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THE TRANSFORMATION OF DISCRETE VARIABLES
Annals of Human Genetics, 1955SummaryIn all data in which the response is all or none the application of tests of significance should take account of inevitable discontinuities and of possible divergencies from the normal model. The present paper discusses the application of the probability integral transform to discontinuous data in order that tests of significance based on ...
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The polynomial discrete Radon transform
Signal, Image and Video Processing, 2014This paper presents a new approach called polynomial discrete Radon transform (PDRT), regarded as a generalization of the classical finite discrete Radon transform. Specifically, the PDRT transforms an image into Radon space by summing the pixels according to polynomial curves. The PDRT can be applied on square
Ines Elouedi +3 more
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On the Computation of the Discrete Cosine Transform
IEEE Transactions on Communications, 1978An N -point discrete Fourier transform (DFT) algorithm can be used to evaluate a discrete cosine transform by a simple rearrangement of the input data. This method is about two times faster compared to the conventional method which uses a 2N -point DFT.
Madihally J. Narasimha +1 more
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Discrete Chrestenson transform
Problems of Information Transmission, 2010The author considers some generalizations of the discrete Fourier transform and the discrete Walsh transform. The discrete Chrestenson-Kronecker transform is generated by a matrix which is a Kronecker product of Fourier matrices. The discrete Chrestenson-Lévy transform is generated by a matrix which is a new direct product of Fourier matrices.
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Journal of the Optical Society of America A, 2019
We define a discrete Bargmann transform for discrete and finite functions by means of the coherent states in the su(2) finite harmonic oscillator model. The transform space is over a corresponding finite square mesh in the complex plane. From there, the inverse discrete Bargmann transform reconstitutes the original function with an average error of 10 ...
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We define a discrete Bargmann transform for discrete and finite functions by means of the coherent states in the su(2) finite harmonic oscillator model. The transform space is over a corresponding finite square mesh in the complex plane. From there, the inverse discrete Bargmann transform reconstitutes the original function with an average error of 10 ...
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Fast computation of the discrete cosine transform and the discrete Hartley transform
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1987A new factorization of the discrete Hartley transform (DHT) is presented. It is used to derive new algorithms for the DHT and the discrete cosine transform (DCT) with reduced number of multiplications.
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Discrete Lattice Wavelet Transform
IEEE Transactions on Circuits and Systems II: Express Briefs, 2007The discrete wavelet transform (DWT) has gained a wide acceptance in denoising and compression coding of images and signals. In this work we introduce a discrete lattice wavelet transform (DLWT). In the analysis part, the lattice structure contains two parallel transmission channels, which exchange information via two crossed lattice filters.
Olkkonen, H., Olkkonen, Juuso
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On Computing the Discrete Cosine Transform
IEEE Transactions on Computers, 1978Haralick has shown that the discrete cosine transform of N points can be computed more rapidly by taking two N-point fast Fourier transforms (FFT's) than by taking one 2N-point FFT as Ahmed had proposed. In this correspondence, we show that if Haralick had made use of the fact that the FFT's of real sequences can be computed more rapidly than general ...
Ben-Dau Tseng, William C. Miller
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Canonical transformations of the discrete cosine transform
Signal Processing, 2007We provide different transformation formulae between the different discrete cosine transform (DCT) types of the same size. The transformations use only diagonal and special lower/upper triangular matrices that minimize the overhead of transformation. These transformations provide a tool for using any of the DCT types as a core module for computing all ...
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On the Invertibility of the Discrete Radon Transform
SIAM Journal on Discrete Mathematics, 1989Summary: The Radon transform is a useful device for analyzing multidimensional data. It is closely connected to what has become known as ``projection pursuit''. For the case of discrete data, theorems that address its invertibility are proven. Connections to the projective group over GF(2) and block designs naturally arise.
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