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Step response of a LTI system

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Calculate the step response of the system (i.e. response to x(n) = u(n)

    Previously calculated the impulse response becomes h(n) 3/11 [itex](5/8)^{n}[/itex] u(n) + 5/22[itex](1/8)^{n}[/itex]u(n)


    2. Relevant equations

    H(z) =[itex]\frac{Y(z)}{X(z)}[/itex]

    u(n) =[itex]\frac{1}{1-z^{-1}}[/itex]

    3. The attempt at a solution

    Convolution seems a possible way but that would involve an insane amount of maths. But convolution is multiplication in the z domain. Transforming the impulse response back we get
    H(z)=3/11 [itex]\frac{1}{1-\frac5 8z^{-1}}[/itex] + 5/22[itex] \frac{1}{1-\frac1 8z^{-1}}[/itex]

    Then take from the other side x(z) and multiple the top halves by X(z).

    After that switch x(z) for the u(n). After doing that it becomes something incredibly stupid that i actually cant manage to write it on this! Any help would be appreciated!
     
  2. jcsd
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