Hartley transform


Also found in: Wikipedia.

Hartley transform

[ ]
(mathematics)
An analog of the Fourier transform for finite, real-valued data sets; for a function ƒ defined at N data values, 0, 1, 2, …, N - 1, the Hartley transform is a function, F, also defined on the set (0, 1, 2, …, N - 1), whose value at n is the sum over the variable r, from 0 through N - 1, of the quantity N -1 f (r) cas (2π nr / N), where cas θ=cosθ+sinθ.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In (6), k is the particular sample of Hartley Transform, [y.sub.n] is particular signal sample, n is counter variable and N is overall number of samples that represents signal.
[2] Wen-Liang Hsue, Wei-Ching Chang, "Real discrete fractional Fourier, Hartley, generalized Fourier and generalized Hartley transforms with many parameters", IEEE Trans.
Abuturab, "An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform," Optics and Lasers in Engineering, vol.
Sheridan, "Interferometry based multispectral photonlimited 2D and 3D integral image encryption employing the Hartley transform," Optics Express, vol.
Thus, the use of regular and modular computational structures as cycle convolution and circular correlation having local and regular data communications can be very useful in obtaining a good VLSI implementation for DCT, IDCT [10-18], DST and IDST [20-23], discrete Fourier transform (DFT) [12] or discrete Hartley transform (DHT) [24-29] using both the systolic array architectural paradigm or distributed arithmetic [30-34].
[26] D.F.Chiper, "Radix-2 Fast Algorithm for Computing Discrete Hartley Transform of Type III," IEEE Transactions on Circuits and SystemsII, vol.59, no.5, pp.297-301, 2012.
The orthogonal transform is selected to be the discrete Hartley transform (DHT) in [21], discrete cosine transform in [22], and the Walsh-Hadamardtransform (WHT) in [23],respectively.
For example, with [N.sub.T] = 4, the 4 matrices that are selected are the identity matrix [I.sub.N] corresponding to no transform, the Walsh-Hadamard transform (WHT) matrix [P.sup.W], the discrete cosine transform (DCT) matrix [P.sup.C], and the discrete Hartley transform (DHT) matrix [P.sup.H].
This has motivated researchers to design more secure systems by introducing additional parameters through phase filters and the use of a variety of integral transforms such as the fractional Fourier transform [18, 19], gyrator transform [20, 21], the Hartley transform [22,23], and the Arnold transform [24].
In this paper we propose to measure energy of specific motor imageries in the brain signal using Fast Hartley transform along with the Chebyshev filter and selecting the ideal channels for the classification problem using the proposed support vector machine.
IT'S been two seasons since Paul Hartley transformed himself from wide man to a central midfielder but the Hearts star still gets labelled a winger on almost a weekly basis.
It has Hartley transforms. Its plotting and graphing capabilities are absolutely superb."