Cyclic autocorrelation as a translation invariant transform

The cyclic autocorrelation function (CACF) is compared with the rapid transform (RT) in the speed of computation, the volume of transform, flexibility, number of distinct transforms and noise immunity. It is shown that except for the speed (slower than that of RT) and the volume (equal to that of RT), CACF is superior to RT in the other aspects. When the input patterns are binary sequences, the amplitude bounds on the CACF components are found out. It is also shown that in this case, the CACF components can assume only those values which when added to the length of the sequence result in a multiple of 4.