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Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.


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Journal ArticleDOI
TL;DR: It has been shown that by using linear canonical transform, the author is able to obtain all window parameters successfully as compared to fractional Fourier transform.
Abstract: Linear canonical transform is a four-parameter class of integral transform that plays an important role in many fields of optics and signal processing. Well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as the special cases of the linear canonical transform. This paper presents a new mathematical model for obtaining the linear canonical transforms of Dirichlet, Generalized “Hamming”, and Triangular window functions. The different window function parameters are also obtained from the simulations. By changing the value of four parameters and then changing the adjustable parameter, the main-lobe width, −3 dB bandwidth, −6 dB bandwidth and correspondingly, the minimum stop-band attenuation of the resulting window functions can be controlled. It has been shown that by using linear canonical transform, we are able to obtain all window parameters successfully as compared to fractional Fourier transform.

10 citations

Journal ArticleDOI
Hong Hao1
01 Jul 1987
TL;DR: In this article, the equivalence between pre-and post-permutation algorithms for the fast Hartley transform (FHT) has been discussed, and improvements are made to two recently published FHT programs.
Abstract: This letter discusses the equivalence between the pre- and post-permutation algorithms for the fast Hartley transform (FHT). Some improvements are made to two recently published FHT programs.

10 citations

Proceedings ArticleDOI
15 Dec 2003
TL;DR: The performance of the L-HLT is found to be better than the DCT for near lossless image compression and wavelet-based filter bank approach for lossless compression.
Abstract: It is shown that the discrete Hartley transform (DHT) of length N = 4 can be used to perform an integer-to-integer transformation. This behavior of the DHT can be used to compute a 2-D separable lossless Hartley like transform (L-HLT). The performance of the L-HLT is found to be better than the DCT for near lossless image compression and wavelet-based filter bank approach for lossless compression.

10 citations

Journal ArticleDOI
TL;DR: In this paper, the nonstationary frequency and time distortions and nonphysical energy changes inherent to seismic data processing steps are predicted and quantied by a general one-dimensional integral transform.
Abstract: We use the nonstationary equivalent of the Fourier shift theorem to derive a general one-dimensional integral transform for the application and removal of certain seismic data processing steps. This transform comes from the observation that many seismic data processing steps can be viewed as nonstationary shifts. The continuous form of the transform is exactly reversible, and the discrete form provides a general framework for unitary and pseudounitary imaging operators. Any processing step which can be viewed as a nonstationary shift in any domain is a special case of this transform. Nonstationary shifts generally produce coordinate distortions between input and output domains, and those that preserve amplitudes do not conserve the energy of the input signal. The nonstationary frequency and time distortions and nonphysical energy changes inherent to such operations are predicted and quantied by this transform. Processing steps of this type are conventionally implemented using interpolation operators to map discrete data values between input and output coordinate frames. Although not explicitly derived to perform interpolation, the transform here assumes the Fourier basis to predict values of the input signal between sampling locations. We demonstrate how interpolants commonly used in seismic data processing and imaging approximate the proposed method. We nd that our transform is equivalent to the conventional sinc-interpolant with no truncation. Once the transform is developed, we demonstrate its numerical implementation by matrix-vector multiplication. As an example, we use our transform to apply and remove normal moveout.

10 citations

DOI
01 Feb 1984
TL;DR: The results of a study using Fermat number transforms (FNTs) to compute discrete Fourier transforms (DFTs) are presented and the present technique is very effective in computing discrete Fouriers transforms.
Abstract: In the paper the results of a study using Fermat number transforms (FNTs) to compute discrete Fourier transforms (DFTs) are presented. Eight basic FNT modules are suggested and used as the basic sequence lengths to compute long DFTs. The number of multiplications per point is for most cases not more than one, whereas the number of shift-adds is approximately equal to the number of additions in the Winograd-Fourier-transform algorithm and the polynomial transform. Thus the present technique is very effective in computing discrete Fourier transforms.

10 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202311
202230
202110
202014
201915
201820