Find the impulse response of the following: Assume the system is initially at rest.
y[n] - (1/2) y[n-1] = x[n] + 2 x[n-1] + x[n-2]
The Attempt at a Solution
To find the impulse response y[n]: we know that y[n] = homogenous solution + particular solution
lamda - (1/2) = 0 => lamda= (1/2)
homogenous solution = C1*(1/2)^n
For the particular solution, we assume that a x[n] = delta[n]...am i correct?
so ... y[n] - (1/2) y[n-1] = delta[n] + 2 delta[n-1] + delta[n-2]
so, for n >2, delta[n] = 0
=> y[n] - (1/2) y[n-1] = 0, which means the particular solution is the homogenous solution?
Can someone help me with this?