Algorithms of Two-Dimensional Discrete Orthogonal Transforms Realized in Hamilton–Eisenstein Codes

We consider a set of algorithms of two-dimensional discrete orthogonal transforms of an $(N\times N)$ array for $N=3^r$, namely, Fourier transforms of real and complex input, discrete cosine transform. In all cases we obtain lesser multiplicative complexity compared to the known realizations. This is achieved by means of interpretating data as elements of the quaternion algebra, these elements, in turn, being represented in a form concordant with the structure of a proposed algorithm.