Reduction of noise and bias in randomly sampled power spectra

TL;DR

This paper investigates noise and bias in power spectral estimates from randomly sampled velocity data, proposing new correction methods and a novel spectral estimator to improve accuracy in finite record measurements.

Contribution

It introduces a deconvolution approach to correct spectral bias and noise, and presents a new power spectral estimator based on a fast slotted autocovariance algorithm.

Findings

Effective noise and bias reduction techniques for finite data records.

Demonstration of correction methods for dead time and sampling distortions.

Introduction of a novel spectral estimation algorithm.

Abstract

We consider the origin of noise and distortions in power spectral estimates of randomly sampled data, specifically velocity data measured with a burst-mode laser Doppler anemometer. The analysis guides us to new ways of reducing noise and removing spectral bias, e.g. distortions caused by modifications of the ideal Poisson sample rate caused by dead time effects and correlations between velocity and sample rate. The noise and dead time effects for finite records are shown to tend to previous results for infinite time records and ensemble averages. For finite records we show that the measured sampling function can be used to correct the spectra for noise and dead time effects by a deconvolution process. We also describe a novel version of a power spectral estimator based on a fast slotted autocovariance algorithm.