A two dimensional power spectral estimate for some nonstationary processes

摘要

A two dimensional estimate for the power spectral density of a nonstationary process is being developed. The estimate will be applied to helicopter noise data which is clearly nonstationary. The acoustic pressure from the isolated main rotor and isolated tail rotor is known to be periodically correlated (PC) and the combined noise from the main and tail rotors is assumed to be correlation autoregressive (CAR). The results of this nonstationary analysis will be compared with the current method of assuming that the data is stationary and analyzing it as such. Another method of analysis is to introduce a random phase shift into the data as shown by Papoulis to produce a time history which can then be accurately modeled as stationary. This method will also be investigated for the helicopter data. A method used to determine the period of a PC process when the period is not know is discussed. The period of a PC process must be known in order to produce an accurate spectral representation for the process. The spectral estimate is developed. The bias and variability of the estimate are also discussed. Finally, the current method for analyzing nonstationary data is compared to that of using a two dimensional spectral representation. In addition, the method of phase shifting the data is examined.