(a) Find y(n) for x(n) as above for the system y(n) = ay(n-1) + x(n-1)
(b) Draw a block diagram of this system.
Solution.
(a) In this case, the output is the sum of past outputs as well as the past inputs.
| n | x(n) | x(n-1) | y(n) |
| 0 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 0 | 1 | a+1 |
| 3 | 0 | 0 | a*(a+1) |
| 4 | 0 | 0 | a*a*(a+1) |
| . | . | . | ... |
(b) The block diagram of this system is as follows:
