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
A comparison of alternative transforms for electric power engineering applications
K. Olejniczak,Gerald T. Heydt +1 more
TL;DR: It is conjectured that mathematical transform methods may be deserving of increased awareness in systems analysis in general, and power quality calculations in particular, due to their favorable convolution property when studying linear, time-invariant systems.
Journal ArticleDOI
Multidimensional vector radix FHT algorithms
TL;DR: These algorithms are derived for computing the discrete Hartley transform (DHT) of any dimension using an appropriate index mapping and the Kronecker product and possess properties such as high regularity, simplicity and in-place computation that are highly desirable for software and hardware implementations, especially for the M-D applications.
Proceedings ArticleDOI
A new DA-based array for one dimensional discrete Hartley transform
TL;DR: The author derives a new algorithm that can formulate the 1-D DHT into cyclic convolution, and realizes it in a DA-based array that utilizes identical ROM modules, and eliminates the accumulation loop in the processing elements (PE's).
Journal ArticleDOI
FHT algorithm for length N=q.2/sup m/
N. Vijayakumar,K.M.M. Prabhu +1 more
TL;DR: Fast computation of the discrete Hartley transform of length N=q, where q is an odd integer, is proposed, giving rise to a substantial reduction in computational complexity when compared to other algorithms.
Journal ArticleDOI
Hartley transform ion cyclotron resonance mass spectrometry.
TL;DR: The Hartley transform offers a useful alternative to the Fourier transform for the conversion of a time-domain ion cyclotron resonance (ICR) signal into its corresponding frequency-domain mass spectrum, making the FHT equivalent in speed to a "real" FFT.
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.