Decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
s relative to
full scale (dBFS or dB FS) is a unit of measurement for amplitude levels in digital systems, such as
pulse-code modulation
Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the ...
(PCM), which have a defined maximum peak level. The unit is similar to the units
dBov
Decibels relative to full scale (dBFS or dB FS) is a unit of measurement for amplitude levels in digital systems, such as pulse-code modulation (PCM), which have a defined maximum peak level. The unit is similar to the units dBov and decibels re ...
and decibels relative to overload (dBO).
The level of 0dBFS is assigned to the maximum possible digital level.
[
] For example, a signal that reaches 50% of the maximum level has a level of −6dBFS, which is 6dB below full scale. Conventions differ for
root mean square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...
(RMS) measurements, but all peak measurements smaller than the maximum are negative levels.
A digital signal that does not contain any samples at 0dBFS can still
clip
Clip or CLIP may refer to:
Fasteners
* Hair clip, a device used to hold hair together or attaching materials such as caps to the hair
* Binder clip, a device used for holding thicker materials (such as large volumes of paper) together
** Bulldog ...
when converted to analog form due to the
signal reconstruction
In signal processing, reconstruction usually means the determination of an original continuous signal from a sequence of equally spaced samples.
This article takes a generalized abstract mathematical approach to signal sampling and reconstructi ...
process interpolating between samples. This can be prevented by careful
digital-to-analog converter circuit design. Measurements of the true inter-sample peak levels are notated as dBTP or dB TP ("decibels true peak").
RMS levels
Since a peak measurement is not useful for qualifying the noise performance of a system, or measuring the
loudness
In acoustics, loudness is the subjectivity, subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud". The rel ...
of an audio recording, for instance, RMS measurements are often used instead.
A potential for ambiguity exists when assigning a level on the dBFS scale to a waveform rather than to a specific amplitude, because some engineers follow the mathematical definition of RMS, which for sinusoidal signals is −3dB below the peak value, while others choose the reference level so that RMS and peak measurements of a sine wave produce the same result.
[
]
The unit dB FS or dBFS is defined in
AES
AES may refer to:
Businesses and organizations Companies
* AES Corporation, an American electricity company
* AES Data, former owner of Daisy Systems Holland
* AES Eletropaulo, a former Brazilian electricity company
* AES Andes, formerly AES Gener ...
Standard AES17-1998, IEC 61606, and ITU-T Recs. P.381 and P.382, such that the RMS value of a full-scale sine wave is designated 0dB FS. This means a full-scale square wave would have an RMS value of +3dB FS. This convention is used in
Wolfson
See also Woolf, Woolfe, Wolff, Wolfson and Woolfson (especially for family names).
Wolfson or Volfson is a Jewish surname, and may refer to:
* David Wolfson, Baron Wolfson of Sunningdale (born 1935), British politician and businessman, nephew of ...
and
Cirrus Logic
Cirrus Logic Inc. is an American fabless semiconductor supplier that specializes in analog, mixed-signal, and audio DSP integrated circuits (ICs). Since 1998, the company's headquarters have been in Austin, Texas.
The company's audio processo ...
digital microphone specs, etc.
The unit dBov is defined in the ITU-T G.100.1 telephony standard such that the RMS value of a full-scale square wave is designated 0dBov.
All possible dBov measurements are negative numbers, and a sine wave cannot exist at a larger RMS value than −3 dBov without
clipping.
This unit can be applied to both analog and digital systems.
This convention is the basis for the ITU's
LUFS
Loudness, K-weighted, relative to full scale (LKFS) is a standard loudness measurement unit used for audio normalization in broadcast television systems and other video and music streaming services.
LKFS is standardized in ITU-R BS.1770. In March ...
loudness unit, and is also used in Sound Forge
and Euphonix meters,
and Analog Devices digital microphone specs (though referred to as "dBFS").
Dynamic range
The measured
dynamic range
Dynamic range (abbreviated DR, DNR, or DYR) is the ratio between the largest and smallest values that a certain quantity can assume. It is often used in the context of signals, like sound and light. It is measured either as a ratio or as a base-1 ...
(DR) of a digital system is the ratio of the full scale signal level to the RMS
noise floor. The theoretical minimum noise floor is caused by
quantization noise
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and t ...
. This is usually modeled as a uniform random fluctuation between −
LSB and + LSB. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.)
As the
dynamic range
Dynamic range (abbreviated DR, DNR, or DYR) is the ratio between the largest and smallest values that a certain quantity can assume. It is often used in the context of signals, like sound and light. It is measured either as a ratio or as a base-1 ...
is measured relative to the RMS level of a full scale sine wave, the dynamic range and the level of this quantization noise in dBFS can both be estimated with the same formula (though with reversed sign):
:
The value of ''n'' equals the resolution of the system in bits or the resolution of the system minus 1bit (the measure error). For example, a 16-bit system has a theoretical minimum noise floor of −98.09dBFS relative to a full-scale sine wave:
:
In any real converter,
dither is added to the signal before sampling. This removes the effects of non-uniform
quantization error
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and ...
, but increases the minimum noise floor.
History
The phrase "dB below full scale" has appeared in print since the 1950s, and the term "dBFS" has been used since 1977.
Although the decibel (dB) is permitted for use alongside units of the
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI), the dBFS is not.
Analog levels
dBFS is not defined for analog levels, according to standard AES-6id-2006. No single standard converts between digital and analog levels, mostly due to the differing capabilities of different equipment. The amount of oversampling also affects the conversion with values that are too low having significant error. The conversion level is chosen as the best compromise for the typical headroom and signal-to-noise levels of the equipment in question. Examples:
[http://www.broadcastpapers.com/whitepapers/paper_loader.cfm?pid=393]
* EBU R68 is used in most European countries, specifying +18dBu at 0dBFS.
* In Europe, the EBU recommend that −18dBFS equates to the ''
alignment level''.
** UK broadcasters, ''alignment level'' is taken as 0dBu (PPM4 or −4VU)
** The American SMPTE standard defines −20dBFS as the ''alignment level''.
* European and UK calibration for is −18dBFS = 0VU.
* US installations use +24dBu for 0dBFS.
* American and Australian Post: −20dBFS = 0VU = +4dBu.
* In Japan, France, and some other countries, converters may be calibrated for +22dBu at 0dBFS.
* BBC specification: −18dBFS = PPM"4" = 0dBu
* German ARD and studio, PPM+6dBu = −10 (−9)dBFS. +16 (+15)dBu = 0dBFS. No VU.
* Belgium VRT: 0 dB (VRT ref.) = +6dBu; −9dBFS = 0 dB (VRT ref.); 0dBFS = +15dBu.
See also
*
Audio bit depth
In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample. Examples of bit depth include Compact Disc Digital Audio, which ...
*
Bit rate
In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time.
The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...
*
Full scale
References
External links
AES Pro Audio Reference definition of dBFSdBFS – Sweetwater glossary{{Decibel
Digital audio
Logarithmic scales of measurement
ru:DBFS