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Complex symmetric functions and generalized discrete Fourier transform
Rendiconti del Circolo Matematico di Palermo, 1996Let \(\Omega^{[k]}\) be the class of holomorphic functions \(f(z)\) of the complex variable \(z\) which satisfy, with respect to the \(s\)th root of unity \(\varepsilon_k\), \(k=0,1,\dots,n-1\), the symmetry property \(f(\varepsilon_1z)=\varepsilon_kf(z)\).
Rinaldi, Lucia, Ricci, Paolo Emilio
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The generalized discrete Fourier transform in rings of algebraic integers
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1980The discrete Fourier transform (DFT) in rings of residues of algebraic integers is investigated and some new transforms of low bit-operation complexity are introduced. For a given candidate transform with a DFT structure defined in a ring of residues of algebraic integers conditions are formulated which assure that this transform is a generalized DFT ...
Dubois, Eric +1 more
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Discrete Fourier transform in arbitrary dimensions by a generalized Beevers–Lipson algorithm
Acta Crystallographica Section A Foundations of Crystallography, 2000The Beevers-Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in n-dimensional space would lead to n nested loops over the n coordinates, respectively, and different computer code is required for each dimension.
, Schneider, , van Smaalen S
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Mathematical background for generalized, partial, and incomplete discrete Fourier transforms
ICASSP '80. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005We develop the theory of generalized discrete Fourier transforms (GDFTs) from the point of view of the Chinese Remainder Theorem (CRT). We give a new definition of GDFT, and apply it to the construction of multidimensional convolution algorithms which require significantly fewer multiplications and data transfer operations than the usual methods.
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Fast Discrete Fourier Transform on Generalized Sparse Grids
2014In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational
Michael Griebel, Jan Hamaekers
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Evaluation of two-dimensional discrete Fourier transforms via generalized FFT algorithms
ICASSP '81. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005In this paper two-dimensional fast Fourier transforms (FFT's) are expressed as special cases of a generalization of the one-dimensional Cooley-Tukey algorithm. This generalized algorithm allows the efficient evaluation of discrete Fourier transforms (DFT's) of rectangularly sampled sequences, hexagonally sampled sequences and arbitrary periodically ...
Theresa C. Speake, Russell M. Mersereau
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A power-aware IP core generator for the one-dimensional discrete Fourier transform
2004 IEEE International Symposium on Circuits and Systems (ISCAS), 2004This paper presents a power-aware IP core generator for the 1D DFT design. We optimize the proposed DFT IP design both in algorithm and architecture levels for achieving low hardware complexity. In algorithm level, we first use radix-2/sup c/ algorithm to split a length-N DFT into multiple length-N/2/sup c/ DFTs for facilitating computation sharing ...
Chih-Da Chien +3 more
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On an application of a generalization of the discrete Fourier transform to short time series
Canadian Journal of Physics, 2001A generalization of the discrete Fourier transform (DFT) is discussed. This generalization or GDFT provides a smooth interpolation between the points of the DFT. The GDFT of a sinusoidal function in a finite time window is (a) described in detail and (b) shown to coincide (aside from a simple scaling constant) with the corresponding Fourier transform,
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Symbolic network function generation via discrete Fourier transform
IEEE Transactions on Circuits and Systems, 1984Summary: A new method of symbolic network function generation is presented. The method is based upon the theory of the discrete Fourier transform and not restricted in its application to any particular type of network analysis or network configuration. It is particularly attractive when the number of symbolic variables to be handled is not large.
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