Journal ArticleDOI
Discrete Hartley transform
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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.Abstract:
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. The inverse DHT is identical with the direct transform, and so it is not necessary to keep track of the +i and −i versions as with the DFT. Also, the DHT has real rather than complex values and thus does not require provision for complex arithmetic or separately managed storage for real and imaginary parts. Nevertheless, the DFT is directly obtainable from the DHT by a simple additive operation. In most image-processing applications the convolution of two data sequences f1 and f2 is given by DHT of [(DHT of f1) × (DHT of f2)], which is a rather simpler algorithm than the DFT permits, especially if images are. to be manipulated in two dimensions. It permits faster computing. Since the speed of the fast Fourier transform depends on the number of multiplications, and since one complex multiplication equals four real multiplications, a fast Hartley transform also promises to speed up Fourier-transform calculations. The name discrete Hartley transform is proposed because the DHT bears the same relation to an integral transform described by Hartley [ HartleyR. V. L., Proc. IRE30, 144 ( 1942)] as the DFT bears to the Fourier transform.read more
Citations
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Proceedings ArticleDOI
Design of a constant geometry fast Hartley transformer
TL;DR: A semisystolic architecture is presented for the parallel calculation of the decimation in time and radix-2 fast Hartley transform (FHT) of a real sequence with N=2/sup n/ data items which facilitates its mapping in VLSI technology and minimizes the communications among processors.
Journal ArticleDOI
Effects of finite register length in the fast hartley transform
TL;DR: The effect of finite register length on the computation accuracy of the fast Hartley transform (FHT) is discussed and a theoretical statistical expression for the mean-square computation error is derived.
Journal ArticleDOI
Frequency Speech Scrambler Based on the Hartley Transform and the Insertion of Random Frequency Components
TL;DR: A voice cryptography system based on a scrambler that lends itself to this purpose, providing significant resistance to the breach of information, the ability to reconfigure internal modules and encryption algorithms, and a low cost product.
Journal ArticleDOI
Multidimensional Fourier and Hartley Transforms—Are They Same?
TL;DR: It is shown that the mathematically incorrect version of the multidimensional Hartley transform with a single kernel representation and the corresponding Fourier transform are not the same.
Journal ArticleDOI
Low-complexity three-dimensional discrete Hartley transform approximations for medical image compression.
TL;DR: In this paper, the authors presented a set of multiplierless 3D DHT approximations, which can be implemented with fixed-point arithmetic, and applied them in a lossy 3D-DHT-based medical image compression algorithm.
References
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Book
The Fourier Transform and Its Applications
TL;DR: In this paper, the authors provide a broad overview of Fourier Transform and its relation with the FFT and the Hartley Transform, as well as the Laplace Transform and the Laplacian Transform.
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
Harmonic analysis with a real frequency function—I. aperiodic case
TL;DR: An integral transform which converts a real spatial (or temporal) function into a real frequency function is introduced in this paper, and the properties of this transform are investigated, and it is concluded that this transform is parallel to the Fourier transform and may be applied to all fields in which the FFT has been successfully applied.