Application of the cyclotomic Fast Fourier Transform algorithm to the syndrome evaluation problem in classical Reed-Solomon decoders is described. A number of complexity reduction tricks is suggested. Application of the algorithm leads to significant reductions in the complexity of syndrome evaluation. Moreover, automatic generation of the program code implementing the described algorithm is po...

An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to obtain systematically fast Fourier transforms for solvable groups on a quantum computer. The inherent structure of the Hilbert space imposed by the qubit ar...

Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the sub...

This paper presents a framework for synthesizing I/O-efficient out-of-core programs for block recursive algorithms , such as the fast Fourier transform and matrix transpositions. The programs are synthesized from tensor (Kronecker) product representations of algorithms. These programs are optimized for a striped two-level memory model where in the out-of-core data can have block-cyclic distribu...

We develop an approximate algorithm to efficiently calculate the discrete Fourier transform on the rotation group SO(3). Our method needs O ( L3 logL log(1/ε) + log(1/ε)3Q ) arithmetic operations for a degree-L transform at Q nodes free of choice and with desired accuracy ε. Our main contribution is a method that allows to replace finite expansions in Wigner-d functions of arbitrary orders with...

In this study, yttrium aluminum garnet (YAG) was prepared using a facile electrochemical technique. Four samples were synthesized in 0, 20, 40 and 60°C by electrochemical pulse deposition and were then calcined at 1200°C. The effect of synthesis temperature on morphology and structure of YAG was studied using X-ray diffraction, Fourier transform infrared spectroscopy and scanning electron micro...

An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the Discrete Fourier Transform, with the canonical harmonics replaced by a set of cyclic integers computed using only bit-shifts and additions modulo a prime number...

The terms Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) are used to denote efficient and fast algorithms to compute the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT) respectively. The FFT/IFFT is widely used in many digital signal processing applications and the efficient implementation of the FFT/IFFT is a topic of continuous research.

A method is described for validating fast Fourier transforms (FFTs) based on the use of simple input fiinctions whose discrete Fourier transforms can be evaluated in closed form. Explicit analytical results are developed for one-dimensional and two-dimensional discrete Fourier transforms. The analytical results are easily generalized to higher dimensions. The results offer a means for validatin...