Homework Assignment 1
Due Sep. 1, 1999

1. Problem 2.7.
   1. For Part (c), plot several cycles of the function using MATLAB using the stem function.

2. Problem 2.29. Do the plots in MATLAB using the stem function.

3. Plot the following functions using the stem function of MATAB.
   1. x[n] = (0.9)ⁿ cos(0.1 pi n + pi/6)       0 <= n <= 40
   2. x[n] = (0.9)ⁿ cos(4.1 pi n + pi/6)       0 <= n <= 40
   3. x[n] = (0.75)ⁿ[u(n+6) - u(n-5)] + 5 delta(n-2)       -10 <= n <= 10

4. Consider the discrete-time system y[n] = T{x[n]} = n x[n].
   Assume that the input to this system is x[n] = u[n]-u[n-4].
   1. Is the system time invariant?
   2. Sketch the input x[n].
   3. Sketch the output y[n].
   4. Sketch the output y[n-2].
   5. Let x₁[n] = x[n-2]. Sketch the input x₁[n].
   6. Determine and sketch the output y₁[n].
   7. Is the output y₁[n] equal to y[n-2]?

5. Repeat Problem 4 for the system y[n] = T{x[n]} = (x[n+1] + x[n] + x[n-1])/3