# How does an IIR system affect magnitude and phase of a sinusoidal signal

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 $y[n]=A\cos(n \frac{\pi}{2} + \varphi + \phi)$?

• this is pretty fundamental Linear System Theory. don't you have a textbook somewhere? – robert bristow-johnson Sep 19 '18 at 20:13

1. Compute the system's frequency response $$H(e^{j\omega})=\sum_{n=-\infty}^{\infty}h[n]e^{-jn\omega}$$
3. 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.