ABSTRACT
Estimating a power spectrum in a long random sequence can be accomplished by, first, creating its autocorrelation function and then taking the Fourier transform (FT). However, there are several problems that appear in establishing power spectra densities. First, the sequence may not be long enough and, sometimes can be very short. Second, the spectral characteristics may change with time. Third, data very often are corrupted with noise. Stationary random signals have usually finite average power and, therefore, can be characterized by an average power spectral density (PSD). The authors shall call such a quantity, the PSD. Without loss of generality, the discrete real random sequences will assume a zero mean value. The authors illustrate the ensemble averaging effect on the variance using ten realizations of the PSD only. They also show two periodograms by simulation which indicate that the variance does not decreases with increase in the number of samples.
