# Noise sensitivity transfer function

Consider we have a second order system (plant) described by the following transfer function:

$$P(s) = \frac{b_0}{s^2+a_1*s+a_2}$$

which is controller by a PD-controller:

$$C(s) = K_p+K_ds$$

In order to study the impact that the external noise has to the system, I have come across the so called noise sensitivity function which is described by the below equation:

$$N(s) = \frac{C(s)}{1+P(s)C(s)}$$

However, deriving $$\ N(s)$$ produces an improper transfer function with degree of numerator being $$\ 3$$ and of denominator being $$\ 2$$. This results, for example, to the imcapability of obtaining a step response in order to study the behaviour. Is the definition of the noise sensitivity function wrong or am I missing something ?