I am looking for an analytic description of a continuous-time Butteworth High-pass filter in the time domain (=impulse response)
$\frac{s^n + b_{n-1}s^{n-1}+\cdots+b_0}{s^n + a_{n-1}s^{n-1}+\cdots+a_0} = 1 + \frac{(b_{n-1}-a_{n-1})s^{n-1}+\cdots+b_0 - a_0}{s^n + a_{n-1}s^{n-1}+\cdots+a_0}$, and the inverse Laplace transform of 1 is $\delta(t)$.
Is that enough to get on with?