We calculate the spectrum of a signal derived from a continuous signal by ‘‘sample and hold’’ random sampling. It is seen that an undistorted spectrum is obtained only if the mean sampling frequency is more than an order of magnitude greater than the highest frequency in the original signal. The cases of signal‐independent and signal‐dependent sampling probabilities are investigated. We show how to obtain a good estimate for the spectrum of the unsampled signal and determine the limitations of this form of processing.