Efficient estimation of burst-mode LDA power spectra

The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons. Acquisition is dictated by randomly arriving particles which cause the signal to be highly intermittent. This both creates self-noise and causes the measured velocities to be biased due to the statistical dependence on the velocity and when the particle arrives.

This leads to incorrect moments when the data are evaluated by arithmetically averaging. The signal can be interpreted correctly, however, by applying residence time weighting to all statistics, which eliminates the velocity bias effects. Residence time weighting should also be used to compute velocity spectra.

The residence time-weighted direct Fourier transform can, however, be computationally heavy, especially for the large data sets needed to eliminate finite time window effects and given the increased requirements for good statistical convergence due to the random sampling of the data. In the present work, the theory for estimating burst-mode LDA spectra using residence time weighting is discussed and a practical estimator is derived and applied.

A brief discussion on the self-noise in spectra and correlations is included, as well as one regarding the statistical convergence of the spectral estimator for random sampling. Further, the basic representation of the burst-mode LDA signal has been revisited due to observations in recent years of particles not following the flow (e.g., particle clustering), which was not covered in the previous theory.

An efficient algorithm for computing the residence time weighted power spectra using Matlab is proposed and implemented. The algorithm is applied to two experiments, one with high data density (cylinder wake) and one with relatively low data density (axisymmetric turbulent jet). The burst-mode LDA spectra are compared to corresponding spectra from hot-wire data obtained in the same experiments, and to LDA spectra produced by the sample-and-hold methodology.

The spectra computed from the residence-time weighted burst-mode algorithm proposed herein compare favorably to the hot-wire data for both experiments, independent of the LDA data density. The sample-and-hold spectrum produced from the same LDA data, however, is very different for the low data density due to frequency dependent filtering of the spectrum inherent in the method.