Models and Theories in Human-Computer Interaction/Digitizing the World Around Us

Nyquist
All sound consists of frequencies caused by vibrations in the world around us. A young, healthy human ear can hear in the range of 20Hz to 20kHz and thanks to Nyquist we can electronically record these analog signals into something that can be reproduced later for us to hear. According to Nyquist, for any given frequency, you only need 2 times the bandwidth of that frequency to digitally represent it accurately. Right now, computers are dumb, and they have no idea what analog signal is being pumped into them to record. If you have less than 2 times the bandwidth, the sound will not be accurately recorded. The sampling rates of fairly common sound cards are 44kHz, and some even are at 96kHz. The 44kHz sampling rate can accurately determine analog signals up to 22kHz. A 22kHz signal sampled at 44kHz would look very jagged if looked at on an oscilloscope, and would not sound like a true 22kHz analog signal without some sort of filtering. But this card can still reasonably reproduce all sounds in the range of human hearing. This being said, the more samples per second, the better. Two times the bandwidth of the signal is just the minimum rate stated by this theory. A sound engineer could likely determine the difference in a signal recorded at the Nyquist rate, or something higher.

Shannon
Shannon's theory relates to Nyquist in the sense of being able to accurately determine a signal from noise is pertinent to being able to record it without error. The signal desired needs to be higher than the noise around it, otherwise it will be very difficult, if not impossible, to find it. This is very important for signals traveling through the air like WIFI, and digital TV. In order for our devices to have good connectivity to the local WIFI, the wireless card needs to be able to determine the wireless signal from all other signals traveling through the air. A poor signal to noise ratio (SNR) would result in bit errors and spotty connections to the network or Internet. A good SNR is required for digital TV as well. I'm sure everyone has seen a TV “block up” and look funny. This happens when the SNR dips below the minimum acceptable level to reproduce the transmitted signal error free.

The fruits of Shannon's and Nyquist's theories are very pertinent in the world today but are more behind the scenes than other theories of systems, but that doesn't make either any less important.