# Integration packages to calculate the first N Fourier coefficients

**URL:** <https://discourse.julialang.org/t/integration-packages-to-calculate-the-first-n-fourier-coefficients/114787>\
**Category:** Numerics\
**Tags:** integral, quadrature\
**Created:** [May 27, 2024, 2:26pm UTC](https://discourse.julialang.org/t/integration-packages-to-calculate-the-first-n-fourier-coefficients/114787 "2024-05-27T14:26:57Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![IlianPihlajamaa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ilianpihlajamaa/32/28766_2.png) [@IlianPihlajamaa](https://discourse.julialang.org/u/IlianPihlajamaa)\
**Post date:** [May 27, 2024, 4:42pm UTC](https://discourse.julialang.org/t/integration-packages-to-calculate-the-first-n-fourier-coefficients/114787/3 "2024-05-27T16:42:50Z")

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In addition to the above answer, if your integrant is not periodic and you have a discrete set of fixed (possibly irregular) sampling points, you can try [Filon’s method](https://en.m.wikipedia.org/wiki/Filon_quadrature) or related methods. I implemented it once in Julia, but I’m not sure it is available in a package.

Edit: a quick search gives

> **[GitHub - dkm2/FCCQuad.jl: Filon-Clenshaw-Curtis Quadrature](https://github.com/dkm2/FCCQuad.jl)**
>
> Filon-Clenshaw-Curtis Quadrature. Contribute to dkm2/FCCQuad.jl development by creating an account on GitHub.

And

> [@\[RFC/ANN\] OscillatoryIntegralsODE.jl: Levin method + OrdinaryDiffEq](https://discourse.julialang.org/t/rfc-ann-oscillatoryintegralsode-jl-levin-method-ordinarydiffeq/55601):
>
> I’m requesting feedback on [OscillatoryIntegralsODE.jl](https://github.com/xzackli/OscillatoryIntegralsODE.jl), which numerically evaluates integrals I = \int\_a^b f(x) S(rx) \, dx where f(x) is smooth and not oscillatory, but S(x) is highly oscillatory for large frequencies r. Examples of oscillatory functions include Bessel functions J\_{\nu}(rx), spherical Bessel j\_{\nu}(rx), \cos(\omega x), and the harmonic transform e^{i \omega x}. Gaussian quadrature is inefficient for these integrals, since the number of nodes required for accurate integration …

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