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The multiple-parameter discrete fractional Fourier transform
IEEE Signal Processing Letters, 2006The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this letter, we extend the DFRFT to have N order parameters, where N is the number of the input data points.
Pei, Soo-Chang, Hsue, Wen-Liang
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The discrete multiple-parameter fractional Fourier transform
Science China Information Sciences, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Lang, Ran Tao 0003, Yue Wang 0001
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Multiple Beam Fourier Transform Spectroscopy
Fourier Transform Spectroscopy and Hyperspectral Imaging and Sounding of the Environment, 2015Fourier processing has previously been applied to multiple-beam interferograms. However, Fourier theory is only strictly valid in the two-beam limit. We present a solution method for spectral recovery from multi-beam interferograms.
Christopher W. Miller +2 more
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The poorman's transform: approximating the Fourier transform without multiplication
IEEE Transactions on Signal Processing, 1993A time-domain to frequency-domain transformation for sampled signals which is computed with only additions and trivial complex multiplications is described. This poorman's transform is an approximation to the usual Fourier transform, obtained by quantizing the Fourier coefficients to the four values (+or-1, +or-j), and is especially useful when ...
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Matrix Multiplication and Fast Fourier Transforms
Bell System Technical Journal, 1968Factoring a matrix and multiplying successively by the factors can sometimes be used to speed up matrix multiplications. This is, in fact, the trick which creates the fantastic gains of the fast Fourier transform.
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Fourier Transforms of Multiplicative Convolutions
2017We consider \(\mathbf{P}\)-adic Fourier transform introduced by N.Y. Vilenkin that generalizes famous Walsh transform and \(\mathbf{P}\)-adic convolution of functions defined on \(\mathbb R_+\), where \(\mathbf{P}=\{p_j\}_{j=1}^\infty \subset \mathbb N\) and \(2\le p_j\le N\) for all j.
B. I. Golubov, S. S. Volosivets
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Weighted integrability of multiplicative Fourier transforms
Proceedings of the Steklov Institute of Mathematics, 2010The paper extends some results concerning the classical Fourier transform to the multiplicative Fourier transform (MFT) . In particular, the authors give conditions which ensure that a contraction of an MFT is also an MFT, criteria for determining whether a sufficiently smooth function with nonnegative MFT belongs to \(H^\omega\) or \(h^\omega\) (where
Volosivets, S. S., Golubov, B. I.
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Multiple Fourier transform generation for coherent optical correlators
Applied Optics, 1990An interferometrically generated off-axis holographic optical element images a laser diode light source to a 3 x 5 point array through 10 cm of glass. The element also reduces the elliptical beam cross section from 3:1 to 1.5:1.
J, Upatnieks +3 more
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An Implementation of Multiple and Multivariate Fourier Transforms on Vector Processors
SIAM Journal on Scientific Computing, 1995This is the multiple and multivariate extension of the one-dimensional case treated recently by the same author [Numer. Math. 68, No. 4, 507-547 (1994; Zbl 0808.65145)]. The present algorithms share the properties of the one-dimensional case: they are practically in-place, data access is mainly in stride 1 and they are well suited for vector-parallel ...
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Multiple radix fast fourier transformation based on number theoretic transforms
Journal of the Franklin Institute, 1991Discrete Fourier transform on a prime number of samples is computed by means of the multiple radix fast Fourier transformation based on number theoretic transforms. This proposal is efficient in the transformation of samples \(P=2^{k1}3^{k2}5^{k3}\) with arbitrary integers ki \((i=1,2,3)\).
Lawrence, Brooks +2 more
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