Linked Questions

0 votes
0 answers
55 views

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 : ...
Superunknown's user avatar
9 votes
2 answers
2k views

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: ...
Unbelievable's user avatar
  • 4,887
7 votes
2 answers
7k views

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 ...
Sayakiss's user avatar
  • 859
19 votes
1 answer
5k views

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 ...
stevenvh's user avatar
  • 6,958
7 votes
3 answers
1k views

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 ...
David's user avatar
  • 14.9k
5 votes
1 answer
620 views

Solving partial differential equation involving Hilbert transform

While solving one research paper published in Physical Review Letters, I came across the following equation and I am unable to solve it. $$\frac{\partial f}{\partial t}−(\mathcal{H}(f)\left(\frac{\...
Mohan Aditya Sabbineni's user avatar
4 votes
1 answer
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, ...
user55777's user avatar
  • 671
1 vote
1 answer
456 views

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 ...
user3368447's user avatar
3 votes
1 answer
147 views

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, ...
Shuchang Zhou's user avatar
1 vote
1 answer
251 views

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. ...
user27119's user avatar
  • 2,520
2 votes
1 answer
152 views

Plot nested integration of an InterpolatingFunction efficiently

Suppose we have an InterpolatingFunction from NDSolve ...
lxy's user avatar
  • 189
1 vote
0 answers
398 views

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/...
Kirill's user avatar
  • 11
6 votes
0 answers
249 views

Implementation of the Riesz transform

Implementing the Hilbert transformation \begin{equation}H(f)(x) = \frac{1}{\pi}\lim_{\varepsilon \to 0} \int_{|x-y|>\varepsilon} \frac{1}{x-y}f(y) \, dy,\end{equation} appropriate for 1-...
confused's user avatar