Sampling

Pulse Code modulation as a method to digitize sound has been proposed by  Alec Reeves in 1937. It had to wait until the transistor and the IC become available at low cost before this method was successfully introduced in the consumers market. Almost all of today's digital audio is PCM audio.

The principle is simple, the analogue signal is measured at uniform intervals. The magnitude of the signal is translated into a numeric value and as it is a number, it could be represented in bits.

Sampling rate

Theoretically a sample rate of two times the highest frequency is sufficient to reconstruct the analogue signal (Nyquist frequency) .
Our audible range is 20 – 20.000 Hz. Sampling at 40 kHz is in principle sufficient but there needs to be some additional room for the filtering (transition band).
That’s why CD audio uses a sampling rate of 44.1 kHz.

As long a Nyquist can't be proven wrong, higher sample rates are nonsense.
But practice has not only to deal with mathematics but with technology to.
All kind of problems caused by the steep filtering become less if one increases the sample rate.

Bit depth

Each sample is represented by a number of bits. In case of CD audio, the number of bits is 16. The entire range from silence to the highest possible signal is divided in 2^16=65536 steps. Using 24 bits, the same range is divided in 2^24=16777216 steps.

 

8 bit	16 bit	24 bit

Today almost all recordings are done in 24.
You always need some headroom when recording as you can’t predict the loudest passage. Record at 16 bits with 12 dB headroom (1 bits is 6.02 dB) means you are recording with a 16-2=14 bits resolution. Do the same with 24 bits and you have a 22 bits resolution.

 

As more and more people switch from CD to computer audio, there is no need to stick to the 16/44.1 Redbook audio standard anymore.
Today it is possible to download 24 bits recordings with higher sampling rates.

Oversampling

Playing digital audio is converting the digital samples to an analogue signal. This is done by a piece of circuitry aptly called the DAC (Digital to Analogue Converter).

Inherent to the mathematics involved in the conversion is that higher-frequency multiples of the audible range are created, the so called aliases. In case of CD audio, the sampling rate is 44.1 kHz, the audible range is the half, so the first alias will start at 22.050 kHz.

These aliases are outside the audible range so why bother? Although we can't hear them they are there and can create intermodulation distortion in the audible range. Maybe your tweeters don't like it either.

The answer is a low pass filter (anti alias filter). If this filter starts at 20.000 and has to remove everything before the first alias starts (22.050 assuming CD audio) then it has to be very steep (brick wall filter). Filters this steep are expensive, complex and introduces all kind of artifacts like phase distortion and pre-ringing.

 

The big trick is to apply oversampling. Oversample 8 times and of course we get the same aliases but now the first one starts at 330 kHz. Oversampling pushes the aliases much farther away from the audible range and allows to use a gentle low pass filter.

Upsampling

In principle there is no difference between upsampling and oversampling. It is both about stepping up the sample rate.
In practice oversampling is done using a whole number (8 in today’s DAC's) and is often a implemented in the hardware.

Upsampling is often done in software, you have 44.1 kHz audio file and your sound card supports 48 kHz only. Playing 44.1 with a rate of 48 is like playing a LP with 45 rpm.
To play it properly, the 44100 samples as second must be transformed in 48000 samples a second. This can only be done by interpolating (guessing the points in between using math).