Bumping in hope of an answer.
1. The problem
Consider the difference equation .
What is the
(a) step response for the causal system satisfying this difference equation,
(b) general form of the homogeneous solution of the difference equation?
(c) Consider a different system satisfying the difference equation that is neither causal nor LTI, but that has y[0] = y[1] = 1. Find the response of this system to x[n] = [n].
2. Relevant equations and definitions
Oppenheim's definition of (b), the general form of the homogeneous solution:
3. The attempt at a solution
(a) step response, s[n]
I have calculated the impulse response , and put it to use in calculating s[n] (where I get stuck):
(b) general form of the homogeneous solution
I have no idea (similar problem as (a) in this question on MHF) ... the solution ought to be .
(c) response of a particular system to x[n] = [n]
Confused as well. I do get particular values for y[n]:
y[-1] = 41/5,
y[0] = 1,
y[1] = 1,
y[2] = 2/3,
...
continuing in this manner (and hoping for a pattern to emerge) surely isn't the way to go?
The solution given is:. Other answers are possible.