Flat-top smoothing of periodograms and frequency averagings to increase the accuracy in estimating power spectral density

Abstract

During the last years, many algorithms have been performed which are suitable both to increase the accuracy of estimating techniques in the frequency domain, and the precision and dynamic performance of digital instrumentation affected by a white quantization noise source. However, in the estimation of the power spectral density (PSD) function of a stationary random process through digital techniques, there is still one major drawback due to the trade-off between bias and variance, which the user should control. The performance of the periodogram estimator can be improved by averaging or smoothing the estimates, in the frequency domain, of nonoverlapping sections of the data sample but, for a finite sample size, we cannot completely control both bias and variance; when we attempt to reduce one, the other one increases. The main aim of this paper is to show how the estimation accuracy of a smoothed periodogram can be improved by adopting flat-top tapering in conjunction with averaging of 75% overlapped time slices of the data sample, based on Welch's method. The expressions for both components—those due to variance and bias—of the global (rms) amplitude estimation error have been derived and a lot of comparisons with the accuracy level given by classical cosine windows are proposed in order to confirm the better behaviour of the preoposed measurement technique. It has been developed and optimized to be very useful for control, diagnostics (ATE) and monitoring of electrical and electronic systems, under noisy non-sinusoidal conditions.