scispace - formally typeset
Journal ArticleDOI

Discrete Hartley transform

Ronald N. Bracewell
- 01 Dec 1983 - 
- Vol. 73, Iss: 12, pp 1832-1835
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI

The Walsh-Hadamard/discrete Hartley transform

TL;DR: A new fast algorithm is proposed here to compute the discrete Hartley transform (DHT) via the natural-ordered Walsh-Hadamard transform, which results in substantial saving in the number of multiplications required to obtain the DHT, relative to direct computation.
Proceedings ArticleDOI

A fast running Hartley transform algorithm and its application in adaptive signal enhancement

TL;DR: A fast recursive algorithm for computation of the running discrete Hartley transform (RDHT) is presented and provides substantial computational savings compared with the recursive RDFT algorithm.
Journal ArticleDOI

Power Saving of DHT in Digital Image Photography

TL;DR: A new technique by using Discrete Hartley Transform which will give the same result as that of the existing algorithms with low power consumption is proposed.
Proceedings ArticleDOI

A Novel Framework for Designing Directional Linear Transforms with Application to Video Compression

TL;DR: A new framework is introduced that allows to define a directional transform starting from any two-dimensional separable transform and it can be of interest in many areas of signal processing.
Proceedings ArticleDOI

Noise Resistant Spreading OOFDM Design for Suppressing PAPR of High Data Rate Wireless Optical Communication System

TL;DR: A novel noise resistent diagonal iteration-based carrier interferometry (DICI) codes for spreading optical orthogonal frequency-division multiplexing (OOFDM) symbols, and thereby suppressing the peak to average power ratio (PAPR) for high data rate OOFDM based systems.
References
More filters
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.