Abstract:
Spectral analysis is employed in many fields of applied science for finding periodicities in data collected from various experiments. In many cases, the analysis relies on the use of periodogram. The main drawback is that the periodogram has high variance even if the number of the available measurements is large. Traditional solutions for this problem depend on parameters selected by the user, and this can lead to difficulties when they are employed in practical applications. In this thesis, we present an automatic method which utilizes cepstral nulling. The method has been recently introduced in signal processing literature and seems to be almost unknown in the community of statisticians. It has a solid theoretical foundation and its implementation comprises the following steps: (i) compute the periodogram, (ii) calculate the cepstral coefficients, (iii) turn to zero the coefficients which are smaller than a threshold and (iv) generate a smoothed periodogram from the retained coefficients. We consider various criteria for selecting the threshold and compare their performance by conducting experiments with both simulated data and real-world data. It is worth mentioning that one of the criteria is applied for the first time in cepstral nulling and yields promising results. In our experiments, we also consider the conventional methods for spectral estimation and compare them with cepstral nulling methods. Index Terms-Periodogram, cepstrum, Bayesian information criterion, uniformly most powerful unbiased test, minimum risk inflation, Mallows criterion.