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Complex exponential X delta function

  1. Feb 22, 2012 #1
    1. Problem Statment:
    Sketch the sequence x(n)=[itex]\delta[/itex](n) + exp(j[itex]\theta[/itex])[itex]\delta[/itex](n-1) + exp(j2[itex]\theta[/itex])[itex]\delta[/itex](n-2) + ...

    3. Attempt at the Solution:
    The angle theta is given in this case Can someone remind me of how to multiply a complex exponential by a delta function? This sequence represents impulse signals. Such multiplication yields a real and imaginary component. Would I ignore the imaginary component and essentially keep the cos(k[itex]\theta[/itex])? Thanks very much.
     
    Last edited by a moderator: Feb 22, 2012
  2. jcsd
  3. Feb 22, 2012 #2

    cepheid

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    Okay, so the terms in your sequence are complex valued. So the only way to really represent that is as two separate sequences. You can just use the Euler equation:

    exp(jθ) = cos(θ) + jsin(θ)

    So you could draw two separate sequences, each one representing the real part and the imaginary part x(n) respectively.

    Alternatively, I suppose you could try to draw points in the complex plane.
     
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