**Homework Assignment 2 **

Due Sep. 8, 1999

- Problem 2.2.
- Problem 2.5. Use MATLAB to plot the first 20 samples of both the impulse response and step response.
- Problem 2.18
- No problem 4
- 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 inputx[n] = u[n] - u[n-10]

- 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.- 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]

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

*Bill Rison, <rison@ee.nmt.edu >* - Show that f[n] is the imupulse response of a causal LTI system described
by the difference equation