Power spectrum estimation from randomly sampled velocity data

Random sampling of velocity, as with a laser Doppler anemometer eliminates power spectra aliasing, but it results in higher errors in the estimated spectra. From several methods proposed in the literature, the discretized lagged product method (DLPM) was adopted and evaluated in a controlled manner on several datasets simulating randomly sampled velocity measurements in three flow situations. Due to the absence of a variability formula, a parametric study of DLPM was done. Dataset length, maximum delay time, maximum frequency, mean sampling rate, and delay-time resolution were varied individually. The results confirmed theoretically expected trends. An often-used shortcut of interpolating equi-spaced data from the original randomly sampled data with subsequent FFT-based spectral analysis was shown to be error prone. DLPM was applied next to real velocity measurements using laser Doppler anemometer (LDA) data from (a) steady swirling flow, and (b) cyclic flow in the combustion chamber of an engine. In both cases, the technique worked well.