Characterization and Construction of Ideal Waveforms
نویسنده
چکیده
Using the finite Zak transform (FZT) periodic polyphase sequences satisfying the ideal cyclic autocorrelation property and sequence pairs satisfying 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 necessary and sufficient condition on pairs of permutation matrices in Zak space such that the corresponding pairs of sequences satisfy the optimum cyclic correlation 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, L an odd integer. An algorithm for constructing ∗-permutations is provided.
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