Topic
Discrete sine transform
About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.
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TL;DR: In this paper, the authors characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO (n ).
77 citations
TL;DR: The Hilbert transform is a commonly used technique for relating the real and imaginary parts of a causal spectral response as mentioned in this paper, which is found in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, image reconstruction and remote sensing.
Abstract: The Hilbert transform is a commonly used technique for relating the real and imaginary parts of a causal spectral response. It is found in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, image reconstruction and remote sensing. One useful application in the area of high-power microwave (HPM) technology is in correcting measured continuous wave (CW) transfer function data, so as to insure causality in reconstructed transient responses. Another application of the Hilbert transform is in the area of complex spectral estimation using magnitude-only data. Here, the applications of the transform to several specific spectral filtering and phase reconstruction problems are illustrated. >
77 citations
TL;DR: A scale discrete version of spherical multiresolution is described, starting from a scale discrete wavelet transform on the sphere, and fully discrete wavelets approximation is discussed in the case of band-limited wavelets.
Abstract: Based on a new definition of dilation a scale discrete version of spherical multiresolution is described, starting from a scale discrete wavelet transform on the sphere. Depending on the type of application, different families of wavelets are chosen. In particular, spherical Shannon wavelets are constructed that form an orthogonal multiresolution analysis. Finally fully discrete wavelet approximation is discussed in the case of band-limited wavelets.
76 citations
TL;DR: It is shown that the number of distinct N-point DFTs needed to calculate N*N-point two-dimensional DFT’s is equal to thenumber of linear congruences spanning the N-N grid.
Abstract: An algorithm is presented for computation of the two-dimensional discrete Fourier transform (DFT). The algorithm is based on geometric properties of the integers and exhibits symmetry and simplicity of realization. Only one-dimensional transformation of the input data is required. The transformations are independent; hence, parallel processing is feasible. It is shown that the number of distinct N-point DFTs needed to calculate N*N-point two-dimensional DFTs is equal to the number of linear congruences spanning the N*N grid. Examples for N=3, N=4, and N=10 are presented. A short APL code illustrating the algorithm is given. >
76 citations
01 Jan 2000
TL;DR: A finite implementation of the ridgelet transform is presented that is invertible, non-redundant and achieved via fast algorithms and it is shown that this transform is orthogonal hence it allows one to use non-linear approximations for the representation of images.
Abstract: A finite implementation of the ridgelet transform is presented. The transform is invertible, non-redundant and achieved via fast algorithms. Furthermore we show that this transform is orthogonal hence it allows one to use non-linear approximations for the representation of images. Numerical results on different test images are shown. Those results conform with the theory of the ridgelet transform in the continuous domain-the obtained representation can represent efficiently images with linear singularities. Thus it indicates the potential of the proposed system as a new transform for coding of images.
76 citations