On the noise in statistics of PIV measurements

It is argued herein that when PIV is used to measure turbulence, it can be treated as a time-dependent signal. The `output velocity consists of three primary contributions: the time-dependent velocity, a noise arising from the quantization (or pixelization), and a noise contribution from the fact that the velocity is not uniform inside the interrogation volume. For both of the latter their variances depend inversely on the average number of particles or images) in this interrogation volume. All three of these are spatially filtered by the finite extent of the interrogation window. Since the above noises are associated directly with the individual particles (or particle images), the noise between different realizations and different interrogation volumes is statistically independent.