On Logical and Arithmetic Autocorrelation Functions

Algorithmic properties of logical/dyadic and arithmetic autocorrelation functions (LAF, AAF) of wide-sense stationary processes are investigated. It is shown that the LAF to AAF transformation and vice versa, denoted by LAF ⇄ AAF, can be computed by fast algorithms. These algorithms require N/2(log2 N - 1) additions/subtractions, N divisions/shifts, and approximately N storage locations. It is shown that the LAF ⇄ AAF algorithm enables one to estimate the AAF (and hence the Fourier power density spectrum) appreciably faster than by conventional methods. Illustravie examples are included.