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Thread: Laplace Transforms - find the system response

  1. #1
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    Laplace Transforms - find the system response

    Hello,

    I'm stuck part way through this:

    A Linear, time invariant system has the impulse response $\displaystyle h(t) = tu(t-1) $ Find the transfer function $\displaystyle H(s)$ and use it to find the response to the input $\displaystyle x(t) = u(t) - 2u(t-1) + u(t-2)$

    I have found $\displaystyle H(s) = \frac{e^{-s}}{s^2} + \frac{e^{-s}}{s}$

    And $\displaystyle X(s) = \frac{1}{s} - \frac{2e^{-s}}{s} + \frac{e^{-2s}}{s}$

    But I'm confusing myself in the algebra to find Y(s)... I keep ending up with long, confusing equations. I can't seem to find the correct form for the inverse laplace transform...

    I would prefer a few hints in the right direction or a starter rather than a full blown solution if you could
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: Laplace Transforms - find the system response

    Quote Originally Posted by halfnormalled View Post
    Hello,

    I'm stuck part way through this:

    A Linear, time invariant system has the impulse response $\displaystyle h(t) = tu(t-1) $ Find the transfer function $\displaystyle H(s)$ and use it to find the response to the input $\displaystyle x(t) = u(t) - 2u(t-1) + u(t-2)$

    I have found $\displaystyle H(s) = \frac{e^{-s}}{s^2} + \frac{e^{-s}}{s}$

    And $\displaystyle X(s) = \frac{1}{s} - \frac{2e^{-s}}{s} + \frac{e^{-2s}}{s}$

    But I'm confusing myself in the algebra to find Y(s)... I keep ending up with long, confusing equations. I can't seem to find the correct form for the inverse laplace transform...

    I would prefer a few hints in the right direction or a starter rather than a full blown solution if you could
    The impulse response is $\displaystyle h(t)=t\ u(t-1)$ and it has 'only one' term in t... then why the tranform of h(t) You computed has two terms in s?...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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