Why do we choose 44.1 kHz as recording sampling rate?

Question

Peoples' ears can hear sound whose frequencies range from 20 Hz to 20 kHz. Based on the Nyquist theorem, the recording rate should be at least 40 kHz. Is it the reason for choosing 44.1 kHz?

Answer 1

It is true that, like any convention, the choice of 44.1 kHz is sort of a historical accident. There are a few other historical reasons.

Of course, the sampling rate must exceed 40 kHz if you want high quality audio with a bandwidth of 20 kHz.

There was discussion of making it 48.0 kHz (it was nicely congruent with 24 frame/second films and the ostensible 30 frames/second in North American TV), but given the physical size of 120 mm, there was a limit to how much data the CD could hold, and given that an error detection and correction scheme was needed and that requires some redundancy in data, the amount of logical data the CD could store (about 700 MB) is about half of the amount of physical data. Given all of that, at the rate of 48 kHz, we were told that it could not hold all of Beethoven's 9th, but that it could hold the entire 9th on one disc at a slightly slower rate. So 48 kHz is out.

Still, why 44.1 and not 44.0 or 45.0 kHz or some nice round number?

Then at the time, there existed a product in the late 1970s called the Sony F1 that was designed to record digital audio onto readily-available video tape (Betamax, not VHS). That was at 44.1 kHz (or more precisely 44.056 kHz). So this would make it easy to transfer recordings, without resampling and interpolation, from the F1 to CD or in the other direction.

My understanding of how it gets there is that the horizontal scan rate of NTSC TV was 15.750 kHz and 44.1 kHz is exactly 2.8 times that. I'm not entirely sure, but I believe what that means is that you can have three stereo sample pairs per horizontal line, and for every 5 lines, where you would normally have 15 samples, there are 14 samples plus one additional sample for some parity check or redundancy in the F1. 14 samples for 5 lines is the same as 2.8 samples per horizontal line and with 15,750 lines per second, that comes out to be 44,100 samples per second.

Now, since color TV was introduced, they had to bump down slightly the horizontal line rate to 15734 lines per second. That adjustment leads to the 44,056 samples per second in the Sony F1.

Answer 2

Look http://www1.cs.columbia.edu/~hgs/audio/44.1.html for example. You should use sampling rate more than 40 kHz because of anti-aliasing filters. You should have some reserve in frequency to prevent signal distortion due to filter's reponse slope. The actual value of 44.1 kHz was suggested by Sony corp when audio recording standard was under discussion in 1979. They used this rate widely for that moment.

So it's generally historical reason.

Answer 3

In the transition to digital formats, audio were stored in a pseudo-video waveform that could be seen as either black or white (representing the binary format).

The field rate and structure used by the television standard is as follows for 60 Hz video: 245 lines per field (excluded the first 35 blanked lines). With three samples per line that makes 60 x 245 x 3 = 44100 = 44.1 KHz.

This convention were later used for the CD format, due to equipment compatibility concerns (the very first equipment used to produce CD masters used for CD replication was video based).

Source: The Art of Sound Reproduction, p. 228

Answer 4

The detailed historical reason for the choice of 44.1 khz vs basic Nyquist 40K, etc is given in The Art of Digital Audio by John Watkinson. The excerpt is shown at: http://www1.cs.columbia.edu/~hgs/audio/44.1.html

Essentially it has to do video frequencies, field lines, and the fact that CD authoring was, for a long time, done on gear that was video-based.

Examples:

50hz video had 588 active lines per frame, or 294 per field (37 lines blank). 50 x 294 x 3= 44.1 K.

60hz video: 35 blank lines, 490 active, 245 per field. 60 x 245 x 3=44.1 K

Answer 5

https://en.wikipedia.org/wiki/44,100_Hz#Why_44.1_kHz.3F The Nyquist–Shannon sampling theorem says the sampling frequency must be greater than twice the maximum frequency one wishes to reproduce. Since human hearing range is roughly 20 Hz to 20,000 Hz, the sampling rate had to be greater than 40 kHz.

In addition, signals must be low-pass filtered before sampling to avoid aliasing. While an ideal low-pass filter would perfectly pass frequencies below 20 kHz (without attenuating them) and perfectly cut off frequencies above 20 kHz, such an ideal filter is theoretically impossible (it is noncausal), so in practice a transition band is necessary, where frequencies are partly attenuated. The wider this transition band is, the easier and more economical it is to make an anti-aliasing filter. The 44.1 kHz sampling frequency allows for a 2.05 kHz transition band.

In addition, 44,100 is the product of the squares of the first four prime numbers (2^2 * 3^2 * 5^2 * 7^2) and hence has many useful small factors.

Answer 6

It seems the hearinig limit for humans might be much higher than 20kHz if looked at from "dynamic" time resolution perspective rather than typical static sinusoidal waves. Also interesting comments about the margin between 20kHz and 22 kHz for reconstruction filtering. Actually there's been quie interesting work from Peter Craven on time-domain optimized filtering which argues for at least 96kHz for hi-fi playback.

Pawel

Answer 7

Look [http://batmobile.blogs.ilrt.org/audio-analysis-on-an-iphone for description . .A theorem called the Nyquist sampling theorem states that in order to sample a signal of X Hz without significant loss of quality, you need to sample at 2X the frequency. The limit of human hearing is approximately 20kHz, which hence requires a sample rate of approximately 40Khz. This is why CDs are sampled at 44Khz. i.e. each second of recording in a CD contains 44,000 measurements of the highest possible frequency contained in the recording.