As far as I know, the spectrogram S(tau, omega) of a pulse envelope A(t) is defined as
S(tau,omega) = square of the absolute value of the Fourier Transform with respect to 't' of the function 'A(t)*A(t-tau).
My problem is that at the fiber output I have only A(t) values. From where to obtain the values A(t-tau).
I have also checked the matlab spectrogram function for my purpose. But I am not able to understand it.
Any help will be of great importance.
Thanks in advance
I do not understand your problem: "My problem is that at the fiber output I have only A(t) values. From where to obtain the values A(t-tau)."
If you do know A(t) then you do know A(t-tau)... Just replace t with "x" and "t-tau" with "x": then in both cases you have the same *function* A(x). Thus, if you know A(t) then you know *function* "A"=>you know A(t-tau).
Dear Cara,
Thanks for your kind answer. But I am still in confusion. I know the vector ''A(t)'' at the fiber output which I obtain from the simulation of Generalised Nonlinear Schrodinger Equation.I do not know the vector ''A(t-tau)''. I will be highly grateful to you if you kindly explain in detail the last line ''Thus, if you know A(t) then you know *function* "A"=>you know A(t-tau).'' of your answer.
Thanks a lot.
I hope that you agree with my statement "Thus, if you know A(t) then you know *function* "A"=>you know A(t-tau)." if you knew the analytical form of A(t).
I do not know your specific problem, data, etc. However, you say that A(t) comes from a simulation so I assume it is in a tabulated form. In that case, I would suggest that you use an appropriate interpolation method to obtain a "continuous" (as opposite to tabulated) A(x) function.
Hi,
As I understand its also called a autocorrelation function. In attach you can find the matlab file that calculate abs(real(At*At-tau)).
If you have access to A(t) directly then the spectrogram S(tau, omega) is just the Fourier transform of a temporal "slice". The simplest way to compute that is to define a Gaussian gate function G(t) of width DT and to compute the FFT of the product S(w,tau)=FT[A(t)*G(t-tau)]. The choice of Dt is not unique: you have to select a gate width which is large enough to have a reasonable spectral resolution and small enough to have a reasonable time resolution.
Dear Mastin ,
Thanks for your help. Your file works well. I have done some modifications to produce the spectrogram, which now is matching with text book results.
Thanks again for your valueable help.
Dear Cara and Dear Nicolas,
Thank you too for your valuable suggestions.
- Badges
- Science topic