Consider an IIR system with impulse response $h[n]=\left( \frac{1}{\sqrt{3}} \right)^n u[n]$. If I apply $x[n]=\cos(n \frac{\pi}{2} + \varphi)$ at the input, how can I determine the change in magnitude and phase of the output signal, i.e. what is $A$ and $\phi $ in $y[n]=A\cos(n \frac{\pi}{2} + \varphi + \phi)$?

Matt L. 09/19/2018.

**HINT:**

- Compute the system's frequency response $$H(e^{j\omega})=\sum_{n=-\infty}^{\infty}h[n]e^{-jn\omega}$$
- Compute its magnitude and phase
- Figure out (by searching this site or any textbook on Signals and Systems) how the magnitude and phase of $H(e^{j\omega})$ affect a sinusoidal input signal.

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