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### Hilbert Transform in mathematica [duplicate]

I would like to do a Hilbert transformation in Mathematica on a function. However, it does not seem to give a right result. The Hilbert transform is given by So I did : ...
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1 vote
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### Issue with Inverse Fourier Transform

I'm having some trouble performing an inverse Fourier transform, essentially I have a function which I can Fourier transform with seemingly no issue, but I can't inverse Fourier transform the result. ...
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1 vote
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### Implementing Kramers Kronig Relation in Mathematica for Reflection Spectrum

I'm new to Mathematica and I have to solve this problem but all of my approaches are wrong :( So, please can anyone help me with this equation? Here it is: Here is my data : https://pastebin.com/...
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### Plot nested integration of an InterpolatingFunction efficiently

Suppose we have an InterpolatingFunction from NDSolve ...
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1 vote
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### Convolution integrals

I want to calculate the following integral $$\int_{-\infty}^{\infty} d \omega f(\omega) g(\omega'\pm\omega)$$ where $f$ has the form $$f(\omega)=\frac{a}{\omega- \omega_0\pm i \eta}$$ and $g$ has a ...
447 views

### How to speed up the integral in NDSolve?

On the MMA.SE, there have been several question on how to solve equations including integral using NDSolve, see example 1, example 2, and example 3. Many people, ...
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### plotting a trig functions along with its envelope

Note: This questions is quite different from the ones referred to in the comments. Those deal with numerical questions, while this one is algebraic. I have plots of the following type: ...
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