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Math Help - How to evaluate these convolutions:

  1. #1
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    How to evaluate these convolutions:

    How to evaluate these convolutions:

    a) y(t) = (u(t) - u(t-2)) * u(t)

    b) z(t) = cos(pi*t)(u(t+1) - u(t-1)) * u(t)

    c) n(t) = (e^at)u(t) * (u(t+2) - u(t))

    where * represents convolution symbol
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  2. #2
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    Re: How to evaluate these convolutions:

    Quote Originally Posted by essedra View Post
    How to evaluate these convolutions:

    a) y(t) = (u(t) - u(t-2)) * u(t)

    b) z(t) = cos(pi*t)(u(t+1) - u(t-1)) * u(t)

    c) n(t) = (e^at)u(t) * (u(t+2) - u(t))

    where * represents convolution symbol
    Use the basic L-transform property...

    y(t)=f(t)*g(t) \implies \mathcal{L}\{y(t)\}= \mathcal{L}\{f(t)\}\ \mathcal{L}\{g(t)\} (1)

    Kind regards

    \chi \sigma
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  3. #3
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    Re: How to evaluate these convolutions:

    Quote Originally Posted by chisigma View Post
    Use the basic L-transform property...

    y(t)=f(t)*g(t) \implies \mathcal{L}\{y(t)\}= \mathcal{L}\{f(t)\}\ \mathcal{L}\{g(t)\} (1)

    Kind regards

    \chi \sigma
    Dear Sir,

    In this class, we haven't started using Laplace Transform yet...The only way is to use convolution integral, I would be glad if you could help me...

    With my kind regards,
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  4. #4
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    Re: How to evaluate these convolutions:

    Quote Originally Posted by essedra View Post
    Dear Sir,

    In this class, we haven't started using Laplace Transform yet...The only way is to use convolution integral, I would be glad if you could help me...

    With my kind regards,
    What have you tried and where do you get stuck? Please show all working.
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  5. #5
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    Re: How to evaluate these convolutions:

    a)
    y(t) = (u(t) - u(t-2)) * u(t)
    y(t) = u(t) * u(t) - u(t-2) * u(t)

    and then I couldn't continue because I don't know how to evaluate this convolution.
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  6. #6
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    Re: How to evaluate these convolutions:

    Quote Originally Posted by essedra View Post
    a)
    y(t) = (u(t) - u(t-2)) * u(t)
    y(t) = u(t) * u(t) - u(t-2) * u(t)

    and then I couldn't continue because I don't know how to evaluate this convolution.
    You said in an earlier post that "The only way [you're allowed to do them] is to use convolution integral"

    Surely you can set up the integrals ....? So, again - what have you done and where do you get stuck?
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  7. #7
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    Re: How to evaluate these convolutions:

    ( integral from T= minus infinity to T=infinity u(T) . u(t-T)dT ) - ( integral from T= minus infinity to T=infinity u(T) . u(t-2-T)dT )
    I know that when we integrate with u(t), the integral starts from zero to infinity...Then, I couldn't solve the rest...
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  8. #8
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    Re: How to evaluate these convolutions:

    Quote Originally Posted by essedra View Post
    ( integral from T= minus infinity to T=infinity u(T) . u(t-T)dT ) - ( integral from T= minus infinity to T=infinity u(T) . u(t-2-T)dT )
    I know that when we integrate with u(t), the integral starts from zero to infinity...Then, I couldn't solve the rest...
    What is the function u(t)? How is it defined?
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