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Math Help - Inverse Laplace transform of a function

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by algorithm View Post
    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
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  3. #3
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    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
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