Spectral analysis of randomly sampled signals is discussed with reference to fluid velocity measured by ultrasonic (or laser) Doppler velocimetry. This study summarizes the merits, in the mean square sense, of the polygonal hold vs the zero-order hold interpolator. The comparison is done for different sampling schemes, such as Poisson sampling. It can be shown that if the signal is sampled randomly with a Poisson method, the output signal is equal to the original signal plus an uncorrelated additive white noise. Our purpose is to reduce the effect of this noise by using a simple first-order (or polygonal) interpolator. Similar results can be derived for uniform sampling with some missing samples or with time jitter. Finally, we use a suboptimal method for detection of sampling jitter based on the bispectrum of sampled data.