EE473 Homework #4

Reading : Chapter 3

1. (4pts) A linear shift invariant system is characterized by its unit sample response

   h[n] = e^-n u[n]

   1. Is the system causal? Why?

   2. Is the system stable? Why?

   3. Find the system function H(z) and give a pole-zero plot

   4. Use MATLAB to plot magnitude and phase responses of H(e^jw)

   5. Give a difference equation realization of the system

   6. Find a realization in terms of the convolution sum

2. (4 pts) Given a unit sample response

   h[n]= 0.36788ⁿ, 0 <= n <= 3

   h[n]= 0 otherwise

   1. Find the corresponding system function H(z).

   2. Find the pole-zero plot for this system function. (You might want to use the MATLAB roots function for this)

   3. Use MATLAB to plot magnitude and phase responses of H(e^jw)

   4. Compare the magnitude characteristic of this problem and that of the previous problem by plotting them on the same graph. Comment.

3. (4 pts) Problem 3.33 from Textbook (2nd Edition)

4. (4 pts) Problem 3.46 from Textbook (2nd Edition)