1. Problem 3.2 (a) (b) (f) (h). Also indicate the region of convergence.

2. Problem 3.9

3. Probelm 3.12

4. Problem 3.24

5. Problem 3.25.

6. When the input to an LTI system is

x(n) = (\frac{1}{2})^{n} u(n) + 2^{n}u(−n − 1),

the output is

y(n) = 6 (\frac{1}{2})^{n} u(n) − 6 (\frac{3}{4})^{n} u(n).

• Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the region of convergence.

• Find the impulse response h(n) of the system.

• Write the difference equation that characterizes the system.

• Is the system stable? Is it causal?