Homework Assignment 2
Due Sep. 8, 1999

1. Problem 2.2.

2. Problem 2.5. Use MATLAB to plot the first 20 samples of both the impulse response and step response.

3. Problem 2.18

4. No problem 4

5. Consider a system with the impulse response

                    n
        h[n] = (0.9)  u[n]
   

   Use convolution to find the output of this system to an input

        x[n] = u[n] - u[n-10]
   

6. The sequence of Fibonacci numbers f[n] is a causal sequence defined by

            f[n] = f[n-1] + f[n-2],   n > 2

   with f[0] = 0 and f[1] = 1.
   1. Show that f[n] is the imupulse response of a causal LTI system described by the difference equation

          y[n] = y[n-1] + y[n-2] + x[n-1]

   2. Develop a formula to calculate f[n] directly for any n; i.e., find the impulse response for the difference equation of Part a.
   
   

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   Bill Rison, <rison@ee.nmt.edu >