Discrete Fourier transform over a ring information

In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function...

domain; it is a decomposition of a function into sinusoids of different frequencies; in the case of a Fourier series or discrete Fourier transform, the sinusoids...

the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...

analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key...

function whose Fourier series diverges everywhere. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's...

the case if some other transform, such as the more widespread discrete cosine transform, had been used. Discrete wavelet transform has been successfully...

dt} where s is a complex number. It is related to many other transforms, most notably the Fourier transform and the Mellin transform. Formally, the Laplace...

mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include...

frequency divisions of the FFT (fast Fourier transform) which uses the same basis functions as DFT (Discrete Fourier Transform). It is also important to note...

mathematics which have discrete versions, such as discrete calculus, discrete Fourier transforms, discrete geometry, discrete logarithms, discrete differential...

the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 18 at DTFT § Properties.) A discrete convolution...

Fourier transform can be described in a setting closer to the signal processing. Fourier transform over finite fields The discrete Fourier transform of...

quantum Fourier transform is the quantum analogue of the discrete Fourier transform, and is used in several quantum algorithms. The Hadamard transform is also...

aspects of the Fourier transform of a function. Whereas Fourier analysis decomposes a function defined on a compact set into the discrete spectrum of the...

{\displaystyle {\tilde {\rho }}} is closely related to Fourier transform on finite groups. For a more general field K, whenever the characteristic of K...

work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments...

Weierstrass transform. By contrast, convolving by a circle (i.e., a circular box blur) would more accurately reproduce the bokeh effect. Since the Fourier transform...

important in number theory, the theory of group characters, and the discrete Fourier transform. Roots of unity can be defined in any field. If the characteristic...

The Fourier transform of a purely real-valued even function is real and even. (see Fourier analysis § Symmetry properties) The Fourier transform of a purely...

might transform from the time domain to a frequency or s domain; or from discrete time (n) to frequency or z domains. Systems also can be transformed between...

\left\{\mathbf {X_{k}} \right\}:=X_{0},X_{1},\ldots ,X_{N-1},} be its discrete Fourier transform. Denote by ‖ x ‖ 0 {\displaystyle \|x\|_{0}} the number of non-zero...

{\displaystyle [-1,1]} ). This may also be seen by applying the Fourier transform. Note that the discrete Laplacian on an infinite grid has purely absolutely continuous...

theorems (finite groups) Brauer–Cartan–Hua theorem (ring theory) Bregman–Minc inequality (discrete mathematics) Brianchon's theorem (conics) British flag...

with the theta functions. If a, b, c, are integers (in the ring Z) then one has the discrete Heisenberg group H3(Z). It is a non-abelian nilpotent group...