Fast Hankel transform by fast sine and cosine transforms: the Mellin connection

Knockaert, Luc

doi:10.1109/78.845927

Cited by 31 publications

(19 citation statements)

References 21 publications

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“…We solve the above problem by the proposed algorithm and observe that our method gives a result comparable to [35]. Note that 0 ( ) and̂0( ) are indicated by 0 ( ) (solid line) and ( ) (dotted line) in Figures 9, 11, 13, and 15 and the error ( ) = ( ) − 0 ( ) is shown in Figures 10, 12 Example 3 (sombrero function).…”

Section: Numerical Resultsmentioning

confidence: 99%

A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

Irfan

Siddiqi

2015

International Journal of Engineering Mathematics

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The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ], ] > −1, using wavelets. The philosophy behind the proposed algorithm is to replace the part ( ) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing ] ( ) as a Fourier-Bessel series with coefficients depending strongly on the input function ( ). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.

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Section: Numerical Resultsmentioning

confidence: 99%

A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

Irfan

Siddiqi

2015

International Journal of Engineering Mathematics

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“…expression (27). The autocovariance function of

S_{n}

{false(2 italicπ false)}^{n false/ 2}

times the inverse Fourier transform of the spectral density and, because the spectral density is radial, it can be expressed as the one‐dimensional integral (29).□ A fast algorithm for the numerical computation of Hankel transforms was developed by Knockaert (). If the dimensionality n is odd it is possible to express the spectral density of

S_{n}

in a simpler form and to use this to compute the autocovariance functions explicitly in the particular cases when n =1 and n =3.…”

Section: Isotropic Lévy‐driven Continuous Auto‐regressive Moving Avermentioning

confidence: 99%

Continuous Auto-Regressive Moving Average Random Fields on Rn

Brockwell

Matsuda

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We define an isotropic Lévy‐driven continuous auto‐regressive moving average CARMA(p,q) random field on double-struckRn as the integral of a radial CARMA kernel with respect to a Lévy sheet. Such fields constitute a parametric family characterized by an auto‐regressive polynomial a and a moving average polynomial b having zeros in both the left and the right complex half‐planes. They extend the well‐balanced Ornstein–Uhlenbeck process of Schnurr and Woerner to a well‐balanced CARMA process in one dimension (with a much richer class of autocovariance functions) and to an isotropic CARMA random field on double-struckRn for n>1. We derive second‐order properties of these random fields and extend the results to a larger class of anisotropic CARMA random fields. If the driving Lévy sheet is compound Poisson it is trivial to simulate the corresponding random field on any bounded subset of double-struckRn. A method for joint estimation of the CARMA kernel parameters and knot locations is proposed for compound‐Poisson‐driven fields and is illustrated by applications to simulated data and Tokyo land price data.

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“…cheaper) means to compute H s (θ, r), compared with the 2D Fourier transform. The complexity analysis for computing different fast Hankel transform algorithms, which are available in, 15,16 show that most of the fast Hankel transform algorithms can achieve a complexity of O(N s log 2 N s ), where N s denotes the number of data points in each dimension. Compared to this, the complexities of traditional 2D discrete Fourier transform (DFT) and 2D fast Fourier transform (FFT) are O(N 4 s ) and O(10N 2 s log 2 N s ), respectively.…”

Section: Channel Modelmentioning

confidence: 99%

Novel target design algorithm for two-dimensional optical storage (TwoDOS)

Huang

Chong

2004

SPIE Proceedings

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In this paper we introduce the Hankel transform based channel model of Two-Dimensional Optical Storage (TwoDOS) system. Based on this model, the two-dimensional (2D) minimum mean-square error (MMSE) equalizer has been derived and applied to some simple but common cases. The performance of the 2D Viterbi detector (VD) for different partial response (PR) targets in TwoDOS system is investigated. And an easy way of jointly designing the target and equalizer with suitable constraints on the target for 2D data storage systems is proposed by reducing the 2D target into its one-dimensional (1D) form. Finally, systems with different target constraints are compared and the results show that "2D monic constraint" is a reasonable target constraint for TwoDOS system.

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Fast Hankel transform by fast sine and cosine transforms: the Mellin connection

Cited by 31 publications

References 21 publications

A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

Continuous Auto-Regressive Moving Average Random Fields on Rn

Novel target design algorithm for two-dimensional optical storage (TwoDOS)

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