The novel generating algorithm and properties of hybrid-P-ary generalized bridge functions

In this paper, we develop novel non-sine functions, named hybrid-P-ary generalized bridge functions, based on the copy and shift methods. The generating algorithm of hybrid-P-ary generalized bridge functions is introduced based on the hybrid-P-ary generalized Walsh function’s copy algorithm. The main property, product property, is also discussed. This function may be viewed as the generalization of the theory of bridge functions. And a lot of non-sine orthogonal functions are the special subset of these novel functions. The hybrid-P-ary generalized bridge functions can be used to search many unknown non-sine functions by defining different parameters.