  In this paper, we introduce a new class of transform method --- the
arithmetic cosine transform (ACT). We provide the central mathematical
properties of the ACT, necessary in designing efficient and accurate
implementations of the new transform method. The key mathematical tools used in
the paper come from analytic number theory, in particular the properties of the
Riemann zeta function. Additionally, we demonstrate that an exact signal
interpolation is achievable for any block-length. Approximate calculations were
also considered. The numerical examples provided show the potential of the ACT
for various digital signal processing applications.
