Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: The definition of convolution on the ball is studied in this context, showing explicitly how translation on the radial line may be viewed as convolution with a shifted Dirac delta function.
Abstract: We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as convolution with a shifted Dirac delta function. We review the exact Fourier-Laguerre wavelet transform on the ball, coined flaglets, and show that flaglets constitute a tight frame.
21 citations
TL;DR: In this article, a column vector can be multiplied by the inverse of a Toeplitz-plus-Hankel matrix with the help of 6 Hartley transforms plus O(n) operations.
Abstract: Representations for inverses of Toeplitz-plus-Hankel matrices and more general Bezoutians involving only discrete Hartley transforms and diagonal matrices are presented. Using these representations a column vector can be multiplied by the inverse of a Toeplitz-plus-Hankel matrix with the help of only 6 Hartley transforms plus O(n) operations. This complexity estimate is significantly better than previous ones.
21 citations
TL;DR: A single-channel color image encryption algorithm by combining fractional Hartley transform (FRHT) with vector operation that makes the proposed encryption algorithm more secure than the linear color imageryption algorithm based on the double random phase encoding in FRHT.
Abstract: A single-channel color image encryption algorithm is proposed by combining fractional Hartley transform (FRHT) with vector operation. The original color image is decomposed into RGB components and the G and B components are encrypted into two phase-only masks ? G and ? B with vector operation, respectively. The R, ? G and ? B are transformed by FRHT and vector operation twice to obtain amplitude, random phase and decryption phase key. The new amplitude combined with the random phase is transformed by FRHT once more and then the result is scrambled by the chaotic scrambling to strengthen the security of the algorithm. The private phase key is dependent on the original image, which makes the proposed encryption algorithm more secure than the linear color image encryption algorithm based on the double random phase encoding in FRHT. Simulation results demonstrate the security and effectiveness of the proposed algorithm.
21 citations
TL;DR: A new parallel approach for computing the running DHT and DWT's is proposed by establishing the relationship between the running discrete Hartley transform, the discrete W transforms, and the LMS algorithm.
Abstract: The computation of block-based discrete orthogonal transforms using the adaptive least-mean-square (LMS) algorithm has been studied in literature. The authors extend this work by establishing the relationship between the running discrete Hartley transform (DHT), the discrete W transforms (DWT's), and the LMS algorithm. As a result a new parallel approach for computing the running DHT and DWT's is proposed.
21 citations
TL;DR: In this paper, the Hartley transform is used to calculate transients and nonsinusoidal waveshape propagation in electric power systems, and a general introduction to the use of Hartley transforms for electric circuit analysis is presented.
Abstract: Because the Fourier transform causes the convolution operation to become a simple complex product, it has been used to solve power system problems. A similar convolution property of the Hartley transform is used to calculate transients and nonsinusoidal waveshape propagation in electric power systems. The importance of this type of calculation relates to the impact of loads, particularly electronic loads, whose demand currents are nonsinusoidal. An example is given in which the Hartley transform is used to assess the impact of an electronic load with a demand which contains rapidly changing current. The authors also present a general introduction to the use of Hartley transforms for electric circuit analysis. A brief discussion of the error characteristics of discrete Fourier and Hartley solutions is presented. Because the Hartley transform is a real transformation, it is more computationally efficient then the Fourier or Laplace transforms. >
21 citations