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/pm), the unit group of Z/pm. Consider the space L(Z/pm). For m > 1, we defined the space
of M-decimated and Mm−1 -periodic functions on Z/pm with M = pZ/pm and proved that
where W is the orthogonal complement of L0 in L(Z/pm). The space L0 and W are invariant under the action of the Fourier transform F of Z/pm. 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/pm.
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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
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