  Arithmetic complexity has a main role in the performance of algorithms for
spectrum evaluation. Arithmetic transform theory offers a method for computing
trigonometrical transforms with minimal number of multiplications. In this
paper, the proposed algorithms for the arithmetic Fourier transform are
surveyed. A new arithmetic transform for computing the discrete Hartley
transform is introduced: the Arithmetic Hartley transform. The interpolation
process is shown to be the key element of the arithmetic transform theory.
