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Math Help - Frequency dependent output (Laplace domain)

  1. #1
    dof
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    Frequency dependent output (Laplace domain)

    Hi,

    I am currently describing a system, or at least I am trying Therefore I use simulink to model the system.
    The main part is finished, but I encounter some problems in the feedback loop, so I hope you can help me out.

    The output of the main system are spikes (always with the same height (1.0) and width (0.04)). The spikefrequency will affect the input (feedback loop).

    When the frequency is low (between 1 and 7 Hz) the effect is there, but is not able to really affect the input. From about 10 Hz the effect can be noticed in time (so the effect is not instantenous, but will occur after about a couple of seconds). When the frequency increases also the effect should increase. Until about 50 Hz, when the frequency increases even more the feedbackloop will act like it deals with the 50 Hz frequency.

    I thought it perhaps would be possible to describe the system with a laplace function. However, I was not able to get it ride.

    I made a drawing of the desired result. The green spike is the input and the red function the output.



    The idea is that the overlap will increase the output for frequencys higher than 9 Hz. But I am not able to describe the output function, can someone help?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dof View Post
    Hi,

    I am currently describing a system, or at least I am trying Therefore I use simulink to model the system.
    The main part is finished, but I encounter some problems in the feedback loop, so I hope you can help me out.

    The output of the main system are spikes (always with the same height (1.0) and width (0.04)). The spikefrequency will affect the input (feedback loop).

    When the frequency is low (between 1 and 7 Hz) the effect is there, but is not able to really affect the input. From about 10 Hz the effect can be noticed in time (so the effect is not instantenous, but will occur after about a couple of seconds). When the frequency increases also the effect should increase. Until about 50 Hz, when the frequency increases even more the feedbackloop will act like it deals with the 50 Hz frequency.

    I thought it perhaps would be possible to describe the system with a laplace function. However, I was not able to get it ride.

    I made a drawing of the desired result. The green spike is the input and the red function the output.



    The idea is that the overlap will increase the output for frequencys higher than 9 Hz. But I am not able to describe the output function, can someone help?
    No, that makes little sense. You will need to be clearer if you are to get any sensible help.

    CB
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  3. #3
    dof
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    Ok,

    Basically I would like to have the green gamma distribution:


    This function needs to be mirrored by a line, in this case x=10.
    Furthermore the maximum duration of the function is 0.110 second. But this I can do myself.
    Finally I need the Laplace transform of this function.

    The function of the green line is:
    y=(x.^(k-1)).*(exp(-x./theta))./((theta^k).*R);
    with k=5, theta =1, R=(k-1)!
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