# Transfer Function vs Frequency Response

Talking about Butterworth filters my prof said that a filter is described by its frequency response $$H(\omega )$$.

What I think is that filter is really described by its transfer function, since there can exist many transfer functions that share the same $$H(\omega )$$. Was my prof wrong?

But if you're using something as a (linear, which is often implied) filter, then all you care about is the frequency response (otherwise, you'd probably not be calling the thing "filter"). So, when I define a filter, it's usually sufficient to specify $$H(\omega)$$.