Asymptotic statistics for an uncommon averaged DFT magnitude spectral estimator used in test and measurement equipment

Although numerous advanced signal processing methods are available for spectral estimation, many modern test and measurement systems such as sampling oscilloscopes typically provide only non-parametric FFT-based approaches. One such approach averages the FFT magnitudes rather than averaging the squared magnitudes as is done in the well-known Welch periodogram. Since these simple but non-conventional methods are common in industry, an understanding of their performance is important. This paper investigates the asymptotic bias and variance of the averaged DFT magnitude spectral estimator. It is shown that this averaging method gives a biased spectral estimator and that its mean squared error (MSE) is greater than that of the Welch averaged periodogram.