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A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier
Thoth Technology Inc., Algonquin Radio Observatory, Pembroke, ON, Canada
Department of Earth and Space Science and Engineering, York University, Toronto, Canada
Epic College of Technology, Mississauga, Canada
Department of Physics and Astronomy, York University, Toronto, Canada
- 1 Thoth Technology Inc., Algonquin Radio Observatory, Pembroke, ON, Canada
- 2 Department of Earth and Space Science and Engineering, York University, Toronto, Canada
- 3 Epic College of Technology, Mississauga, Canada
- 4 Department of Physics and Astronomy, York University, Toronto, Canada
Applied Mathematics·Volume 12 (2021)·Pages 947–962·Published 8 November 2021·DOI10.4236/am.2021.1211063
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Abstract
Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from the shifting property of the Fourier transform. In this work, we show how to represent the Fourier transform of a function f ( t ) in form of a ratio of two polynomials without any trigonometric multiplier. A MATLAB code showing algorithmic implementation of the proposed method for rational approximation of the Fourier transform is presented.
KeywordsRational ApproximationFourier TransformSamplingSinc Function
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