Frequency response of a transfer function

  1. If I have a transfer function, and I need the frequency response of it, how do I go about doing it?

    Is there a easier way than inverse Laplace transforming it, then Fourier transforming that?

  2. jcsd
  3. chroot

    chroot 10,351
    Staff Emeritus
    Science Advisor
    Gold Member

    In what variable is your transfer function specified? z? s?

    - Warren
  4. it is in terms of s.
  5. berkeman

    Staff: Mentor

    And what does s expand out to? An expression involving ....

    If you have the transfer function in terms of s, you will just plot the real an imaginary parts of it versus frequency.... (or the magnitude and phase as a function of frequency, like you get on an impedance analyzer).
  6. MATLABdude

    MATLABdude 1,723
    Science Advisor

  7. berkeman

    Staff: Mentor

    LOL. I know, most of the time I go to google to search for related info for a PF question, the dang OP is at the top of the search list! Google is no dummy -- their spiders are all over us.
  8. MATLABdude

    MATLABdude 1,723
    Science Advisor

    They are, except that this is the OP's thread from yesterday (or day before last, or... dammit, 24+ hours ago). I recalled writing something about transfer functions and Laplace to Fourier transforms. I then realized that this was the same poster! Must not've done a terribly good job...
  9. berkeman

    Staff: Mentor

    Ah, got it. No, that other thread looks to contain great help. It's different enough that I won't merge the two threads yet. May even highlight that other thread....
  10. MATLABdude you did a good job clearing up what a transfer function is, etc. in that thread. I dont know why, but in my introductory signals class we didnt cover Leplace transforms or Transfer functions, we only did Fourier transforms for frequency analysis. So I was/am fuzzy about Leplace transforms (im still to take controls classes and advanced signal analysis). Unfortunatley im now takinga class that requires that, and I want to try to at least partially understand it so the class im in now won't be useless.
    Thanks :)

    Anyway, [tex]s = i \omega[/tex].
    I was suposed to plot the frequency response of the transfer function, which was easily done in MATLAB, but I want to know the theory behind it.

    Thanks again
    Last edited: May 7, 2009
  11. In order to get the Frequency response from the transfer function, you just need to plus in jω for all s. Assuming it exists, this will be your frequency response, aka the Fourier transform of your original signal in the time domain.

    I know this is an old forum... but I figure this may help anyone looking at this in the future.
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