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
New split-radix algorithm for the discrete Hartley transform
TL;DR: A split-radix algorithm that can flexibly compute the discrete Hartley transforms of various sequence lengths is presented and it shows that the length-3*2/sup m/ DHTs need a smaller number of multiplications than thelength-2/Sup m/DHTs, but they both require about the same computational complexity.
Book ChapterDOI
Matrix-Free Convex Optimization Modeling
Steven Diamond,Stephen Boyd +1 more
TL;DR: By combining the matrix-free modeling framework and cone solver, this work obtains a general method for efficiently solving convex optimization problems involving fast linear transforms.
Book ChapterDOI
The Discrete Hartley Transform
TL;DR: This chapter introduces the DHT and discusses those aspects of its solution, as obtained via the FHT, which make it an attractive choice for applying to the real-data DFT problem.
Journal ArticleDOI
Fast DHT algorithms for length N=q*2/sup m/
Guoan Bi,Yan Qiu Chen +1 more
TL;DR: In this article, an improved split-radix algorithm is presented that can flexibly compute the discrete Hartley transforms (DHT) of length q*2/sup m/ where q is an odd integer.
Journal ArticleDOI
Assessing the Hartley transform
TL;DR: The fast algorithm for the (real) Hartly transform is discussed in relation to the established fast algorithmFor the (complex) Fourier transform, compared by timing comparably written programs on a given machine, and the discipline of timing is discussed as an adjunct to complexity analysis.
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
Numerical Analysis: A fast fourier transform algorithm for real-valued series
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.