CORRELATION AUTOREGRESSIVE PROCESSES WITH APPLICATION TO HELICOPTER NOISE

This paper introduces a new class of random processes X(t) the autocorrelations Rx(t1, t2) of which satisfy a linear relation of the type Rx(t1, t2)= ∑ j=1 NajRx(t1+τj, t2+τj) for all t1 and t2 in some interval of the time axis. Such random processes are denoted as correlation autoregressive. This class is shown to include the familiar stationary and periodically correlated processes as well as many other, both harmonizable and non-harmonizable, non-stationary processes. When a process is correlation autoregressive for all times and harmonizable, its two-dimensional power spectral density Sx(ω1, ω2) is shown to take a particularly simple form, being non-zero only on lines such that ω1 - ω2 = rk, where the rk s are (not necessarily equally spaced) real roots of a characteristic function. The relationship of such processes to the class of stationary processes is examined. In addition, the application of such processes in the analysis of typical helicopter noise signals is described. © 1990.