Showing papers on "Kernel (image processing) published in 1971"
TL;DR: In this paper, the authors prove the discrete convolution theorem by means of matrix theory and make use of the diagonalization of a circulant matrix to show that a circular convolution is diagonalized by the discrete Fourier transform.
Abstract: In this paper we prove the discrete convolution theorem by means of matrix theory. The proof makes use of the diagonalization of a circulant matrix to show that a circular convolution is diagonalized by the discrete Fourier transform. The diagonalization of the circular convolution shows that the eigenvalues of a circular convolution operator are identical with the discrete Fourier frequency spectrum.
110 citations
TL;DR: In this article, it was shown that for positive energies, the use of the symmetric kernel of Meetz and Weinberg is not practical, and that it is preferable to solve the fully-connected equation for the three-body wave function rather than the fully connected equations for the two-body t - or K -matrix.
11 citations
TL;DR: In this paper, an ocean bottom earthquake is modelled as motion of a rigid boundary adjacent to a fluid half-space, and the resulting water pressure, for a wide class of source motions, is obtained exactly as a convolution integral.
Abstract: An ocean-bottom earthquake is modelled as motion of a rigid boundary adjacent to a fluid half-space. The resulting water pressure, for a wide class of source motions, is obtained exactly as a convolution integral. The kernel has a physical interpretation as a fundamental solution, and may be obtained explicitly by a Cagniard method. A worked example is given, in which the convolution is carried out, and steps in pressure are found which are approximately equivalent to an extra 200 m in the water column.
3 citations
TL;DR: In this article, the unique solvability of integral convolutional kernels of a general kind is established for kernels of general kind, an approximate factorization is given a foundation, and a method for construction of the approximate solution is also indicated.