Topic
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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06 Nov 2012
TL;DR: The literature review of the Natural transform and existing definitions and connections to the Laplace and Sumudu transforms are discussed in this article, where the relation of Bessel's function to Natural transform is defined.
Abstract: The literature review of the Natural transform and the existing definitions and connections to the Laplace and Sumudu transforms are discussed in this communication. Along with the complex inverse Natural transform and Heaviside's expansion formula, the relation of Bessel's function to Natural transform (and hence Laplace and Sumudu transforms) are defined.
57 citations
TL;DR: A joint space-wavenumber localized quaternion S transform is presented in this study for a simultaneous determination of the local color image spectra using a two-dimensional Gaussian localizing window that scales with wavenumbers.
57 citations
16 Aug 2010
TL;DR: An orthogonal multiplication-free transform of order that is an integral power of two by an appropriate extension of the well-known fourthorder integer discrete cosine transform is proposed and an efficient algorithm for its fast computation is developed.
Abstract: In this paper, we propose an orthogonal multiplication-free transform of order that is an integral power of two by an appropriate extension of the well-known fourthorder integer discrete cosine transform. Moreover, we develop an efficient algorithm for its fast computation. It is shown that the computational and structural complexities of the algorithm are similar to that of the Hadamard transform. By applying the proposed transform to image compression, we show that it outperforms the existing transforms having complexities similar to that of the proposed one.
57 citations
TL;DR: In this article, the authors derived the linear and parabolic [tau]-p transform formulas for the continuous function domain and showed that the derived formulas are identical to the DRT equations obtained by other researchers.
Abstract: New derivations for the conventional linear and parabolic [tau]-p transforms in the classic continuous function domain provide useful insight into the discrete [tau]-p transformations. For the filtering of unwanted waves such as multiples, the derivation of the [tau]-p transform should define the inverse transform first, and then compute the forward transform. The forward transform usually requires a p-direction deconvolution to improve the resolution in that direction. It aids the wave filtering by improving the separation of events in the [tau]-p domain. The p-direction deconvolution is required for both the linear and curvilinear [tau]-p transformations for aperture-limited data. It essentially compensates for the finite length of the array. For the parabolic [tau]-p transform, the deconvolution is required even if the input data have an infinite aperture. For sampled data, the derived [tau]-p transform formulas are identical to the DRT equations obtained by other researchers. Numerical examples are presented to demonstrate event focusing in [tau]-p space after deconvolution.
56 citations
TL;DR: A new method for optical image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform.
56 citations