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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17 citations
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12 Jun 1998
TL;DR: In this article, the authors employ a texture filter in a graphics processor to perform a transform such as a Fast Fourier Transform (FFT), which can include an array of linear interpolators.
Abstract: The method and apparatus employ a texture filter in a graphics processor to perform a transform such as, for example, a Fast Fourier Transform. The texturizer can include an array of linear interpolators. The architecture reduces the computational complexity of the transform processes.
17 citations
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TL;DR: In this article, the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternions functions was derived using properties of convolution, and the correlation was further extended to the other functions.
Abstract: In this paper we introduce convolution theorem for the Fourier transform (FT) of two complex functions. We show that the correlation theorem for the FT can be derived using properties of convolution. We develop this idea to derive the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternion functions.
17 citations
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TL;DR: A novel opto-digital method of color image encryption which utilizes compound chaotic mappings, the reality preserving fractional Hartley transformation and piecewise linear chaotic map for substitution, optical processing and permutation of image pixels, respectively proves its better efficacy as compared to other similar state-of-the-art schemes.
Abstract: We propose a novel opto-digital method of color image encryption which utilizes compound chaotic mappings, the reality preserving fractional Hartley transformation and piecewise linear chaotic map for substitution, optical processing and permutation of image pixels, respectively. The image to be encrypted initially undergoes a chaos-based substitution in the spatial domain through the compound chaotic maps followed by a transformation to the combined time–frequency domain using the fractional Hartley transform. A reality preserving version of the fractional Hartley transform is used to eliminate the complexity associated with transform coefficients. Optical transformation of the image, in the fractional Hartley domain, is followed by a permutation through piecewise linear chaotic maps. Due to the intertwined application of optical transformation and chaos-based substitution and permutation processes, the proposed image encryption scheme possesses higher security. The input parameters (initial conditions, control parameters, and number of iterations) of chaotic maps along with fractional orders of the fractional Hartley transform collectively form the secret keys for encryption/decryption. The proposed scheme is a lossless and symmetric encryption scheme. The level of security provided in terms of high sensitivity to keys, resistivity to brute-force attack, classical attacks, differential attacks, entropy attack, noise and occlusion attack along with the elimination of complex coefficients proves its better efficacy as compared to other similar state-of-the-art schemes.
17 citations
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TL;DR: Fast algorithms for computing generalized discrete Hartley transforms in a sliding window are proposed, based on second-order recursive relations between subsequent local transform spectra.
Abstract: Fast algorithms for computing generalized discrete Hartley transforms in a sliding window are proposed. The algorithms are based on second-order recursive relations between subsequent local transform spectra. New efficient inverse algorithms for signal processing in a sliding window are also presented. The computational complexity of the algorithms is compared with that of known fast discrete Hartley transforms and running recursive algorithms
17 citations