Let us define the q-point DFT of a sequence z as follows:
FSC is a complex sequence of a unit envelope with DFT of a unit envelope.
We found that FSCs have another remarkable property, e.g., applying to an FSC the DFT twice yields the same FSC. The proof is numerical. Specifically, a Matlab script was written that, for given q and p, it computes several functions of p and q. The first function is:
In Equation (C.2), gcd stands for the greatest common divisor of two natural numbers, and % denotes computing a remainder of division one integer by another. The function r equals 1 for mutually prime p and q ...