Ensure you understand what the below complex questions entail before attempting to answer any. Give detailed explanations and examples where required.

1. The origin at 2 of sample x(n)={1,2,3,1} and h(n)={1,2,1,-1} is 7. Determine whether this statement is true or false. Explain

2. Equation h[n]*h1[n]=[n] is a proof of a certain property of an LTI system. Which property?

3. What is represented by y[n] = x[n] * t[n] * r[n]? Expound on your answer.

4. Give an example of a causal system. Explain

5. Given two discrete time sequences and their convolution sum, find the sum of impulses.

6. What does x[n] * h[n] represent?

7. Determine the tools used to graphically find the convolution of discrete signals of time.

8. Through which equation can we determine output of a discrete time convolution.

9. Determine the convolution of x[n]=e-n2 and h[n]=n2 .

10.Givenx[n][n] = x[0][n], x[n][n] = [n], andx[n][n] = x[0] determine the correct one in regard to impulse signal.