Power Spectrum Estimation of Randomly Sampled Signals

Clara M. Velte, Preben Buchhave, William K. George

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The random, but velocity dependent, sampling of the LDA presents non-trivial signal processing challengesdue to the high velocity bias and the arbitrariness of particle path through the measuring volume, among other factors.To obtain the desired non-biased statistics, it has previously been shown analytically as well as empirically thatresidence time weighting is the suitable choice. Unfortunately, due to technical problems related to the processors providing erroneous measurements of the residence times, this previously widely accepted theory has been questioned and instead a wide spectrum of alternative methods attempting to produce correct power spectra have been invented andtested. The objective of the current study is to create a simple computer generated signal for baseline testing of residence time weighting and some of the most commonly proposed algorithms (or algorithms which most modernalgorithms ultimately are based on), sample-and-hold and the direct spectral estimator without residence time weighting, and compare how they perform in relation to power spectra based on the equidistantly sampled reference signal. The computer generated signal is a Poisson process with a sample rate proportional to velocity magnitude that consist of well-defined frequency content, which makes bias easy to spot. The idea is that if the algorithms are not able to produce correct statistics from this simple signal, then they will certainly not be able to function well for a more complex measured LDA signal. This is, of course, true also for other methods that are based on the tested algorithms.The extremes are tested by increasing, e.g., the ‘turbulence intensity’ and the ‘shear’. It is observed that sample and hold and the free-running processor perform well only under very particular circumstances with high data rate and low inherent bias, respectively, while residence time weighting provides non-biased estimates regardless of setting. The free-running processor was also tested and compared to residence time weighting using actual LDA measurements in a turbulent round jet. Power spectra from measurements on the jet centerline and the outer part of the jet illustrate a distinct difference between the residence time weighted and the non-weighted spectra, in particular for positions far off the jet center axis where the bias increases.
Original languageEnglish
Title of host publicationProceedings of the 17th International Symposium on Applications of Laser Techniques to Fluid Mechanics
Publication date2014
Publication statusPublished - 2014
Event17th International Symposium on Applications of Laser Techniques to Fluid Mechanics - Lisbon, Portugal
Duration: 7 Jul 201410 Jul 2014
Conference number: 17


Conference17th International Symposium on Applications of Laser Techniques to Fluid Mechanics


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