DBFS
Encyclopedia
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s relative to full scale
Full scale
In electronics and signal processing, full scale or full code represents the maximum amplitude a system can present.-Electronics and signal processing:...
, commonly abbreviated dBFS, measures decibel amplitude levels in digital systems such as pulse-code modulation
Pulse-code modulation
Pulse-code modulation is a method used to digitally represent sampled analog signals. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems...
which have a defined maximum available peak level.
0 dBFS is assigned to the maximum possible digital level. for example, a signal that reaches 50% of the maximum level at any point would peak at -6 dBFS i.e. 6 dB below full scale. All peak measurements will be negative numbers, unless they reach the maximum digital value.
A digital signal which does not contain any samples at 0 dBFS can still clip
Clipping (audio)
Clipping is a form of waveform distortion that occurs when an amplifier is overdriven and attempts to deliver an output voltage or current beyond its maximum capability...
when converted to analog due to the signal reconstruction
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 reconstruction...
process. This possibility can be prevented by careful digital-to-analog converter
Digital-to-analog converter
In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...
circuit design.
RMS levels
Since a peak measurement is not useful for qualifying the noise performance of a system, or measuring the loudnessLoudness
Loudness is the quality of a sound that is primarily a psychological correlate of physical strength . 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."Loudness, a subjective measure, is often...
of an audio recording, for instance, RMS
Root mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
measurements are often used instead.
There is a potential for ambiguity when assigning a level on the dBFS scale to a waveform rather than to a specific amplitude, since some choose the reference level so that RMS and peak measurements of a sine wave produce the same number, while others want the RMS and peak values of a square wave to be equal, as they are in typical analog measurements.
- For the case in which the RMS value of a full-scale square wave is designated 0 dBFS, all possible dBFS measurements are negative numbers. A sine wave could not exist at a larger RMS value than −3 dBFS without clipping, by this convention. This is the convention used in Euphonix meters.
- For the case in which the RMS value of a full-scale sine wave is designated 0 dBFS, a full-scale square wave would be at +3 dBFS. This is the definition specified in AESAudio Engineering SocietyEstablished in 1948, the Audio Engineering Society draws its membership from amongst engineers, scientists, other individuals with an interest or involvement in the professional audio industry. The membership largely comprises engineers developing devices or products for audio, and persons working...
Standard AES17-1998 and IEC 61606 and used in Dorrough meters.
Dynamic range
The measured dynamic rangeDynamic range
Dynamic range, abbreviated DR or DNR, is the ratio between the largest and smallest possible values of a changeable quantity, such as in sound and light. It is measured as a ratio, or as a base-10 or base-2 logarithmic value.-Dynamic range and human perception:The human senses of sight and...
of a digital system is the ratio of the full scale signal level to the RMS noise floor
Noise floor
In signal theory, the noise floor is the measure of the signal created from the sum of all the noise sources and unwanted signals within a measurement system, where the noise is defined as any signal other than the one being monitored....
. The theoretical minimum noise floor is caused by quantization noise. This is usually modeled as a uniform random fluctuation between −1/2 LSB
Least significant bit
In computing, the least significant bit is the bit position in a binary integer giving the units value, that is, determining whether the number is even or odd. The lsb is sometimes referred to as the right-most bit, due to the convention in positional notation of writing less significant digits...
and +1/2 LSB. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.)
As the dynamic range
Dynamic range
Dynamic range, abbreviated DR or DNR, is the ratio between the largest and smallest possible values of a changeable quantity, such as in sound and light. It is measured as a ratio, or as a base-10 or base-2 logarithmic value.-Dynamic range and human perception:The human senses of sight and...
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 1 bit (the measure error). For example, a 16-bit system will have a theoretical minimum noise floor of -98.09 dBFS relative to a full-scale sine wave:
In any real converter, dither
Dither
Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images...
is added to the signal before sampling. This removes the effects of non-uniform quantization error
Quantization error
In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation...
, but increases the minimum noise floor.
Analog levels
dBFS is not to be used for analog levels, according to AES-6id-2006. There is no single standard for converting 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:- EBU R68 is used in most European countries, specifying +18 dBu at 0 dBFS
- In Europe, the EBU recommend that -18 dBFS equates to the Alignment Level
- European & UK calibration for Post & Film is −18 dBFS = 0 VU
- UK broadcasters, Alignment Level is taken as 0 dBu (PPM4 or -4VU)
- US installations use +24 dBu for 0 dBFS
- American Post: −20 dBFS = 0 VU = +4 dBu
- The American SMPTE standard defines -20 dBFS as the Alignment Level
- In Japan, France and some other countries, converters may be calibrated for +22 dBu at 0 dBFS.
- BBC spec: −18 dBFS = PPM "4" = 0 dBu
- German ARD & studio PPM +6 dBu = −10 (−9) dBFS. +16 (+15)dBu = 0 dBFS. No VU.
- Belgium VRT: 0dB (VRT Ref.) = +6dBu ; -9dBFS = 0dB (VRT Ref.) ; 0dBFS = +15dBu.