A quadrature formula for the Hankel transform

In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal processing. The well-known integral transforms: Fourier, fractional Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT. In this paper we obtain an O(N log N) algorithm to compute the LCT by using a chirp-FFT-chirp transformation yielded by a convergent quadrature formula for the fractional Fourier transform. This formula gives a unitary discrete LCT in closed form. In the case of the fractional Fourier transform the algorithm computes this transform for arbitrary complex values inside the unitary circle and not only at the boundary. In the case of the ordinary Fourier transform the algorithm improves the output of the FFT.

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“…, N − 1, and N k=1 F jk f (x k ) is an approximation of g(4y j /π). If now we choose κ = 4b/π, but we keep the same matrix (13)…”

Section: A Fast Linear Canonical Transformmentioning

confidence: 99%

A fast algorithm for the linear canonical transform

Campos

Figueroa

2011

Signal Processing

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“…Firstly, we reformulate the procedure followed in [2,3] and [4] to obtain a quadrature formula for the integral Fourier transform yielding a discrete Fourier transform. Proofs and further applications can be found in these references.…”

Section: A Discrete Laplace Transformmentioning

confidence: 99%

Quadrature formulas for the Laplace and Mellin transforms

Campos¹,

Díaz²

2009

Bit Numer Math

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A discrete Laplace transform and its inversion formula are obtained by using a quadrature of the integral Fourier transform which is given in terms of Hermite polynomials and its zeros. This approach yields a convergent discrete formula for the two-sided Laplace transform if the function to be transformed falls off rapidly to zero and satisfies given conditions of integrability, achieving convergence also for singular functions. The inversion formula becomes a quadrature formula for the Bromwich integral. The use of asymptotic formulae yields an algorithm to compute the discrete Laplace transform by using only exponentials.

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“…Once fixed the predictor's order one could simply establish a threshold and assume that if the error is below that, then we must be dealing with a voiced sound and unvoiced otherwise. E n is defined in (1), (2) and 3as the sum of the squares of the differences between the synthesized signal and the original signal samples.…”

Section: The Use Of the Prediction Errormentioning

confidence: 99%

“…Form vector x with the roots of the Hermite polynomial of degree P 4. Construct the Fourier's Kernel matrix F using equation (11) according to [2]. This Matrix is Hermitian so…”

Section: Using a Discretization Of The Continuos Fourier Transform Tomentioning

confidence: 99%

Using a new Discretization of the Fourier Transform to Discriminate Voiced From Unvoiced Speech

Camarena-Ibarrola

Chávez

2006

2006 Seventh Mexican International Conference on Computer Science

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In Automatic Speech Recognition, Voice Synthesis, Speaker Identification and identifying laringeal diseases, it is critical to classify speech segments as voiced or unvoiced. Several techniques have been proposed for this issue during the last twenty years, unfortunately, they either have especial cases where the result is unreliable or need to use not only the present segment of speech but the next one as well, this fact limits its applications (i.e Continuos Speech recognition). In this paper we present an alternative to voiced/unvoiced classification using a Discretization of the Continuos Fourier Transform.

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A quadrature formula for the Hankel transform

Cited by 10 publications

References 6 publications

A fast algorithm for the linear canonical transform

A fast algorithm for the linear canonical transform

Quadrature formulas for the Laplace and Mellin transforms

Using a new Discretization of the Fourier Transform to Discriminate Voiced From Unvoiced Speech

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