Optimizing stream programs using linear state space analysis
Proceedings of the 2005 international conference on Compilers, architectures and synthesis for embedded systems
Factorizations and representations of the backward second-order linear recurrences
Journal of Computational and Applied Mathematics
Harmonic Analysis of Finite Lamplighter Random Walks
Journal of Dynamical and Control Systems
Systematic construction of real lapped tight frame transforms
IEEE Transactions on Signal Processing
IWDW'10 Proceedings of the 9th international conference on Digital watermarking
Improvement of the Discrete Cosine Transform calculation by means of a recursive method
Mathematical and Computer Modelling: An International Journal
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It is known that the discrete Fourier transform (DFT) used in digital signal processing can be characterized in the framework of the representation theory of algebras, namely, as the decomposition matrix for the regular module ${\mathbb{C}}[Z_n] = {\mathbb{C}}[x]/(x^n - 1)$. This characterization provides deep insight into the DFT and can be used to derive and understand the structure of its fast algorithms. In this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of Chebyshev polynomials. Then we derive most of their known algorithms by pure algebraic means. We identify the mathematical principle behind each algorithm and give insight into its structure. Our results show that the connection between algebra and digital signal processing is stronger than previously understood.