Determining if a discrete signal is BIBO stable

[Lolsauce]

Homework Statement

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!

 

[KataKoniK]

it is important to always double check your work and make sure it is accurate. Here are some suggestions to verify your answers:

1. Check your calculations: Make sure you have correctly calculated the output y(n) for each input x(n) in parts a, b, and d. Also, for part c, make sure you have correctly identified the system as periodic.

2. Use mathematical proofs: In order to prove that a system is unstable, you need to show that there exists at least one input that results in an unbounded output. Can you provide a mathematical proof for each part to support your answer?

3. Consider different types of inputs: In your solutions, you have assumed that the inputs grow or decrease exponentially. However, there could be other types of inputs that could result in bounded outputs. Can you think of any other possible inputs for each part and analyze their effects on the system?

4. Consult with a colleague or professor: It is always helpful to discuss your solutions with someone else who has knowledge in the subject. They may be able to provide additional insights or point out any errors in your reasoning.

By following these steps, you can ensure that your answers are correct and well-supported. Keep up the good work!