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: In this paper, ten types of discrete Fourier transforms of Weyl orbit functions are developed, each of which represents an exponential symmetrized with respect to a subgroup of the Weyl group.
Abstract: Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.
14 citations
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15 Mar 1999TL;DR: The new lapped transform is real-valued, and at the same time allows unambiguous detection of spatial orientation, and its performance in spectral approaches to image restoration and enhancement in comparison to the DFT is investigated.
Abstract: We propose a new real-valued lapped transform for 2D-signal and image processing Lapped transforms are particularly useful in block-based processing, since their intrinsically overlapping basis functions reduce or prevent block artifacts Our transform is derived from the modulated lapped transform (MLT), which, as a real-valued and separable transform like the discrete cosine transform, does not allow to unambiguously identify oriented structures from modulus spectra This is in marked contrast to the (complex-valued) discrete Fourier transform (DFT) The new lapped transform is real-valued, and at the same time allows unambiguous detection of spatial orientation Furthermore, a fast algorithm for this transform exists As an application example, we investigate the transform's performance in spectral approaches to image restoration and enhancement in comparison to the DFT
14 citations
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01 Jan 2015TL;DR: The paper shows the performance of additional four orthogonal transforms using transformed fractional content as feature for image classification where the Kekre, Hartle, Slant and Haar transform are used in addition to earlier proposed use of sine, cosine and walsh transforms.
Abstract: Image classification has become one of the important research field as hundreds of images are generated everyday which implies the need to build the classification system. To build faster and easy classification system, the visual content of images is used. Accuracy of classification depends upon the feature extraction which is one of the most important step in image classification. The paper shows the performance of additional four orthogonal transforms using transformed fractional content as feature for image classificationwhere the Kekre, Hartle, Slant and Haar transform are used in addition to earlier proposed use of sine, cosine and walsh transforms. Twelve assorted classifiers across five data mining classifier family (Bayes, Function, Lazy, Rule and Tree) are used. Here 504 number of variations for proposed image classification method are experimented using twelve classifiers, seven orthogonal transforms and six fractions of transformed content. The Simple Logistic classifiers with Kekre transform gives better image classification closely followed by Simple Logistic with sine transform and Simple Logistic with Hartley transform.
14 citations
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TL;DR: In this article, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods, and it is shown that the said transform can be simply calculated by differentiation of the original function.
Abstract: In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation of the original function. Various analytic consequent results are given. The simplicity and efficacy of the method are illustrated through many examples with shown Maple graphs, and transform tables are provided. Finally, a new infinite series representation related to Laplace transforms of trigonometric functions is proposed.
14 citations
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TL;DR: This paper proposes a newer version of Fourier transform, namely, Distributed Multiresolution Discrete Fourier Transform (D-MR-DFT) and its application in digital watermarking and shows better visual imperceptibility and resiliency of the proposed scheme against intentional or unintentional variety of attacks.
Abstract: The Fourier transform is undoubtedly one of the most valuable and frequently used tools in signal processing and analysis but it has some limitations. In this paper, we rectify these limitations by proposing a newer version of Fourier transform, namely, Distributed Multiresolution Discrete Fourier Transform (D-MR-DFT) and its application in digital watermarking. The core idea of the proposed watermarking scheme is to decompose an image into four frequency sub-bands using D-MR-DFT and then singular values of every sub-band are modified with the singular values of the watermark. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or unintentional variety of attacks.
14 citations