Assume there's a FIR filter with three zeros locate at $e^{j\frac{\pi}{4}}$, $e^{-j\frac{\pi}{4}}$ and $-\sqrt{2}$, while three poles locate at the origin.
Please:
(a) find its transfer function.
(b) determine if this filter is stable, why or why not?
(c) find and sketch its impulse response.
