A Polymorphic Radix- n Framework for Fast Fourier Transforms
نویسندگان
چکیده
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.
منابع مشابه
Polymorphic Algorithms FFT-Implementations That Share
We denote by a polymorphic radix-n FFT an abstract algorithm scheme that is shared by all radix-n FFT algorithms, similar to the way polymorphic data types share. Given such polymorphic algorithm, particular radix-n algorithms can be obtained by specialization, thus need not be implemented separately. How to accomplish sharing between different radix-n algorithms is not obvious: for example the...
متن کاملRadix-2 Fast Hartley Transform Revisited
A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast DHT algorithms and a multiplication-free fast algorithm for the Hadamard Transform. Key-words Discrete transforms, Hartley transform, Hadamard Transform.
متن کاملFast algorithms of multidimensional discrete nonseparable -wave transforms
Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...
متن کاملA modified split-radix FFT with reduced arithmetic complexity
Recent results by Van Buskirk et al. have broken the record set by Yavne in 1968 for the lowest arithmetic complexity (exact count of real additions and multiplications) to compute a power-of-two discrete Fourier transform. Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the co...
متن کاملFast Multiplication of Polynomials over Arbitrary Rings*
An algorithm is presented that allows to multiply two univariate polynomials of degree no more than n with coefficients from an arbitrary (possibly non-commutative) ring in O(n log(n) log(log n)) additions and subtractions and O(n log(n)) multiplications. The arithmetic depth of the algorithm is O(log(n)). This algorithm is a modification of the Schönhage-Strassen procedure to arbitrary radix f...
متن کامل