What is an Alias?

• Discrete sinusoids have infinite aliases but it is the one lowest in frequency ($< f_s/2$) that will sound.
  

• Infinite sinusoids (with frequencies $f_0 \pm l f_s$) will produce the same sample values as the sinusoid at $f_0$.

• Challenge: show by proving the following equality:
  $$A\cos(2\pi f_0nT_s + \phi) = A\cos(2\pi (f_0 \pm lf_s)nT_s + \phi),$$