In particular I am having trouble with 6b).
From what I understand, we can split a difference LTI equation into two sums, the sum of the previous responses, and the sum of the previous inputs. Something like this:
Now to get a zero-state response, I have to zero out the first part of the formula. This I understand.
So to get the zero-state step response, I must use
x[n] = u[n] and zero out all past outputs of the system.
The problem I'm having is deriving
y[n] in the first place.
I have had a couple ideas, however am not confident in their correctness:
H(z) = Y(z)/X(z)I could compare the given
Y(z)(1 - 1/z)because that's the z-transform of 1/u[n]. Correct me if I'm wrong. Then I could make Y subject of the formula and figure out the inverse transform from there.
I thought about using convolution with the inverse transform of
H(z)and input signal
However I'm not convinced these are correct because nowhere am I "enforcing" the definition of zero-ing out the previous outputs.
Any guidelines would be appreciated!