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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TL;DR: The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT.
Abstract: This paper presents a novel approach to the Fourier analysis of multichannel time series. Orthogonal matrix functions are introduced and are used in the definition of multichannel Fourier series of continuous-time periodic multichannel functions. Orthogonal transforms are proposed for discrete-time multichannel signals as well. It is proven that the orthogonal matrix functions are related to unitary transforms (e.g., discrete Hartley transform (DHT), Walsh-Hadamard transform), which are used for single-channel signal transformations. The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT. Therefore, fast algorithms for their computation can be easily constructed. Simulations on the use of discrete multichannel transforms on color image compression have also been performed.
17 citations
TL;DR: A new encryption scheme using phase masks based on devil’s vortex Fresnel lens (DVFL) has been presented in this study and is evaluated for its robustness against the occlusion and noise attacks.
Abstract: A new encryption scheme using phase masks based on devil’s vortex Fresnel lens (DVFL) has been presented in this study. The encryption is performed using fractional Hartley transform (FRHT) in both spatial and frequency domains. Prior to subjecting the plaintext to operations of the conventional 4f system, it is made to undergo Arnold transform (AT) for additional security. The scheme is validated for grayscale amplitude images. In its optical realization, the use of DVFL eliminates the problem of axis-alignment. The parameters of DVFL, and the orders of FRHT in addition to AT order serve as encryption keys. The scheme has been tested for its sensitivity to these parameters. Also, the scheme is evaluated for its robustness against the occlusion and noise attacks. The use of multiple encryption parameters adds to security of the scheme.
17 citations
TL;DR: A new general optimal approach is presented, for those cases where one and multidimensional Fourier transforms are used for pattern recognition, which consists in using both the real and imaginary components of Fourier transform as features.
17 citations
TL;DR: In this paper, the authors considered integral equations of convolution type with the Toeplitz plus Hankel kernels firstly posed by Tsitsiklis and Levy (1981) and obtained a necessary and sufficient condition for the solvability and unique explicit L 2 -solution.
17 citations
01 Jan 1995
TL;DR: In this article, a new high precision gravimetric determination of the geoid of the Iberian Peninsula has been made, using the following data types: a) a global geopotential model, namely the OSU91A spherical harmonic coefficients set, b) a set of 186813 point free air gravity anomalies, including recent new data, and c) a 1000x1000 meters digital terrain model for Spain and the ETOPO5U for the rest of the area.
Abstract: A new high precision gravimetric determination of the geoid of the Iberian Peninsula has been made, using the following data types: a) a global geopotential model, namely the OSU91A spherical harmonic coefficients set, b) a set of 186813 point free air gravity anomalies covering the Iberian Peninsula and surrounding regions, including recent new data, and c) a 1000x1000 meters digital terrain model for Spain and the ETOPO5U for the rest of the area. The method used for the computations was the Stokes' integral in convolution form. The input data were gridded gravity anomalies. To evaluate the integral, the Fast Fourier Transform and Fast Hartley Transform techniques were applied. Discrete spectra of the kernel function is used. 100 % zero padding was appended around the signal matrix to avoid circular convolution effects. The terrain correction was applied to the data and the corresponding indirect effect was taken into account. The geoid computed has been compared to geoid undulations obtained by GPS/Levelling, and a precision of 1.0 ppm has been obtained. The results, corresponding to the 1D-FFT solution, in the GRS80 system, are presented in form of contour maps.
17 citations