Spectral estimates from nonuniform samples

Abstract

Errors in power spectral density estimates are analyzed for a problem in which the estimator processes nonuniformly spaced data samples as if they were uniformly spaced (e.g., via fast Fourier transform). The sample position errors, or jitter, are thought to be the result of fluctuations in the spacings between the sampling positions. One application of this model is to samples taken from a magnetic tape whose speed is fluctuating randomly. When the spacing errors are uncorrelated, the position errors are shown to be approximately wide-sense stationary, with an autocorrelation function that depends on the length of the line (number of data samples). This approximation is more valid if the number of samples is increased. Closed form bounds are given for the resulting frequency-dependent spectral density error when the true spectral density is bounded by a simple analytical function. Computational examples also show the effects of sample length and true spectral density bandwidth on this spectral error. The main effect of the spacing errors is a slower high-frequency fall off in the apparent spectral density. These results suggest criteria for judging if nonuniformities in spacing will cause significant errors in spectral density estimates. If so, these errors can be reduced, for estimates at higher frequencies, by cutting a long data sample into shorter pieces and averaging the corresponding spectral estimates.