# What is the difference between an impulse response and a transferfunction?

An imupulse response, is the output you get when you apply an impulse, like a delta dirac function, to your system (only for LTI?). By knowing the impulse response you know the system.

The transferfunction relates the input to the output. I.e. this is a representation of the system.

So aren't both the same? Or Did I misunderstand something?

• They are same . – Salihcyilmaz Dec 29 '15 at 21:09
• from the vocabulary I learnt and the one used on wikipedia, the transfer function is the laplace/fourier/Z transform of the impulse response. – reuns Dec 30 '15 at 23:41

For any partially continuous function $f : \mathbb{R} \to \mathbb{R}$, the Dirac delta function has the nice property
$$f(t) = \int_{-\infty}^\infty f(s) \delta(t - s) ds$$
The Laplace transform of the inpulse response is called the transfer function. It is also useful since $\mathcal{L}\{\delta(t)\} = 1$ and $\mathcal{L}\{f * g\} = \mathcal{L}\{f\} \mathcal{L}\{g\}$. Because of this property, it gives a nice rational polynomial representation of input/output behavior of LTI systems.