Fast Fourier Optimization: Sparsity Matters
, 2012 Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier transform} (fft)
C. Papadimitriou +19 more
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Generalizing the discrete fourier transform
Discrete Mathematics, 1985 The author defines the generalized discrete Fourier transform (GDFT (\({\mathbb{F}}G))\) as being the mapping \(\sigma_ G: {\mathbb{F}}G\to A_ 1\oplus...\oplus A_ s\) which decomposes the semisimple group algebra \({\mathbb{F}}G\) into simple Wedderburn components \(A_ i\), \(i=1,...,s\).
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A Fourier based algorithm to estimate the period of a sampled signal
Visión Electrónica, 2017 Given a sampled signal, in general, is not possible to compute its period, but just an approximation. We propose an algorithm to approximate the period, based on the Discrete Fourier Transform. If that transformation uses data length for multiples of the
José Danilo Rairán Antolines
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On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity [PDF]
, 2009 It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform.
Allaway Wm R +21 more
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Discrete Fourier transform associated with generalized Schur polynomials
Proceedings of the American Mathematical Society, 2018 We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this recovers the sixteen classic discrete sine- and cosine transforms DST-1,...,DST-8 and DCT-1,...,DCT-8, as well as ...
J. F. van Diejen, E. Emsiz
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Coherent optical implementations of the fast Fourier transform and their comparison to the optical implementation of the quantum Fourier transform [PDF]
, 2013 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
Birch, Philip M +2 more
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Matrix-Vector Based Fast Fourier Transformations on SDR Architectures [PDF]
Advances in Radio Science, 2008 Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast ...
Y. He +3 more
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MODIFIED METHOD FOR SIGNAL DELAY ESTIMATION USING ROBUST DFT
Радіоелектронні і комп'ютерні системи, 2019 Modified method for estimating delay and direction of arrival for random wideband signals received by two displaced sensors and corrupted by non-Gaussian noise is designed.
Вячеслав Алексеевич Олейник +1 more
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Numerical Approximation of Probability Mass Functions Via the Inverse Discrete Fourier Transform
, 2012 First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging.
Warr, Richard L.
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Detection of variable frequency signals using a fast chirp transform [PDF]
, 2000 The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of ...
Jenet, F. A., Prince, T. A.
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