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Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.


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TL;DR: Considering paired transforms, this work analyzes simultaneously the splitting of the multidimensional Fourier transform as well as the presentation of the processed multiddimensional signal in the form of the short one-dimensional "signals", that determine such splitting.
Abstract: A concept of multipaired unitary transforms is introduced. These kinds of transforms reveal the mathematical structure of Fourier transforms and can be considered intermediate unitary transforms when transferring processed data from the original real space of signals to the complex or frequency space of their images. Considering paired transforms, we analyze simultaneously the splitting of the multidimensional Fourier transform as well as the presentation of the processed multidimensional signal in the form of the short one-dimensional (1-D) "signals", that determine such splitting. The main properties of the orthogonal system of paired functions are described, and the matrix decompositions of the Fourier and Hadamard transforms via the paired transforms are given. The multiplicative complexity of the two-dimensional (2-D) 2/sup r//spl times/2/sup r/-point discrete Fourier transform by the paired transforms is 4/sup r//2(r-7/3)+8/3-12 (r>3), which shows the maximum splitting of the 5-D Fourier transform into the number of the short 1-D Fourier transforms. The 2-D paired transforms are not separable and represent themselves as frequency-time type wavelets for which two parameters are united: frequency and time. The decomposition of the signal is performed in a way that is different from the traditional Haar system of functions.

71 citations

Journal ArticleDOI
TL;DR: Two new sampling formulae for reconstructing signals that are band limited or time limited in the fractional Fourier transform sense are obtained, each taken at half the Nyquist rate.

70 citations

Journal ArticleDOI
TL;DR: The Data Encryption Standard (DES) can be regarded as a nonlinear feedback shift register (NLFSR) with input and the properties of the S-boxes of DES under the Fourier transform, Hadamard transform, extended Hadamards transform, and the Avalanche transform are investigated.
Abstract: The Data Encryption Standard (DES) can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under the Fourier transform, Hadamard transform, extended Hadamard transform, and the Avalanche transform are investigated. Two important results about the S-boxes of DES are found. The first result is that nearly two-thirds of the total 32 functions from GF (2/sup 6/) to GF(2) which are associated with the eight S-boxes of DES have the maximal linear span G3, and the other one-third have linear span greater than or equal to 57. The second result is that for all S-boxes, the distances of the S-boxes approximated by monomial functions has the same distribution as for the S-boxes approximated by linear functions. Some new criteria for the design of permutation functions for use in block cipher algorithms are discussed.

70 citations

Journal ArticleDOI
TL;DR: The method is found to be suitable for the processing of digital fault recorder data to identify synchronous machine parameters and tested for noise corruption likely to be found in measurements.
Abstract: This paper presents a novel alternative to estimate armature circuit parameters of large utility generators using real time operating data. The proposed approach uses the Hartley series for fitting operating data (voltage and currents measurements). The essence of the method is the use of linear state estimation to identify the coefficients of the Hartley series. The approach is tested for noise corruption likely to be found in measurements. The method is found to be suitable for the processing of digital fault recorder data to identify synchronous machine parameters.

70 citations

Journal ArticleDOI
TL;DR: In this paper, the Sumudu transform was applied to solve a one-dimensional wave equation having a singularity at the initial conditions, and the authors also applied this transform to the distribution of the wave equation.
Abstract: In this paper, we generalize the concepts of a new integral transform, namely the Sumudu transform, to distributions and study some of their properties. Further, we also apply this transform to solve one-dimensional wave equation having a singularity at the initial conditions.

68 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202311
202230
202110
202014
201915
201820