigh fading used in simulation or hardware testing of communications links. Measurements of the cumulative distribution, mean fade duration, and mean fade separation are compared to ensemble values. It is found that 100 decorrelation time realizations accurately reproduce the statistics of fades ... [Show full abstract] which are less than 20 dB, and 400 decorrelation time realizations accurately reproduce the statistics of fades which are less than 30 dB. It is also found that 10 samples per decorrelation time is adequate for 30 dB or less fades as long as interpolation is used between realization points. Keywords: Temporal statistics; Rayleigh fading; Realizations.