Say I have the following transfer function:
$$\mathcal{H}(s) = \frac{Bs^2}{a^2 + \frac{a}{Q}s +s^2}$$
I want to prove it is a Low-Pass filter. In order to do it I'd like to change it to phasor form so I can calculate the gain \$|G|\$ when \$\omega \rightarrow 0\$ and \$\omega \rightarrow \infty\$ (as I do with impedance). But how could I transform it to the phasor form?
On the other hand, would it be correct if I just did \$\mathcal{H}(s \rightarrow \infty) = B\$ and \$\mathcal{H}(s \rightarrow 0) = 0\$ to assume it is a Low-Pass filter? That way I would also say that for
$$ \mathcal{H}_1(s) = \frac{B}{a^2 + \frac{a}{Q}s +s^2} $$
we have \$\mathcal{H}_1(s \rightarrow \infty) = 0\$ and \$\mathcal{H}_1(s \rightarrow 0) = \frac{B}{a^2}\$ so it is a High-Pass filter?
Is my approach correct?