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Determine the unit-step response of the discrete-time LTI systems

  1. Mar 24, 2013 #1
    Determine the unit-step response of the discrete-time LTI
    systems described by the following impulse responses:

    h[n]=(0.9)[itex]^{n}[/itex]e[itex]^{j(\pi/2)n}[/itex]u[n]


    So I am completely confused. . . I don't even know how to start. . . I want to say that I need to do a summation but the more examples and text I look up the more I'm in the dark. . . any help is appreciated.

    The only thing I can think to start is you assume

    x[n] = u[n]
     
  2. jcsd
  3. Mar 24, 2013 #2

    rude man

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    How about convolving u[n] with your h[n]?
     
  4. Mar 25, 2013 #3
    My apologies for taking so long to reply. I was able to talk to my professor and this is what I have now.

    [itex]\sum[/itex](0.9)[itex]^{k}[/itex]e[itex]^{j(\pi/2)k}[/itex]u[n-k] from k = -∞ to ∞.

    this turns into

    [itex]\sum[/itex](0.9)[itex]^{k}[/itex]e[itex]^{j(\pi/2)k}[/itex] from k = 0 to n.

    using the property of summation :

    [itex]\sum[/itex] a[itex]^{k}[/itex] = [itex]\frac{1-a^{n+1}}{1-a}[/itex]

    my new snag is what do I define as a?
     
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