An evaluation of time redundant DFT processing of stochastic signals with time varying spectra

This paper addresses the problem of applying an implementation of the DFT to obtain a periodogram estimate of the power spectral density of a stochastic signal which has a time varying power spectral density. For the situation when a sample function of a stationary process is observed over a period such that the time-measurement resolution bandwidth product is greater than unity, processing redundancy can be used to enhance the quality of the resulting spectral measurements. Of particular interest in this presentation is an evaluation of estimate quality associated with time redundant implementations of the DFT when harmonic content of the observation changes in a well-defined way during the processing interval. Simulation results are given to show that the estimate variance can be predicted on the basis of the effective degrees-of-freedom associated with the observation. Results are related to previous work with stationary signals.