Compare the result obtained in part 3 with the first 20 samples of the analytical ZSR obtained in part 2. You can plot the difference between two signals. It should be a signal with very small samples.

1. Use the function “impz” in MATLAB to find the first 20 samples of the impulse response of the following system:

]1[2][]2[4][ ––=–+ nxnxnyny

Verify that the impulse response of the above system is (plot the result obtained from “impz” and the first 20 samples of in two subplots on the same window).

2. Analytically (without MATLAB) calculate the zero–state response (ZSR) of the system to the input . The zero–state response is

3. Find the first 20 samples of the ZSR of the above system to the input (step response) using MATLAB (you may use “filter” or “stepz” functions in MATLAB).

4. Compare the result obtained in part 3 with the first 20 samples of the analytical ZSR obtained in part 2. You can plot the difference between two signals. It should be a signal with very small samples.