Compact Disc History and 20 kHz lowpass filtering

According to the Nyquist Theorem,
in order to achieve lossless sampling,
the sample rate must be at least twice as high
as the highest recorded frequency. Thus, an audio signal
with a bandwidth of 20 kHz would require a sampling rate
of at least 40,000 samples/second. It is of equal importance
that no audio signal that is greater than half the sampling frequency
enters into the digitizing process. Such sampled frequencies
introduce erroneous frequencies, known as alias frequencies,
whose lower harmonic multiples enter the audio signal
as false descending frequencies, producing harmonic distortion.
To eliminate the effects of aliasing, a low-pass filter is used
before the analog-to-digital conversion process
in order to remove frequencies above the Nyquist
half-sampling frequency limit.

As the frequency of an incoming signal increases, the shorter period
will be represented by fewer samples, until, at 20 kHz,
the reproduced waveform is represented as a square wave.
In order to eliminate these types of higher-frequency
output distortions and to preserve the lossless nature of sampling,
another low-pass filter is placed at the output of the device.
This has the effect of blocking the upper harmonic components
of a 20-kHz square wave, leaving only the original
undistorted waveform.

The latter is the reason for the low-passing
in CD-Audio (or so called Red Book) players.



Ever since the late seventies, the concept of The Compact Disc
has been a project by Philips and Sony working closely together
on the development of this laser-based audio-carrier.
Leader in this research has been Dr.Kramer,
and he was busy with it in Eindhoven, The Netherlands, ever
since 1968. In 1978 the first actual physical CD-format
was there to experiment on.

44.1kHz was chosen to fit a digital audio signal onto video tape,
in the area used to store the picture. Video was the digital audio
storage medium before we had CD, and the rate of 44.1
is a logical result of that and the need for a safe rate
that could include up to 20kHz, which was considered to be
the human threshold of hearing back then. The first rate
that simply worked (and was interchangeable with video,
since CD-mastering was done on video) was 44.1 kHz.
The 44100 Hertz comes from the calculation
using video-frames, where you can have
3 samples per field of 490/2 lines;
3 x 245 x 60 Hz = 44100 Hz


Red Book Audio in wikipedia

We've deleted the paragraphs about the Red Book CDDA standard;
There seemed to be too many similarities with some writing
presumably done by some girl/guy named Dana J. Parker.
We're considering creating a Dana J. Parker sucks page though,
since he/she thought it was appropriate to threaten us with 'legal action'.
Oh how we hate those types. As if we'd do a copy-paste just like that.
If anything it was rewritten to teach readers about Red Book the best way possible.
It was kinda lengthy and boring anyway, so nobody will really miss it.
And like anyone would even give a shit who wrote what; It's
common knowledge now; Red Book is quite a retarded standard.

The bandwidth myth
Reports about encoder testing often include the mention of the bandwidth of the compressed audio signal. In a lot of cases this is due to misunderstandings about human hearing on one hand and encoding strategies on the other hand.

Hearing at high frequencies
It is certainly true that a large number of (especially young) subjects are perfectly able to hear single sounds at frequencies up to and sometimes well above 20 kHz. However, contrary to popular belief, the author is not aware of any scientific experiment which showed beyond doubt that there is any listener (trained or not) able to detect the difference between a (complex) musical signal with content up to 20 kHz and the same signal, but bandlimited to around 16 kHz. To make it clear, there are some hints to the fact that there are listeners with such capabilities, but the full scientific proof has not yet been given. As a corollary to this (for a lot of people unexpected) theorem, it is a good encoding strategy to limit the frequency response of an MP3 or AAC encoder to 16 kHz (or below if necessary). This is possible because of the brick-wall characteristic of the filters in the en-coder/decoder filterbank. The generalization of this ob-servation to other types of audio equipment (in particular analog) is not correct: Usually the frequency response of the system is changed well below the cutoff point. Since any deviation from the ideal straight line in frequency re-sponse is very audible, normal audio equipment has to support much higher frequencies in order to have the required perfectly flat frequency response up to 16 kHz.

Encoding strategies
While loss of bandwidth below the frequency given by the limits of human hearing is a coding artifact, it is not necessarily the case that an encoder producing higher bandwidth compressed audio sounds better. There is a basic tradeoff where to spent the bits available for encoding. If they are used to improve frequency response, they are no longer available to produce a clean sound at lower frequencies. To leave this tradeoff to the encoder algo-rithm often produces a bad sounding audio signal with the high frequency cutoff point varying from block to block. According to the current state of the art, it is best to introduce a fixed bandwidth limitation if the encoding is done at a bit-rate where no consistent clean reproduction of the full bandwidth signal is possible. Technically, both MP3 and AAC can reproduce signal content up to the limit given by the actual sampling frequency. If there are en-coders with a fixed limited frequency response (at a given bit-rate) compared to another encoder with much larger bandwidth (at the same bit-rate), experience tells that in most cases the encoder with the lower bandwidth pro-duces better sounding compressed audio. However, there is a limit to this statement: At low bit-rates (64 kbit/s for stereo and lower) the question of the best tradeoff in terms of bandwidth versus cleanness is a hotly contested question of taste. We have found that even trained listeners sometimes completely disagree about the bandwidth a given encoder should be run at.