Dear Researcher,
I am willing to perform Spectrum Analysis of a Transport tool and I was wondering weither a Shock Signal in the time domain can be transformed to a PSD in the frequency domain by means of Finite Fourier Transform or not?
So given an amplitude of 10g over 11ms (Sock Signal in the time domain) and I wanna transfere it in the frequency domain to obtain the input PSD for Response Spectrum Analysis.
So, x(t) ist given over a finite time interval 0
The problem with spectral analysis of non-stationary signals such as shock is that the spectral content of the signal is not statistically constant in time. That means the spectrum will vary with respect to the time window you consider.
Dear Mohamed,
Your function can be considered as a rectangular pulse with a duration T= 11 ms, So transforming it to frequency domain using Fourier transform, one gets the very famous sinc x function = sin (fT)/ (fT). Theoretically this function extends to infinite frequency. However one can truncate it to a limited frequency range since its amplitude decays with increased f.
To see the shape of the function please follow the link: http://www.thefouriertransform.com/pairs/box.php,
In fact one can reconstruct an approximate pulse to the rectangular pulse even with the major loop and the two adjacent side loops. This makes out a bandwidth of the signal of about 5/T. Even the major pulse with a bandwidth of 2/T makes out about 90 percent of the rectangular pulse energy.
Then you can approximately analyse your system in the frequency domain by considering the major loop as an input to your system and in this way you can get an approximate solution to the system.
Best wishes
Dear Prof. Zekry,
Thank you for your answer, I apperciated it so much but I think it wouldnt give the correct response in the frequency domani since it will be aproximated by a rectangular puls.
I found another method to calculate the Response spectrum using a Numerical Solution Based on Interpolation of the Excitation Function. In which, the response x(τ ) over time 0 i ≤τ ≤ Δt is the sum of three parts:
1) Free vibration due to initial displacement and velocity
2) Response to step force with zero initial condition
3) Response to ramp force with zero initial condition
and then by defining a suitable time step, the response could be determined in the frequency domain.
Best regards
Mohamed
Dear Mohamed,
what is the transfer characteristics of the your system in frequency domain, H(jw) of your system?
Why do you want to solve the problem in frequency domain?
You can solve your problem in time domain?
From the conceptual point of view you do not need to truncate your sinc x function you can use it and multiply it by the transfer characteristics in the frequency domain H(jw).
What i tried is to approximate the sic x function to get an approximate solution.
Best wishes