On leakage reduction associated with spectral power domain averaging to improve estimate quality

In Fourier analysis when estimating the power spectrum of a stochastic process from a sample function when the time-measurement resolution bandwidth product is large, typically transform lengths are selected which correspond closely to the desired measurement bandwidth and then time integration is used to increase the degrees of freedom of the spectral estimate. From the standpoint of estimation error an equally valid approach is to increase the time window associated with each transform and average across adjacent narrowband power estimates within the desired measurement bandwidth. This approach can be practical and offers some inherent leakage reduction which can be directly related to the data time window function characteristics. This paper uses an often overlooked result of spectral estimation to illustrate the relationship between the data time window and leakage associated with bandwidth averaging. Results associated with some commonly used window modification functions are presented.