منابع مشابه
Computation of Convolutions and Discrete Fourier Transforms by Polynomial Transforms
Discrete transforms are introduced and are defined in a ring of polynomials. These polynomial transforms are shown to have the convolution property and can be computed in ordinary arithmetic, without multiplications. Polynomial transforms are particularly well suited for computing discrete two-dimensional convolutions with a minimum number of operations. Efficient algorithms for computing one-d...
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We provide a polymorphic framework for radix-n Fast Fourier Transforms (FFTs) where all known kinds of monomoporhic radix-n algorithms can be obtained by specialization. The framework is mathematically based on the Cooley-Tukey mapping, and implemented as a C++ template meta-program. Avoiding run-time overhead, all specializations are performed statically.
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It is often the case that an operation originally defined for integer orders can be generalized to fractional or even complex orders in a meaningful and useful way. A basic example is the power operation. The ath power of x, denoted by Xa, might be defined as the number obtained by multiplying unity a times with x. Thus X = X X X X X. This definition makes sense only when a is an integer. Howev...
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ژورنال
عنوان ژورنال: Acta Crystallographica
سال: 1952
ISSN: 0365-110X
DOI: 10.1107/s0365110x52002604