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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Journal ArticleDOI
Coherent optical generation of Hartley transform of real images
Yao Li,George Eichmann +1 more
TL;DR: A new method to generate optical Hartley transform for 2D real images is proposed, based on polarization encoding of the coherent optical beam, and different coherent optical image processing techniques are discussed.
Posted Content
Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction
TL;DR: In this article, the authors introduced a technique to derive fast algorithms for polynomial transforms by decomposing the regular modules of these algebras as a stepwise induction.
Posted ContentDOI
Hartley Spectral Pooling for Deep Learning
Hao Zhang,Jianwei Ma +1 more
TL;DR: The proposed spectral pooling avoids the use of complex arithmetic for frequency representation and reduces the computation, and preserves more structure features for network's discriminability than max and average pooling.
Journal ArticleDOI
New high-speed prime-factor algorithm for discrete Hartley transform
TL;DR: The proposed algorithm is more efficient compared to the radix-2 FHT in terms of the computational requirements, as well as the execution time for transform lengths higher than 30 and is faster than the prime-factor FFT algorithm for real-valued series.
Journal ArticleDOI
Quantization errors in the computation of the discrete Hartley transform
Avideh Zakhor,Alan V. Oppenheim +1 more
TL;DR: A variety of efficient DHT algorithms including Bracewell's original decimation-in-time radix-2 algorithm are summarized and statistical models for fixed- and floating-point arithmetic roundoff errors are used as the basis for a theoretical study of roundoff noise characteristics of several discrete Hartley transform algorithms.
References
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Journal ArticleDOI
Discrete Hartley transform
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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TL;DR: In this article, a new procedure for calculating the complex, discrete Fourier transform of real-valued time series is presented for an example where the number of points in the series is an integral power of two.