Journal ArticleDOI
The fast Hartley transform
Ronald N. Bracewell
- Vol. 72, Iss: 8, pp 1010-1018
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TLDR
The Fast Hartley Transform (FHT) is as fast as or faster than the Fast Fourier Transform (FFT) and serves for all the uses such as spectral analysis, digital processing, and convolution to which the FFT is at present applied.Abstract:
A fast algorithm has been worked out for performing the Discrete Hartley Transform (DHT) of a data sequence of N elements in a time proportional to Nlog 2 N. The Fast Hartley Transform (FHT) is as fast as or faster than the Fast Fourier Transform (FFT) and serves for all the uses such as spectral analysis, digital processing, and convolution to which the FFT is at present applied. A new timing diagram (stripe diagram) is presented to illustrate the overall dependence of running time on the subroutines composing one implementation; this mode of presentation supplements the simple counting of multiplies and adds. One may view the Fast Hartley procedure as a sequence of matrix operations on the data and thus as constituting a new factorization of the DFT matrix operator; this factorization is presented. The FHT computes convolutions and power spectra distinctly faster than the FFT.read more
Citations
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Proceedings ArticleDOI
A Flexible Implementation of a Matrix Laurent Series-Based 16-Point Fast Fourier and Hartley Transforms
TL;DR: A flexible architecture for implementing a new fast computation of the discrete Fourier and Hartley transforms, which is based on a matrix Laurent series is described, which handled a 16-point fast transform in 65 nsec, with a Xilinx SPARTAN 3E device.
Journal ArticleDOI
Changes in sleep electroencephalogram and nocturnal hormone secretion after administration of the antidyskinetic agent sarizotan in healthy young male volunteers
H. E. Kuenzel,Axel Steiger,Katja Held,Irina A. Antonijevic,Ralf-Michael Frieboes,Harald Murck +5 more
TL;DR: While REM sleep was suppressed, the endocrine effects of 20 mg sarizotan at night were weak and its sleep-endocrine profile is comparable to the effects provoked by selective 5-HT reuptake inhibitors.
Proceedings ArticleDOI
Design of digital IIR integrator using discrete Hartley transform interpolation method
Chien-Cheng Tseng,Su-Ling Lee +1 more
TL;DR: The interpolation formula of discrete-time sequence is derived by using discrete Hartley transform (DHT) and the numerical integration rules and DHT interpolation are applied to obtain the transfer function of digital integrator.
Proceedings ArticleDOI
Fast algorithms for the discrete Fourier transform and for other transforms
N. Suehiro,M. Hatori +1 more
TL;DR: A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms and a new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm.
Journal ArticleDOI
Comparative study of time efficiency of several algorithms for discrete W transform and discrete Hartley transform
TL;DR: Results show that the subroutines for the fast W transform algorithm reported recently are more efficient than subroutedines for radix-2,Radix-4 and the split radix fast Hartley transform algorithms.
References
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Journal ArticleDOI
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TL;DR: The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free from two characteristics of the DFT that are sometimes computationally undesirable and promises to speed up Fourier-transform calculations.
Journal ArticleDOI
A More Symmetrical Fourier Analysis Applied to Transmission Problems
TL;DR: In this article, the Fourier identity is expressed in a more symmetrical form which leads to certain analogies between the function of the original variable and its transform, and it permits a function of time to be analyzed into two independent sets of sinusoidal components, one of which is represented in terms of positive frequencies, and the other of negative.
Journal ArticleDOI
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