The arithmetic cosine transform: exact and approximate algorithms

Authors:
Renato J. Cintra;Vassil S. Dimitrov
Affiliations:
Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil;Advanced Technology Information Processing Systems Laboratory, University of Calgary, Calgary, AB, Canada
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

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.