A new class of shift-invariant operators

This letter proposes a class of operators with a shift invariance property. These operators are derived from two-dimensional (2-D) complex moment invariants based on the observation that there is a duality between rotation invariance and shift invariance. A general form of the shift invariants belonging to this class is presented, which shows that polyspectral invariants such as the power spectrum and the bispectrum are members of the class. Methods for computing shift invariants for one-dimensional (1-D) and 2-D signals are also presented. The examples given in the paper suggest that the higher order operators can preserve the original signal waveform better than autocorrelation.