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Determining if a discrete signal is BIBO stable

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data
    VTVuM.jpg


    2. Relevant equations
    BIBO stability requires, for every input, that the system output y(n) is:

    |y(n)| ≤ By < ∞

    Linear time invariant systems are BIBO stable when:

    Summation from -∞ to ∞ |h(n)| ≤ Bn < ∞


    3. The attempt at a solution

    For part a, I got the system was unstable. As n increase the input grows exponentially by a factor of 2. So that means depending on my input x(n) can never be bounded.

    Part b, I also got unstable, since the inputs are not bounded. And it may grow exponentially or decrease exponentially depending on x(n).

    Part C, it's periodic so it's always unstable

    Part D, I got BIBO unstable since the inputs are not bounded. It's the summation from negative infinity to n.


    Can anyone help verify my answers? Thank in advance!
     
  2. jcsd
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