Digital Signal Processing Practice Test 2

1. What is the set of all values of z for which X(z) attains a finite value?

2. What is the inverse z-transform of X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z| < 0.5?

3. If X(z) is the z-transform of the signal x(n) then what is the z-transform of aⁿx(n)?

4. If Z{x₁(n)}=X₁(z) and Z{x₂(n)}=X₂(z) then Z{x₁(n)*x₂(n)}=?

5. If X+(z) is the one sided z-transform of x(n), then what is the one sided z-transform of x(n-k)?

6. A linear time invariant system is characterized by the system function H(z)=\(\frac{1}{1-0.5z^{-1}}+\frac{2}{1-3z^{-1}}\). What is the ROC of H(z) if the system is causal?

7. What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)?

8. For what kind of signals one sided z-transform is unique?

9. Which of the following is a Dirichlet condition with respect to the signal x(t)?

10. If all the poles have small magnitudes, then the rate of decay of signal is __________