Journal ArticleDOI
Discrete Hartley transform
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
Improved FHT Algorithms for Fast Computation of the Discrete Hartley Transform
TL;DR: An improved radix-2 fast Hartley transform (FHT) algorithm with arithmetic complexity comparable to that of the real-valued fast Fourier transform (RFFT) is developed and has a simple and regular butterfly structure and possesses the in-place computation property.
Journal ArticleDOI
Unified parallel lattice structure of block time-recursive real-valued discrete Gabor transforms
Liang Tao,Hon Keung Kwan +1 more
TL;DR: Block time-recursive algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are developed in both the critical sampling case and the oversampling case.
Journal ArticleDOI
Uniqueness and sampling conditions for image reconstruction from the Hartley-transform intensity
TL;DR: It is shown that a real two-dimensional image is uniquely determined by the intensity of its Hartley transform if the latter is sampled on a particular set of points whose density is approximately half the Nyquist density for the intensity.
Proceedings ArticleDOI
Unified VLSI lattice architectures for discrete sinusoidal transforms
K.J.R. Liu,Ching-Te Chiu +1 more
TL;DR: A new scheme employing the time-recursive approach to compute these transforms is presented and Unified parallel lattice structures that can dually generate the DCT and DST simultaneously as well as the DHT are developed using such an approach.
Proceedings ArticleDOI
A new class of seeded real lapped tight frame transforms
TL;DR: A design procedure for the real, equal-norm, lapped tight frame transforms (LTFTs), which have been recently proposed as both a redundant counterpart to lapped orthogonal transforms and an infinite-dimensional counterpart to harmonic tight frames.
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.