What are the Fourier-, Laplace- and Z-transforms of the impulse response of a filter called? I've seen $H(s)$ referred to as the system function or transfer function, what about $H(i\omega)$ and the discretized $H(z)$?

  • 1
    $\begingroup$ The nomenclature depends on which authority you cite. See some of the comments following my answer to this question $\endgroup$ Nov 8 '11 at 15:12
  • $\begingroup$ @Dilip: Interesting, I think your comment there contains the answer (except for $H(z)$). $\endgroup$
    – Andreas
    Nov 8 '11 at 15:31
  • $\begingroup$ A comment made by someone else in that thread claims that $H(z)$ is also called the transfer function by some authorities. $\endgroup$ Nov 8 '11 at 18:35

I would consider them to all be 'transfer' or 'system' functions. Those two names are interchangable, but in control theory books I see then listed more as transfer functions rather than system functions.

The domain you are in, whether it be fourier, laplace, Z or time, isn't entirely relevant to the name in that respect.

  • 3
    $\begingroup$ I agree with your assessment. I don't think nomenclature specifics are all that important, but I've typically heard the $H(j\omega)$ version called the "frequency response." $\endgroup$
    – Jason R
    Nov 9 '11 at 2:49
  • $\begingroup$ true... I would consider "Frequency response" another name for it. H(jw) is a transfer function, that more specifically is a frequency response $\endgroup$
    – Fuzz
    Nov 9 '11 at 6:57

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