Determining if a discrete signal is BIBO stable

  • #1
Lolsauce
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Homework Statement


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Homework 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 < ∞


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!
 

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