- #1
EugP
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Homework Statement
For the discrete-time system:
[tex]y[k+2]+\frac{1}{6}y[k+1]-\frac{1}{6}y[k]=f[k+1]+f[k][/tex]
Find the impulse response.
Homework Equations
The Attempt at a Solution
Alright so I started like this:
[tex]h_0[k+2]+\frac{1}{6}h_0[k+1]-\frac{1}{6}h_0[k]=0[/tex]
[tex]h_0[1]=0[/tex]
[tex]h_0[2]=1[/tex]
Now this is where I'm stuck. I know I need to get the equation for [tex]h_0[k][/tex], but I don't know how. The equation they got is:
[tex]h_0[k]=C_1(-\frac{1}{2})^k+C_2(\frac{1}{3})^k[/tex]
Can anyone tell me how they got there?