# What are $H(i\omega)$, $H(s)$ and $H(z)$ called?

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 $H(z)$?

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

• 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." – Jason R Nov 9 '11 at 2:49