Topic
DFT matrix
About: DFT matrix is a research topic. Over the lifetime, 676 publications have been published within this topic receiving 10548 citations.
Papers published on a yearly basis
1 / 2
Papers
19 May 2012
TL;DR: An automated approach for designing matrix multiplication algorithms based on constructions similar to the Coppersmith-Winograd construction is developed and a new improved bound on the matrix multiplication exponent ω<2.3727 is obtained.
Abstract: We develop an automated approach for designing matrix multiplication algorithms based on constructions similar to the Coppersmith-Winograd construction. Using this approach we obtain a new improved bound on the matrix multiplication exponent ω
1,247 citations
TL;DR: The fast matrix multiplication algorithm by Strassen was used to obtain the triangular factorization of a permutation of any nonsingular matrix of order n in 2.35, i.e. if n > (2.35)5 t 100 as discussed by the authors.
Abstract: The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of order n in 2.35, i.e. if n > (2.35)5 t 100. Strassen uses block LDU factorization (Householder (2, p. 126)) recursively to compute the inverse of a matrix of order m2k by m2k divisions, < (6/5)m37k - m2k multiplications, and < (6/5)(5 + m)m27k - 7(m2k)2 additions. The inverse of a matrix of order n could then be computed by ? (5.64)nlO02 7 arithmetic operations.
376 citations
TL;DR: This article presents computationally simple algorithms that provide substantial refinement of the frequency estimation of tones based on DFT samples without the need for increasing the DFT size.
Abstract: This article presents computationally simple algorithms that provide substantial refinement of the frequency estimation of tones based on DFT samples without the need for increasing the DFT size. When estimating the frequency of a tone, the idea is to estimate the frequency of the spectral peak based on three DFT samples is discussed
275 citations
TL;DR: The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are {1, -1,j, -j} and an eigenvector basis is constructed for the DFT.
Abstract: The principal results of this paper are listed as follows. 1) The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are {1, -1,j, -j} . 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.
238 citations
TL;DR: A unified matrix treatment for the various orderings of the Walsh-Hadamard (WH) functions using a general framework is presented in this article, which clarifies the different definitions of the WH matrix, the various fast algorithms and the reorderings of WH functions.
Abstract: A unified matrix treatment is presented for the various orderings of the Walsh-Hadamard (WH) functions using a general framework. This approach clarifies the different definitions of the WH matrix, the various fast algorithms and the reorderings of the WH functions.
225 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2023 | 3 |
| 2022 | 3 |
| 2021 | 5 |
| 2020 | 15 |
| 2019 | 5 |