Generation of the Band-Limited White Noise on Digital Computer
Takuya Katayama · Transactions of the Society of Instrument and Control Engineers · 1971
Generation of the band-limited white noise x(t) on a digital computer is discussed. The method for generating x(t) is: (1) to expand x(t) into a series according to the sampling theorem, and (2) to truncate the series at some finite term, that is, the following xN(t) is composed on the digital computer.xN(t)=NΣn=-N+1xn+[t/t0]φn(t/t0-[t/t0])where φn(t)=sinπ(t-n)/π(t-n), {xi}: random numbers, t0=π/ωc(ωc: cut-off angular frequency).The autocorrelation function and the power spectral density of xN(t) are studied theoretically. It is shown that the effect of truncation and incompleteness of random number {xi} is negligible in an ordinary condition if N≥50.The method for speeding-up of generation is also discussed. The sample autocorrelation function and the power spectral density are calculated from xN(t) generated by the above method, and the results are shown to coincide with the theoretical analysis.From these analyses, we can conclude that the band-limited white noise can be generated satisfactorily on a digital computer.