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A general construction of Reed-Solomon codes based on generalized discrete Fourier transform [PDF]
Algebraic structures and their applications, 2019 In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co ...
Najme Sahami, Majid Mazrooei
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On the computational complexity of the general discrete fourier transform
Theoretical Computer Science, 1987 The complexity of computing the General Discrete Fourier Transform over group algebras of finite groups is studied. Starting with a short introduction to known results, the complexity gains of a new algorithm derived from Clifford's theorem are discussed.
Thomas Beth
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The Chromatic Fourier Transform [PDF]
Forum of Mathematics, Pi, 2022 We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$ , as well as a certain duality for the $E_n$ -(co)homology of $\pi
Tobias Barthel +3 more
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More on algebraic properties of the discrete Fourier transform raising and lowering operators★
4 open, 2019 In the present work, we discuss some additional findings concerning algebraic properties of the N-dimensional discrete Fourier transform (DFT) raising and lowering difference operators, recently introduced in [Atakishiyeva MK, Atakishiyev NM (2015), J ...
Atakishiyeva Mesuma K. +2 more
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2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, 2006 We first show that the real version of the discrete Fourier transform (called RDFT) can be characterized in the framework of polynomial algebras just as the DFT and the discrete cosine and sine transforms.
Yevgen Voronenko, Markus Püschel
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Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization [PDF]
Journal of Mathematical Physics, 2003 A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of ...
A. Atoyan +15 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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The prime factor non-binary discrete Fourier transform and use of Crystal_Router as a general purpose communication routine [PDF]
Conference on Hypercube Concurrent Computers and Applications, 1988 Giovanni Aloisio +3 more
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Duality theory of $p$-adic Hopf algebras [PDF]
Categories and General Algebraic Structures with Applications, 2021 We show the monoidal functoriality of Schikhof duality, and cultivate new duality theory of $p$-adic Hopf algebras. Through the duality, we introduce two sorts of $p$-adic Pontryagin dualities.
Tomoki Mihara
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