Power density spectrum F(jω) to time domain input signal F(t)

Hi there,

For this problem, I have the input signal's Power density spectrum [S(jω)] and its Standard deviation [σ] this is all the given information. I need to get the signal in time domain as [h(t)].

How can I do this either using MATLAB code or Simulink blocks?.

I would be grateful for any help, thanks in advance.

Answer 1

[John BG]

Hi Mahmoud

this is John BG ( [e-mail] )

May the readers of the question know the following:

1.

from

http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782011000300005

instead of getting the pavement roughness spectral density time response, wouldn't it make more sense to aim at the [x y] response after applying the vehicle signal?

2.

the above source shows pavement roughness PSD with units [m^3], the PSD of your question Sh(w) has units [cm^2*s] . Is the model of your question 1D or 2D?

3.

from

http://www.slac.stanford.edu/econf/C110825/hepmad11_talks/randriatefison.pdf

the inverse transform of the pavement roughness is a surface, not a time signal, right? so you are asking for the surface that has the PSD in the question table?

[mahmoud]

Hi John BG

My case study is a validation of the results in this paper,

:

>> http://arch.neicon.ru/xmlui/handle/123456789/3478715

:

The pic. below shows the main model (quarter car model) and its mathematical equations. Also, in the right you can find the Simulink model that I made to represent this problem.

The output in interest is the acceleration of [M1] with time but, in order to get that I need the excitation force also in time domain [h(t)]

This model takes in interest the vertical motion component only of the vehicle. So, I believe that this model is 1D and so just the excitation signal is needed, not a whole surface as the other case you mentioned.

:

[John BG]

ok,

• the road profile (the surface roughness) is the input signal
• the car model is the channel
• and the output is the vibration that the driver experiences

Mahmoud, there is a MATLAB file exchange contribution that you may find interesting, by James Alison

https://uk.mathworks.com/matlabcentral/fileexchange/35478-simulation-and-animation-of-a-quarter-car-automotive-suspension-model?s_tid=srchtitle

It's also quarter car model

John BG

<mailto:[e-mail] [e-mail]>