Questions tagged [fourier]

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How can I change th code to implement the Fourier series as defined?

I want to compute the Fourier series expansion of the function $$f:[-1,1] \to \mathbb{R}$$ with $$f(x) = \begin{cases} -x & x < 0 \\ 0 & x \geq 0 \end{cases} $$ .The code ...
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Scale of x-axis for Fourier transform

Consider a function $f(t)$ and its Fourier transform $F(\omega)$. The amplitude of the Fourier transform $F(\omega)$ depends on the frequency $\omega$ and thus also depends on the scale of the $t$-...
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Pros of Fourier-Galerkin spectral methods

What are the pros of Fourier-Galerkin spectral methods while solving PDEs? Here's the one that came in my mind first: Easy implementation: using this method, differentiation operator computation is ...
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Adaptive quadrature methods for Fourier Optics

In Fourier Optics one often needs to compute approximations to bivariate integrals like $$ \int_{-\frac{l}{2}}^{\frac{l}{2}}\int_{-\frac{l}{2}}^{\frac{l}{2}} {\rm e}^{i\phi(\xi,\eta)}\mathrm{exp}\left[...