Aliasing- according to Wikipedia is an effect that causes artifacts or distortions that differ form the original signal. To be most blunt in relation to this course, the sampling rate is not frequent enough to adequately reconstruct the original signal being sampled.
Nyquist Therom: Fn = 2B
By just looking at that it's not very apparent what it means. Fn is the Nyquist rate, which is defined by two times the highest frequency found in the signal that is being sampled.
Why do we care? Well if we want to limit the amount of aliasing we get in out reconstructed signal, it becomes necessary to sample the original signal with a higher frequency than the Nyquist rate or Fs > Fn.
What is sampling? That's essentially when you take a signal and hit it with a delta function at a certain frequency or rate.
Fun things that happen if the original is sampled faster than the Nyquist rate: The reconstructed signal can appear to be going the opposite direction than the original or not be moving at all.
Sampling at the Nyquist rate gives a signal that only shows two points of the period and a recreated signal would not be able to reconstruct the direction of the original signal.
Real World Applications: A to D converter or analog to digital converter. Lets say we want to record the latest greatest hit from our favorite music artist, because we realize that said artist isn't always going to be available when we sudden get the urge to hear their songs. So we convinced them to play for us and we setup a microphone and a digital recorder. We need to setup a sampling rate so we can catch and recreate every note being played. We have to sample frequently enough to catch the highest frequency the human ear can hear. If we set our sampling rate too low certain notes will sound just fine while higher ones will will come out as different notes entirely (mostly noise,which would be very sad). That's why we want to set our sampling rate to more than twice the highest frequency that can be heard so we can accurately recreate the song (well as accurately as hardware will allow)!
