Anyone who has even a cursory interest in digital audio might have come across the name Harry Nyquist, and the theorem that bears his name. That’s because without his work (but not just his alone), good, clean, modern digital audio wouldn’t exist. So, who exactly was Harry Nyquist, and why should we care? Well, the good news for those that don’t care is that you don’t need to know. Unless you’re an engineer working on digital sampling in either audio or video, life will continue without interruption.
However, for those interested, we need to look at the work Harry Nyquist (1889-1976) did for Bell Labs (originally AT&T) with particular reference to the early use of the telegraph. Born in Sweden, Nyquist began work for AT&T in 1917 and, in the mid- to late 1920s, he published two papers that dealt with communication problems as applied to telegraph transmission and thermal noise in electric conductors. His work was later taken up by Claude Shannon (1916-2001) who applied that earlier work to digital sampling.
To be precise, what is commonly referred to as the “Nyquist theorem,” in reference to digital audio sampling, should really be called the Nyquist-Shannon sampling theorem, since Nyquist’s contribution didn’t deal with sampling, but rather with the maximum amount of information that can be sent down transmission wires and successfully recreated at the other end. The Nyquist-Shannon sampling theorem states that to successfully digitize an analog audio signal, and later accurately reconstitute it, requires that the sampling frequency used by the analog-to-digital converter be twice the highest frequency rate contained in the original signal.
"...the filter cutoff is moved up to 22.05kHz, which brings us to today’s CD sampling rate of 44.1kHz."
If you are sampling audio that contains frequencies at the extremes of human hearing (approximately 20Hz to 20kHz), you would need to sample that material, at the very least, 40,000 times a second, or at 40kHz. To make sure there are no other frequencies present above the top range, steep low-pass filters are applied to the source material prior to sampling. And since a steep 20kHz low-pass filter would impact frequencies just below that, the filter cutoff is moved up to 22.05kHz, which brings us to today’s CD sampling rate of 44.1kHz.
But why filter? Why not just sample at 22.05kHz? This is the crux of Nyquist’s and Shannon’s respective research. It was found that a one-to-one ratio of audio-to-sampling frequency would not provide sufficient information for the digital-to-analog converter (DAC) to accurately reconstitute the original signal. Certain frequencies might appear to the decoder as being higher than they actually were, causing false frequencies or “aliases” to be generated instead of the original frequency—hence the term "anti-aliasing" filters.