Random sampling: Its effect on spectral density

There are sampled-data systems of interest in which the sampling intervals are random variables. An example is a track-while-scan radar with a non-ideal blip scan ratio. In the statistical design of such systems it may be necessary to compute the spectral density of a random signal at the output of a random sampler. If the sampling intervals are independent, this spectral density may be determined from a complex convolution integral which, in many cases of practical interest, is easily evaluated in closed form by the method of residues. Consider a sampler which ideally operates periodically but actually misses samples with some probability. For this case the following result is obtained: the spectral density at the output of the non-ideal sampler is unchanged by replacing the non-ideal sampler by an ideal (periodic) sampler and adding to its output uncorrelated white noise of specified spectral density. When this result is used in the statistical design of a track-while-scan extrapolator it is found that the miss probability profoundly affects the system design. Neglect of this factor may, in fact, result in systems which are unstable in the mean square. This paper is to be published in the Proceedings of the First IFAC Moscow Congress by Butterworth Scientific Publications in 1960.