On partial fractions. Remember this: Always start by multiplying both sides by \(z^{-1}\), so we end up with
\(\frac{X\left ( z\right ) }{z}\), and do partial fraction on the RHS, which now should be with one less zero in the numerator. Once done, then find \(X\left ( z\right ) \) by multiplying the result with \(z\) again. Here is an example:
Looked at case with multipoles for partial fractions. This requires derivatives. See the notes. I do not think we will get one like this in the example.
Then went over HW3, the sampling problem. This is important. Remember that aliasing happens at frequencies which are \(f_{0}+kf_{s}\) where \(f_{0}\) is the frequency of the signal (highest) and \(f_{s}\) is the sampling frequency, and \(k=1,2,3,etc..\)
Looked at more partial fractions. Just multiply both sides by \(z^{-1}\) and should be ok.