Topic
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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TL;DR: In this article, the authors employed the Hilbert Huang transform (HHT), the wavelet transform and the Fourier transform to analyze the road surface profiles of three pavement profiles and found that the strength of HHT is the ability to process non-stationary and non-linear data.
Abstract: This study employs the Hilbert–Huang transform (HHT), the wavelet transform and the Fourier transform to analyse the road surface profiles of three pavement profiles. The wavelet and Fourier transforms have been the traditional spectral analysis methods, but they are predicated on a priori selection of basis functions that are either of infinite length or have fixed finite widths. The central idea of HHT is the empirical mode decomposition, which decomposes a signal into basis functions called the intrinsic mode functions (IMFs). The Hilbert transform can then be applied to the IMFs to generate an energy–time–frequency spectrum called the Hilbert spectrum. The strength of HHT is the ability to process non-stationary and non-linear data. Unlike the Fourier transform, which transforms information from the time domain into the frequency domain, the HHT does not lose temporal information after transformation, i.e. energy–frequency information is maintained in the time domain. This paper attempts to reveal the...
68 citations
TL;DR: In this article, a new technique based on double affine Hecke algebras was applied to the Harish-Chandra theory of spherical zonal functions, and the formulas for the Fourier transforms of the multiplications by the coordinates were obtained as well as a simple proof of the inversion theorem using the Opdam transform.
Abstract: We apply a new technique based on double affine Hecke algebras to the Harish-Chandra theory of spherical zonal functions. The formulas for the Fourier transforms of the multiplications by the coordinates are obtained as well as a simple proof of the Harish-Chandra inversion theorem using the Opdam transform.
67 citations
TL;DR: In this paper, the authors present a Hankel transform algorithm using a fast (linear time) Abel transform, followed by an FFT, which maps an axisymmetric two-dimensional function into a line integral projection, and a one-dimensional Fourier transform.
Abstract: The Hankel, or Fourier-Bessel, transform is an important computational tool for optics, acoustics, and geophysics. It may be computed by a combination of an Abel transform, Which maps an axisymmetric two-dimensional function into a line integral projection, and a one-dimensional Fourier transform. This paper presents a Hankel transform algorithm using a fast (linear time) Abel transform, followed by an FFT.
67 citations
TL;DR: An extension of the Fresnel transform to first-order optical systems that can be represented by an ABCD matrix is analyzed in this article, which is recognized to belong to the class of linear canonical transforms.
Abstract: An extension of the Fresnel transform to first-order optical systems that can be represented by an ABCD matrix is analyzed. We present and discuss a definition of the generalized transform, which is recognized to belong to the class of linear canonical transforms. A general mathematical characterization is performed by listing a number of meaningful theorems that hold for this operation and can be exploited for simplyfying the analysis of optical systems. The relevance to physics of this transform and of the theorems is stressed. Finally, a comprehensive number of possible decompositions of the generalized transform in terms of elementary optical transforms is discussed to obtain further insight into this operation.
67 citations
TL;DR: In this article, the advantages of adaptive Fourier transform and analytical wavelet transform as compared to traditional Fourier Transform have been discussed, which make it possible to reliably detect wave-like disturbances against a background of noise at a signal-to-noise ratio not less than 0.1.
Abstract: Backgrounds of adaptive Fourier transform and analytical wavelet transform have been briefly described in comparison with traditional Fourier transform using a time window. As an example, all three transforms are used to analyze quasiperiodic wave-like processes in the ionosphere, which accompanied the passage of the solar terminator and rocket launch from the Plesetsk site. The advantages of adaptive Fourier transform and analytical wavelet transform as compared to traditional Fourier transform, which make it possible to reliably detect wave-like disturbances against a background of noise at a signal-to-noise ratio not less than 0.1, have been demonstrated.
67 citations