EEL5701: MATLAB#3

Due Tuesday, July 8 at the beginning of class Read chapter four in I&P before you start this assignment. As usual, turn in all of the matlab code that you write. Make sure that all plots contain appropriate titles with correct axis numbering and labeling. Answer the following questions about the following difference equation for a causal, stable system:

1. Derive the system response function H(z). Be sure to specify the ROC.
2. Create a pole-zero plot in matlab. List the location of all of the poles and zeros of the system.
3. Derive an expression for the inverse Z-transform.
4. Write the inverse transform in a way that contains no complex numbers.
5. Plot either inverse transform in matlab and show that it matches the impulse response when directly applying the filter function to an impulse.
6. Plot the magnitude and phase of the frequency response . Use linear scales for both axes on each graph. (HINT: If you don't get a low pass filter response then you have done something wrong).