Families of 2D arrays can be constructed where each array has perfect autocorrelation, and the cross-correlation between any pair of family members is optimally low. We exploit equivalent Hadamard matrices to construct many families of p p × p arrays, where p is any 4k-1 prime. From these families, we assemble extended families of arrays with members that exhibit perfect autocorrelation and nex...

The autocorrelation function of the all-pole filter given by conventional linear prediction (LP) matches exactly the autocorrelation function of the input signal between indices 0 and m, when the prediction order equals m. A recently developed technique, Weighted Sum of the Line Spectrum Pair (WLSP), yields a stable all-pole filter of order m, whose autocorrelation function coincides to that of...

Elementary algebraic constraints on the form of an autocorrelation function C(t(w)+tau,t(w)) rule out some two-time scalings found in the literature as possible long-time asymptotic forms. The same argument leads to the realization that two usual definitions of many-time scale relaxation for aging systems are not equivalent.