b) Response of Signal in Question 1
From Question 1: Unfortunately, I did not make a DT signal for Parts 1/2. Instead of going back and redoing my work, I am going to "steal" the work of a Mr. Collin Phillips (my apologies and gratitude to Mr. Collin Phillips).
According to his work:
- $ \,\ X[n] = 3cos(3\pi n + \pi) $
- $ \,\ a_0 = 0 $
- $ \,\ a_1 = -3 $
- $ \,\ a_k = 0 $ elsewhere
- $ \,\ N = 2 $
Response of the System $ \,\ y[n] = \sum_{k = <N>}^{\infty} a_k H[e $$ j2\pi k/N $$ \,\ ]e $$ jk(2\pi /N) n $
Because $ a_k $ only has one value, this shouldn't be that hard to calculate.
$ \,\ a_k $ is only valid at $ a_1 = -3 $. Therefore...
$ \,\ y[n] = -3 * $
