Frank signal and its generalizations (Q1347395)

The Frank signal (FS) is a well-known tool in coding and signal theory. It is introduced in the following way. First, one considers a Fourier matrix of rank \(n\). If its rows are arranged in order, then a one-dimensional discrete signal of length \(N= n^2\) is obtained. More precisely, an FS is the restriction on \(\{0,N-1\}\) of a discrete periodic signal of period \(N\), contained in \(S_{dp}(N)\), the space of discrete periodic signals of period \(N\). An FS possesses two specific properties: (1) all its samples are of equal moduli and (2) the set of cyclic shifts of an FS constitute a basis in \(S_{dp}(N)\). The authors introduce two new sets of signals derived from FS ones. The first class possesses the same properties of FS, whereas the second one possesses a new property; specifically, the basis is composed of the \(n\)-adic shifts. The paper is of interest for researchers in the CDMA domain.