How Can You Implement the Numerical Fourier Transform in MATLAB or FORTRAN?

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SUMMARY

The discussion focuses on implementing the Numerical Fourier Transform using MATLAB and FORTRAN (specifically g90). Participants emphasize the need to evaluate integrals for both the Fourier Transform and its inverse, particularly in the context of solving the Wiener-Hopf equation. The consensus is that due to the infinite domain and range of the Fourier Transform, utilizing the Discrete Fourier Transform (DFT) is essential for practical numerical evaluation.

PREREQUISITES
  • Understanding of Numerical Integration techniques
  • Familiarity with MATLAB programming
  • Knowledge of FORTRAN (g90) syntax and functions
  • Concept of Discrete Fourier Transform (DFT)
NEXT STEPS
  • Research MATLAB's built-in functions for Discrete Fourier Transform
  • Explore FORTRAN libraries for numerical integration
  • Study the Wiener-Hopf equation and its applications
  • Learn about Fast Fourier Transform (FFT) algorithms
USEFUL FOR

Mathematicians, engineers, and researchers involved in numerical analysis, signal processing, or applied mathematics, particularly those working with Fourier Transforms and related computational methods.

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hi, i would need some info on how can implement in MATLAB or FORTRAN (g90) the Numerical evaluation of the integral

\int_{-\infty}^{\infty}dxf(x)exp(iux)

and the evaluation of the ivnerse Fourier transform

\int_{-\infty}^{\infty}du\frac{F(u))}{\int_{-\infty}^{\infty}g(x)exp(iux)dx}

the idea is to implement some numerical tool to evaluate Fourier transform integral, in order to apply them to solve Wiener-Hopf equation.
 
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It's not possible to implement the complete Fourier transform numerically because it has infinite domain and range. You need to use the Discrete Fourier Transform instead.
 

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