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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Journal ArticleDOI
Computation of discrete Hilbert transform through fast Hartley transform
Soo-Chang Pei,Sy-Been Jaw +1 more
TL;DR: A fast algorithm is proposed to compute the discrete Hilbert transform via the fast Hartley transform (FHT), where the computation complexity can be greatly reduced from two complex FFTs into two real FHTs.
Journal ArticleDOI
New Parametric Discrete Fourier and Hartley Transforms, and Algorithms for Fast Computation
TL;DR: A new reciprocal-orthogonal parametric discrete Fourier transform (DFT) is proposed by appropriately replacing some specific twiddle factors in the kernel of the classical DFT by independent parameters that can be chosen arbitrarily from the complex plane.
Proceedings ArticleDOI
An efficient unified systolic architecture for the computation of discrete trigonometric transforms
Wen-Hsien Fang,Ming-Lu Wu +1 more
TL;DR: A novel unified systolic architecture which can efficiently implement various discrete trigonometric transforms (DXT) including the discrete Fourier transform (DFT), the discrete Hartley transform, the discrete cosine transform, and the discrete sine transform is described.
Proceedings ArticleDOI
Discrete Hartley transform based multicarrier modulation
TL;DR: This paper presents a real-valued discrete multicarrier modulation approach that is based on the use of the discrete Hartley transform and its inverse (IDHT) to perform the modulation and demodulation operations.
Journal ArticleDOI
High-Throughput Memory-Based Architecture for DHT Using a New Convolutional Formulation
TL;DR: The proposed structures for direct-memory-based implementation of an -point discrete Hartley transform from two pairs of [(N/2-1)/2]-point cyclic convolutions are found to involve nearly the same hardware complexity as those of the existing structures, but offers two to four times more throughput and two toFour times less latency compared with others.
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.