Homework Assignment 5
Due Oct. 3, 1997

1. Problem 4.20 from Orfanidis. In addition, write the state space matrices for the transposed system.

2. A discrete-time system has the impulse response

                 /
                |  3             n =  0
                | 
        y(n) =  |  2             n =  1
                |
                |  cos(pi n/4)   n >= 2
                 \
   

   1. Find the difference equation which describes the system which generates this response.
   2. Use MATLAB to verify your result. I.e., use MATLAB to generate y(n) for n = 0:9, and use the MATLAB dimpulse function to generate the impulse response from the difference equation. Show that they are the same.

3. Consider the following difference equation:

   
        y(n) + 0.2 y(n-1) - 0.48 y(n-2) = x(n) - 2 x(n-1) + 2 x(n-2)
   
   

   1. Find the step response of the difference equation.
   2. Use the MATLAB dstep function to verify your result.
4. Problem 5.2 from Orfanidis.
5. Problem 5.3 (a) and (b) from Orfanidis.
6. Problem 5.4 from Orfanidis.