Multiplicative Characters and the FFT
Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)
Fix an odd prime p throughout this chapter, and set U(m) ≡ U(Z/p m ), the unit group of Z/p m . Consider the space L(Z/p m ). For m > 1, we defined the space
of M-decimated and M m−1 -periodic functions on Z/p m with M = p Z /p m and proved that
where W is the orthogonal complement of L0 in L(Z/p m ). The space L0 and W are invariant under the action of the Fourier transform F of Z/p m . The action of F on L0 was described in the preceeding chapter. We will now take up the action of F on W. For this purpose, we introduce the multiplicative characters on the ring Z/p m .
KeywordsOrthonormal Basis Discrete Fourier Transform Unit Group Orthogonal Basis Orthogonal Complement
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- Winograd, S. Arithmetic Complexity of Computations, CBMS Regional Conf. Ser. in Math. Vol. 33, Soc. Indus. Appl. Math., Philadelphia, 1980.Google Scholar
© Springer Science+Business Media New York 1989