We show that the multiple zeta sum: ζ(s1, s2, ..., sd) = ∑ n1>n2>...>nd 1 n1 1 n s2 2 ...n sd d , for positive integers si with s1 > 1, can always be written as a finite sum of products of rapidly convergent series. Perhaps surprisingly, one may develop fast summation algorithms of such efficiency that the overall complexity can be brought down essentially to that of one-dimensional summation. ...

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...

a School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia e-mail: [email protected] 1 Department of Mathematics, Hasanuddin University, KM 10 Tamalanrea Makassar, Indonesia b Department of Applied Physics, University of Fukui, 910-8507 Fukui, Japan e-mail: [email protected] c Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japa...

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...

| The windowed Fourier transform of a time signal is considered, as well as a way to reconstruct the signal from a suuciently densely sampled version of its windowed Fourier transform using a Gabor representation; following Gabor, sampling occurs on a two-dimensional time-frequency lattice with equidistant time intervals and equidistant frequency intervals. For suuciently dense sampling, the sy...