dBFS

Clipping of a digital waveform

Decibels relative to full scale (dBFS) 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 dBO.

The level of 0 dBFS is assigned to the maximum possible digital level.^[1] For example, a signal that reaches 50% of the maximum level has a level of −6 dBFS, which is 6 dB below full scale. Conventions differ for root mean square (RMS) measurements, but all peak measurements smaller than the maxium are negative levels.

A digital signal that does not contain any samples at 0 dBFS can still clip when converted to analog form due to the signal reconstruction process interpolating between samples. This can be prevented by careful digital-to-analog converter circuit design.^[2]

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.

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 is −3 dB below the peak value, while others choose the reference level so that RMS and peak measurements of a sine wave produce the same result.^[3][4][5]

• 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 cannot exist at a larger RMS value than −3 dBFS without clipping by this convention.^[6] This definition is consistent with the ITU-T G.100.1 telephony unit dBov, which can be applied to both analog and digital systems.^[7][8] It is used in Sound Forge^[9] and Euphonix meters.^[10]
• 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.^[11][12] This is the definition specified in AES Standard AES17-1998^[13] and IEC 61606 and used in Dorrough meters,^[10] Analog Devices^[14] and Wolfson^[15] 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. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.)^[16]

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 (though with reversed sign):

${\mathrm {DR}}={\mathrm {SNR}}=20\log _{{10}}{\left(2^{n}{\sqrt {{\tfrac {3}{2}}}}\right)}\approx 6.0206\cdot n+1.761$

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 has a theoretical minimum noise floor of -98.09 dBFS relative to a full-scale sine wave:

${\mathrm {DR}}={\mathrm {SNR}}=20\log _{{10}}{\left(2^{{16}}{\sqrt {{\tfrac {3}{2}}}}\right)}\approx 6.0206\cdot 16+1.761\approx 98.09\,$

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.

History

The phrase "dB below full scale" has appeared in print since the 1950s,^[17][18][19] and the term "dBFS" has been used since 1977.^[20]

Although the decibel (dB) is permitted for use alongside units of the International System of Units (SI), the dBFS is not.^[21]

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:^[22][23][24]

• 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 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 (−9) dBFS. +16 (+15)dBu = 0 dBFS. No VU.
• Belgium VRT: 0 dB (VRT Ref.) = +6dBu ; -9dBFS = 0 dB (VRT Ref.) ; 0dBFS = +15dBu.

See also

• Audio bit depth
• Bit rate
• Full scale

References

1. Price, Jim. "Understanding dB". Professional Audio. Retrieved 2007-03-13.
2. Aldrich, Nika (July 2003). "Digital Distortion in CD's and DVD's: The Consequences of Traditional Digital Peak Meters" (PDF). Trillium Lane Labs. Archived from the original (PDF) on 2010-08-16. Retrieved 20 November 2010.
3. "RMS Settings" (PDF). Adobe Audition – User Guide for Windows. Adobe. 2003. Retrieved 2007-03-16. - Allows "0dB = FS Sine Wave" or "0dB = FS Square Wave"
4. "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"
5. "Audio FAQ – Search Results – Digital Domain: CD Mastering – Mastered for iTunes – Audio Mastering – Blu-Ray Mastering". Digido. Retrieved 30 January 2016.
6. "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 (1995).
7. "ITU-T Recommendation database". ITU. Retrieved 2016-04-29. The level of a tone with a digital amplitude (peak value) of x_over is therefore L= –3.01 dBov.
8. Zopf, Robert. "Real-time Transport Protocol (RTP) Payload for Comfort Noise (CN)". tools.ietf.org. Retrieved 2016-04-30. For example, in the case of a u-law system, the reference would be a square wave ... and this ... represents 0dBov
9. "Zero dBFS Defined". www.digido.com. Retrieved 2016-04-30.
10. http://connect.euphonix.com/documents/S5_App_1_Metering.pdf
11. Digital and Analog Measurement Units for Digital CMOS Microphone Preamplifier ASICs (Analog Devices) - "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"
12. "10 Audio Recording". Tonmeister. 23 October 2011. Retrieved 30 January 2016.
13. "AES Standard » AES17-2015: AES standard method for digital audio engineering - Measurement of digital audio equipment". www.aes.org. Retrieved 2016-04-29. 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.
14. "Understanding Microphone Sensitivity". Analog. Retrieved 30 January 2016.
15. "Analog and Digital Processing ICs, Semiconductor Company, Cirrus Logic" (PDF). Wolfson Micro. Retrieved 30 January 2016.
16. Watkinson, John (2001). The Art of Digital Audio 3rd Edition. Focal Press. ISBN 0-240-51587-0.
17. Automatic Control. Reinhold Publishing Corporation. 1957-01-01.
18. Hewlett-Packard Journal. Hewlett-Packard Company. 1962-01-01.
19. The General Radio Experimenter. General Radio Company. 1969-01-01.
20. Robert, Talambiras, (1977-05-01). "Some Considerations in the Design of Wide-Dynamic-Range Audio Digitizing Systems". It is convenient when working with A/D converters to define a 0 dB reference for a full-scale-to-full-scale sine wave. ... The quantizing noise in the Nyquist bandwidth for a 16 bit converter would be -98.08dbFS
21. Taylor 1995, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811
22. http://wiki.ibs.org.uk/faq/index.php?title=dBFS#dBFS
23. Eberhard Sengpiel. "Decibel (dB) level conversion to volt". Sengpiel Audio. Retrieved 30 January 2016.
24. http://www.broadcastpapers.com/whitepapers/paper_loader.cfm?pid=393

External links

• Rane pro audio reference definition of dBFS
• dBFS – Sweetwater glossary