THE HYBRID ARCHITECTURE PARALLEL FAST FOURIER

at the target knots yj ∈ [−14 , 1 4 ], j = 1, . . . ,M , where σ = a + ib, a > 0, b ∈ R denotes a complex parameter. Fast Gauss transforms for real parameters σ were developed, e.g., in [15, 8, 9]. In [12], we have specified a more general fast summation algorithm for the Gaussian kernel. Recently, a fast Gauss transform for complex parameters σ with arithmetic complexity O(N log N + M) was int...

Abstract The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating computationally efficient estimate the frequency content time series. Its limitations include: (1) information only provided at discrete steps, so further calculation, for example interpolation, often used to obtain improved estimates peak frequencies and amplitudes; (2) ‘energy' from sp...

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...

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...

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...

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.