Results 51 to 60 of about 257,484 (138)
Calculation Scheme Based on a Weighted Primitive: Application to Image Processing Transforms
EURASIP Journal on Advances in Signal Processing, 2007 This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope ...
Gregorio de Miguel Casado +3 more
doaj +2 more sources
The discrete Fourier transform: A canonical basis of eigenfunctions [PDF]
arXiv, 2008 The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the DFT. The transition matrix from the standard basis to the canonical basis defines a novel transform which we call ...
arxiv
Asymptotically Steerable Finite Fourier-Bessel Transforms and Closure under Convolution [PDF]
arXiv, 2023 This paper develops a constructive numerical scheme for Fourier-Bessel approximations on disks compatible with convolutions supported on disks. We address accurate finite Fourier-Bessel transforms (FFBT) and inverse finite Fourier-Bessel transforms (iFFBT) of functions on disks using the discrete Fourier Transform (DFT) on Cartesian grids.
arxiv
Software and Hardware Solutions for Channel Estimation based on Cyclic Golay Sequences [PDF]
Radioengineering, 2016 This paper presents channel estimation methods based on cyclic complementary Golay sequences. First, the conventional Golay correlator is investigated, then a frequency domain approach using Discrete Fourier Transform (DFT) is provided.
B. Csuka, Z. Kollar
doaj
Prime Factor Cyclotomic Fourier Transforms with Reduced Complexity over Finite Fields [PDF]
arXiv, 2010 Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in error correction coding. Hence, reducing the computational complexities of DFTs is of great significance, especially for long DFTs as increasingly longer error control codes are chosen for digital communication and storage systems.
arxiv
Discovering Transforms: A Tutorial on Circulant Matrices, Circular Convolution, and the Discrete Fourier Transform [PDF]
arXiv, 2018 How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In particular, the DFT can be derived as the change of basis that simultaneously diagonalizes all circulant matrices.
arxiv
Fast generalized DFTs for all finite groups [PDF]
arXiv, 2019 For any finite group $G$, we give an arithmetic algorithm to compute generalized Discrete Fourier Transforms (DFTs) with respect to $G$, using $O(|G|^{\omega/2 + \epsilon})$ operations, for any $\epsilon > 0$. Here, $\omega$ is the exponent of matrix multiplication.
arxiv
Recovering Missing Slices of the Discrete Fourier Transform using Ghosts [PDF]
, 2010 The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts. In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT
arxiv +1 more source
Cogent Education, 2015 The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing.
Ludwig Kohaupt
doaj +1 more source
Application of the Weil representation: diagonalization of the discrete Fourier transform [PDF]
arXiv, 2009 We survey a new application of the Weil representation to construct a canonical basis of eigenvectors for the discrete Fourier transform (DFT). The transition matrix from the standard basis to the canonical basis defines a novel transform which we call the discrete oscillator transform (DOT for short).
arxiv