Need another brain to pick as getting brain drained now. I got an LTI system and I was able to calculate my system up to H(z):
$H(z) = 1 - \frac{2}5z^{-1} +z^{-2} - \frac{2}5z^{-3} $
I have an input $x(n) =2\cos(\frac{\pi}2n)$ so I tried to get the frequency response at $\omega = \frac{\pi}2$ but I get zero as a result.
$H(e^{i\frac{\pi}2}) = 1 - (\frac{2}5)(\frac{1}j)+(\frac{1}{j^2})-(\frac{2}5)(\frac{1}{j^3})=0$
Is my process correct? Is it possible for the frequency response to be zero at an angle? If so, how can I convolve it with the input so I can get the output? Been researching and reading about this but this is the first I encountered that the frequency response was zero and I don't know how to proceed from there. Appreciate any thoughts. cheers!
The system you are studying is a low-passfilter with a zero at $\omega=\pi/2$. The output at this particular frequency is indeed zero as you found which means that the output of the filter is zero, $y[n]=0$ for an input signal $x[n]=\cos(n\pi/2)$