Properties of the Zhang-Hartley spectrum of patterns

A relationship is developed between the 2-D Chrestenson transform and the 2-D Zhang-Hartley transform so that the computation of the Chrestenson spectrum can be reduced to real arithmetic. It is proved that the situation is similar to the well-known 1-D case, apart from some necessary permutations. Moreover, if the original function satisfies a specific decomposition condition, the relationship may be extended from the 1-D case to the 2-D case in a canonical way