The time series data collected during the HIFiRE-1 flight experiment was sampled unevenly due to telemetry dropouts and the sampling scheme selected. Sampling unevenly results in frequency translation of power to artificial sidelobes. These sidelobes distort the real and imaginary components of the Fourier transform such that the spectrum of the sampled data no longer represents the spectrum of the physical process generating the data. These sidelobes can be eliminated by resampling the data onto an evenly spaced grid at the cost of under predicting the power of the higher frequency components in the data. In this paper, a compensation procedure is developed to recover the power loss caused by resampling. This compensation procedure is suitable for stochastic time series data having red-noise spectra such as the pressure fluctuations recorded underneath laminar and turbulent boundary layers.
Nomenclaturea i = regression coefficient a 50 = overlap correlation constant b i = regression coefficient c xy = coherency D = location data point of a partition f = frequency, Hz This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Fluid Dynamics and Co-located Conferences f 0 = fundamental frequency, Hz f c = Nyquist frequency, Hz G xx = autospectrum, Pa 2 / Hz G xy = cross-spectrum, Pa 2 / Hz K = number of partitions K eff = effective number of partitions L = number of data samples in a partition N = number data samples in a time series R = sum of squares t = time, sec t f = time used to account for different time origins of time series used in cross spectral analysis, sec t L = time at the end of a partition, sec T p = period, sec T R = sampling interval, sec w n = Hanning window function coefficients y n = time series data σ 2 = variance τ = time shift, sec ω = angular frequency, rad