Sampling depth

The sampling depth , also called bit depth , indicates the number of bits that are used for the quantization of an analog signal per sample (= sample). It determines in how many gradations the amplitude can be represented. In addition to the sampling rate, the sampling depth is the second parameter that describes the digitization process.

Basics

The sampling depth determines the dynamic range of the signal. The dynamic increases approximately by 6 dB with each bit. The higher the sampling depth, the higher the dynamic range and the more space the digitized signal can occupy.

Typical sampling depths are 8, 12, 16, 24 or 32 bit. The exact resolution of the analog-digital conversion can also fall below these nominal values. Real 8/16 / ... bits are only used when the entire digital range of values is used. It reflects the quality of the change.

Example: audio

An analog signal (red) is recorded digitally and stored (blue). The sampling depth corresponds to 4 bits, which enables 16 different states. Each value of the oscillation is assigned to the state that comes closest to the original value. It can be clearly seen that with increasing sampling depth, the gradations can be mapped more finely and thus the quality increases.

The range of values is usually divided linearly, but non-linear or adaptive graduations are also possible.

Most audio applications use higher accuracy internally than the audio they are editing. Since mixing processes (multiplication, addition of samples) often produce intermediate results outside of the possible sample values, the margin for calculations is increased in order to avoid clipping or overdriving . In the case of linear subdivisions, the value 0 represents the central position of the loudspeaker membrane, whereas the minimum and maximum values of the data type correspond to the maximum deflection of the membrane forwards or backwards.

8-, 16- and 24-bit samples are often signed integer types, 32-bit samples are also used as studio environments IEEE - floating point numbers before. Exceeding or falling below the associated value ranges leads to overflow or underflow in integer arithmetic . A slight increase in volume at the upper end of the possible level therefore does not result in even louder tones, but is mapped cyclically to the lower end of the value range. As a result, the loudspeaker would have to swing from the maximum deflection to the maximum opposite position in a flash, which is perceived by the listener as extreme distortion. To prevent this, the overflow / underflow is often (generally in AD converters) replaced by a saturation function (clipping).

Arithmetic example for 16 bit linear PCM

The audio CD uses 16 bit linear PCM :

Range of values: ... ${\ displaystyle -2 ^ {15}}$ ${\ displaystyle 2 ^ {15} -1}$
C type: int16 (signed)
Ada: type cd_sample is range -2 ** 15… (2 ** 15) - 1;

To the maximum positive value (0111111111111111, decimal 32767), 1 is added, and you get the maximum negative deflection (minimum value) (1000000000000000, decimal −32768):

	0111111111111111	(32767)
+	0000000000000001	(1)
=	1000000000000000	(−32768)

This overflow, audible as clipping, can be avoided by performing calculations on 16-bit samples with, for example, 24-bit accuracy.

literature

Hubert Henle: The recording studio manual. Practical introduction to professional recording technology. 5th, completely revised edition. Carstensen, Munich 2001, ISBN 3-910098-19-3 .
Thomas Görne: Sound engineering. Fachbuchverlag Leipzig in Carl Hanser Verlag, Munich et al. 2006, ISBN 3-446-40198-9 .
Roland Enders: The home recording manual . 3rd edition, Carstensen Verlag, Munich, 2003, ISBN 3-910098-25-8

Web links

Sampling - the world as we hear it