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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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### 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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### How to get the frequency information of an mp3 audio?

I have: music = Import["http://www.qlcoder.com/uploads/145425353234642.mp3", "mp3"] Then I get: But what I want to get is ...
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### How to demodulate an FM signal in continuous-time?

I'm not sure if this is a math or Mathematica question, but I'm posting it here because I'm interested in possible Mathematica tools/functions to solve the problem. I'm stuck. I want to simulate ...
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### Envelope for harmonic oscillator [duplicate]

I am able to take the expression $\cos 11t-\cos 12t$ and use the sum to product identity to write it in the form $$\left(2\sin\frac t2\right)\sin\frac{23}{2}t.$$ I can then plot the function and use ...
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### PrincipalValue option of Convolve not working in 9.0.1?

The PrincipalValue option of Convolve is used in this question to define the Hilbert transform. However, in Mathematica 9.0.1, ...
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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### Plot nested integration of an InterpolatingFunction efficiently

Suppose we have an InterpolatingFunction from NDSolve ...
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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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Implementing the Hilbert transformation $$H(f)(x) = \frac{1}{\pi}\lim_{\varepsilon \to 0} \int_{|x-y|>\varepsilon} \frac{1}{x-y}f(y) \, dy,$$ appropriate for 1-...