# Thread: Inverse Laplace transform of a function

1. ## Inverse Laplace transform of a function

Hi

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...?

Thanks.

2. Originally Posted by algorithm
Hi

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...?

Thanks.
See 2.1 and 2,2 here: http://www.vibrationdata.com/math/La...Transforms.pdf

3. Hi,

Thanks. I also found a lecture which explains it in more detail (MIT edu, Signals and Systems, Lecture 4): http://dspace.mit.edu/bitstream/hand...s/lecture4.pdf