A simple filter has the Laplace transform
H(s) = 1/(s + 1)
This gives its time-domain impulse response, h(t), as a decaying exponential:
h(t) = exp[-t] * (Heaviside step function)
I want to find the inverse impulse response, h_inv(t). To do this, I first take the reciprocal of H(s):
G(s) = reciprocal of H(s) = 1/H(s) = s + 1
Now, to find h_inv(t), I need to take the inverse Laplace transform of G(s). The difficulty I'm having is working out the inverse transform of s.
Have I done something wrong...?