Properties and relations for hybrid multi-polarity arithmetic-Walsh transform

A novel combined multi-polarity arithmetic-Walsh transform is introduced in this paper. Recursive relationships between higher and lower matrix orders of hybrid multi-polarity arithmetic-Walsh transform are developed. The new multi-polarity transform has a structure similar to that of the multi-polarity Walsh and multi-polarity arithmetic transform matrices, so it combines the computational advantages of these two transforms and has similar fast forward and inverse transforms based on recursive Kronecker product equations.