CHARACTERIZATION AND CONSTRUCTION OF IDEAL WAVEFORMS

Using the finite Zak transform (FZT) periodic polyphase sequences satisfying the ideal cyclic autocorrelation property and sequence pairs satis- fying the optimum cyclic cross correlation property are constructed. The Zak space correlation formula plays a major role in the design of signals having special correlation properties. Sequences defined by permutation matrices in Zak space always satisfy the ideal cyclic autocorrelation property. A neces- sary and sufficient condition on pairs of permutation matrices in Zak space such that the corresponding pairs of sequences satisfy the optimum cyclic cor- relation property is derived. This condition is given in terms of a collection of permutations, called ∗-permutations. The development is restricted to the case N = L 2 , L an odd integer. An algorithm for constructing ∗-permutations is provided.