A Fast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms
Copyright policy )A Fast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms
The authors describe a technique based on the fractional Fourier transform (FRFT) previously developed by themselves [SIAM Rev. 33, No. 3, 389-404 (1991; Zbl 0734.65104)], to compute numerical approximations of the continuous Fourier transforms, with a saving of computation respect to the conventional fast Fourier transform (FFT). As an illustration, an implementation example for numerically computing the Fourier transform of the Gaussian probability density function is treated. The above FRFT- scheme can be also applied to the numerical evaluation of continuous Laplace transforms.
Laplace transform, continuous Fourier transforms, Laplace transforms, Numerical methods for trigonometric approximation and interpolation, fractional Fourier transform, fast Fourier transform, Complexity and performance of numerical algorithms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Numerical methods for integral transforms, Numerical methods for discrete and fast Fourier transforms, Gaussian probability density function
Laplace transform, continuous Fourier transforms, Laplace transforms, Numerical methods for trigonometric approximation and interpolation, fractional Fourier transform, fast Fourier transform, Complexity and performance of numerical algorithms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Numerical methods for integral transforms, Numerical methods for discrete and fast Fourier transforms, Gaussian probability density function
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