Answer the following difficult questions correctly and ensure your working is also correctly and easy to understand!

1.Given signal x(n)= anu(n)+bnu(-n-1), determine the ROC of the z- transform.

2.The entire z- plane, except at z=0 is the ROC of which signal?

3.How can you illustrate the following sequence 1/2[X(z)+X*(z*)]. Give an assumption.

4.Solve and illustrate your finding in the signal x(n)=(n-n0).

5.Solve and illustrate for x(n)=(n-k) the 1- sided z- transform.

6.Given 5+7z-1+z-3 as a one-sided z- transform X+(z), solve for the signal x(n)

7.The LTI of a causal system has function H(z)=1/10.5z1+2/13z1. Determine the ROC of H(z).

8.When does a system become BIBO stable and causal?

9.Determine the equation satisfied where |z| equals 101/2 .

10.Re(z)-Im(z) equals to 1 for complex numbers z where z+z is the root of x2-10x+16=0. Determine the equation with roots Re(z) and Im(z).