Decibels relative to full scale, commonly abbreviated dBFS, measures
decibel amplitude levels in digital systems such as pulse-code modulation
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 reach −6 dBFS
at that point, 6 dB below full scale. Conventions differ for RMS measurements,
but 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 when converted to analog due to the
signal reconstruction process interpolating between samples. This
possibility can be prevented by careful digital-to-analog converter circuit
design. RMS levels
Since a peak measurement is not useful for qualifying the noise performance of
a system, or measuring the loudness of an audio recording, for instance, RMS
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. RMS: 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. Peak: For the case in which the RMS
value of a full-scale sine wave is designated 0 dBFS, a full-scale square
wave would have an RMS of +3 dBFS. This is the definition specified in AES
Standard AES17-1998 and IEC 61606 and used in Dorrough meters, Analog Devices
and Wolfson digital microphone specs, etc.
Dynamic range The measured dynamic range 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. This is
usually modeled as a uniform random fluctuation between −1/2 LSB and +1/2
LSB. As the dynamic range 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: The value of n equals the resolution of
the system in bits or the resolution of the system minus 1 bit. 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 is added
to the signal before sampling. This removes the effects of non-uniform
quantization error, but increases the minimum noise floor.
Notes Although the decibel is permitted for
use alongside SI units, the dBFS is not. The term dBFS was first coined in the
early 1980s by James Colotti, an analog engineer who pioneered some of the
dynamic evaluation techniques of high-speed A/D and D/A Converters. Mr.
Colotti first introduced the term to industry at the RF Expo East in Boston
Massachusetts in November 1987, during his presentation “Digital Dynamic
Analysis of A/D Conversion Systems through Evaluation Software based on
FFT/DFT Analysis". 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 US installations use +24 dBu for 0 dBFS
American and Australian 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 dBFS. +16dBu = 0 dBFS. No VU.
Belgium VRT: 0dB = +6dBu ; -9dBFS = 0dB ; 0dBFS = +15dBu.
ITU: In G.100.1 dBov cannot exceed -3.01 dBov when measuring a tone played at
maximum level See also
Audio bit depth Bit rate
Full scale References
^ Price, Jim. "Understanding dB". Professional Audio. Retrieved
2007-03-13. ^ Aldrich, Nika. "Digital Distortion in
CD’s and DVD’s: The Consequences of Traditional Digital Peak Meters".
Trillium Lane Labs. Archived from the original on 2010-08-16. Retrieved 20
November 2010. ^ "RMS Settings". Adobe Audition - User
Guide for Windows. Adobe. 2003. Retrieved 2007-03-16. - Allows "0dB =
FS Sine Wave" or "0dB = FS Square Wave" ^ "0 Db Reference". Active Voice / Noise
Level Monitor User's Guide. GL Communications, Inc. Retrieved
2007-03-16. - "0 Db" reference can be either "FS Sine Wave" or "FS Square1
1Wave" ^ Audio FAQ - Search Results
^ "Decibel - Voltage ratios for electric signals". sizes.com. Retrieved
2007-03-13. In such a system, the maximum level before clipping of a sine
wave is -3 dBFS. The relevant standard is IEC 268-18.
^ a b onnect.euphonix.comS5_App_1_Metering.pdf
^ Digital and Analog Measurement Units for Digital CMOS Microphone Preamplifier
ASICs - "The definition of 0 dBFS as a full-scale sine wave is used by several
audio analyzers, and the rms and peak values in the digital domain for a sine
wave are equal for these analyzers. ... Thus, a square wave whose top and bottom
are at the maximum digital codes has an rms value of 1.414 FFS or 3.01 dBFS"
^ 10 Audio Recording ^ http:www.aes.orgstandards/ "Because
the definition of full scale is based on a sine wave, it will be possible with
square-wave test signals to read as much as + 3,01 dB FS."
^ Understanding Microphone Sensitivity ^ WM7210 datasheet, TERMINOLOGY section
^ Watkinson, John. The Art of Digital Audio 3rd Edition. Focal Press. ISBN
0-240-51587-0. ^ Taylor 1995, Guide for the Use of the
International System of Units, NIST Special Publication SP811
wiki.ibs.org.ukindex.php?title=dBFS#dBFS ^ Decibel level conversion to volt
adcastpapers.compaper_loader.cfm?pid=393 External links
Rane pro audio reference definition of dBFS
dBFS - Sweetwater glossary