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How do I know if this discrete-time system is stable?

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data
    Given the following system:

    [tex]s[n] = (\frac{1}{4})^{n}u[n+10]u[n] [/tex]

    Prove if this is a stable or unstable system.


    2. Relevant equations



    3. The attempt at a solution

    I know that in order for a system to be stable, the input must be bounded in order for the output to be bounded. For example,

    [tex] x[n] \leq B_{x} [/tex]
    [tex]y[n] \leq B_{y} [/tex]
    [tex]So, y[n] = \sum_{k = 0}^{\infty}x[n]h[n][/tex]
    [tex]y[n] = \sum_{k = 0}^{\infty}B_{x}h[n] = B_{y}[/tex]
     
    Last edited: Oct 3, 2011
  2. jcsd
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