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

  • 3
    $\begingroup$ this is pretty fundamental Linear System Theory. don't you have a textbook somewhere? $\endgroup$ Sep 19, 2018 at 20:13

1 Answer 1



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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.