applied mathematics, a DFT matrix is a square matrix as an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied...

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

\\v_{n-1}\end{bmatrix}}.} The matrix for this transformation is called the DFT matrix. Similarly, the matrix notation for the inverse Fourier transform...

algorithm that computes the discrete Fourier transform (DFT) of prime sizes by re-expressing the DFT as a cyclic convolution (the other algorithm for FFTs...

discrete Fourier transform is defined by a specific Vandermonde matrix, the DFT matrix, where the x i {\displaystyle x_{i}} are chosen to be nth roots...

factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O ( n...

{\displaystyle {\mathcal {F}}} ⁠ be the Discrete Fourier Transform (DFT) matrix; then C = F ⋅ Σ ⋅ F ∗ , C + = F ⋅ Σ + ⋅ F ∗ . {\displaystyle...

discrete Fourier transform (DFT) of an arbitrary composite size N = N 1 N 2 {\displaystyle N=N_{1}N_{2}} in terms of N1 smaller DFTs of sizes N2, recursively...

non-linear power systems. It can be seen that the transformation matrix A above is a DFT matrix, and as such, symmetrical components can be calculated for any...

are coefficients of a discrete Fourier transform (DFT) matrix. Each row or column of the DFT matrix provides an orthogonal CI spreading code which spreads...

the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating...

new variants. Each multidimensional DFT computation is expressed in matrix form. The multidimensional DFT matrix, in turn, is disintegrated into a set...

In linear algebra, a circulant matrix is a square matrix in which all rows are composed of the same elements and each row is rotated one element to the...

the unitary DFT, note that as defined above D F T . D F T ∗ = S {\displaystyle DFT.DFT^{*}=S} , where S {\displaystyle S} is a diagonal matrix consisting...

Beevers–Lipson strip Constant-Q transform Discrete Fourier transform DFT matrix Fast Fourier transform Fourier integral operator Fourier inversion theorem...

as a unitary matrix (or quantum gate) acting on quantum state vectors, where the unitary matrix F N {\displaystyle F_{N}} is the DFT matrix F N = 1 N [...

Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate...

outwards to infinity in all four directions. This is analogous to the DFT matrix but, in this case, is continuous and infinite in extent. The value of...

transform, consider the DWT and DFT of the following sequence: (1,0,0,0), a unit impulse. The DFT has orthogonal basis (DFT matrix): [ 1 1 1 1 1 − i − 1 i 1...

first column element of the matrix is denoted by ( H n ) 0 , 0 {\textstyle (H_{n})_{0,0}} . H1 is precisely the size-2 DFT. It can also be regarded as...

{\displaystyle m} -th column of the N {\displaystyle N} -point inverse DFT matrix. Intuitively, the computational complexity growing with N {\displaystyle...

spectrum Discrete Fourier series Non-uniform discrete Fourier transform DFT matrix Entropy influence conjecture Fast cosine transform Fast Fourier transform...

character table for general cyclic groups is (a scalar multiple of) the DFT matrix. Another example is the character table of S 3 {\displaystyle S_{3}} :...

accordingly. Clifford algebra Generalizations of Pauli matrices DFT matrix Circulant matrix Weyl, H. (1927). "Quantenmechanik und Gruppentheorie". Zeitschrift...

{{\tfrac {2}{N-1\,}}\,}}} , makes the DCT-I matrix orthogonal but breaks the direct correspondence with a real-even DFT. The DCT-I is exactly equivalent (up...

A complex Hadamard matrix is any complex N × N {\displaystyle N\times N} matrix H {\displaystyle H} satisfying two conditions: unimodularity (the modulus...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

{\displaystyle \Omega } is non-zero. Equivalently, all submatrices of a DFT matrix of prime length are invertible. In signal processing, the theorem was...

Binomial transform Discrete Fourier transform, DFT Fast Fourier transform, a popular implementation of the DFT Discrete cosine transform Modified discrete...

5-step FFT, 6-step FFT, etc. The Bailey FFT is typically used for computing DFTs of large datasets, such as those used in scientific and engineering applications...