dBFS

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Clipping of a digital waveform. The red lines indicate full scale, and the waveform is shown before and after hard clipping (grey and black outlines respectively).

dBFS or dB FS (decibels relative to full scale) 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 relative to overload (dBO).[1]Template:R/superscript

The level of 0Template:NnbspdBFS is assigned to the maximum possible digital level.[2]Template:R/superscript For example, a signal that reaches 50% of the maximum level has a level of −6Template:NnbspdBFS, which is 6Template:NnbspdB below full scale. Conventions differ for root mean square (RMS) measurements, but all peak measurements smaller than the maximum are negative levels.

A digital signal that does not contain any samples at 0Template:NnbspdBFS can still clip when converted to analog form due to the signal reconstruction process interpolating between samples.[3]Template:R/superscript This can be prevented by careful digital-to-analog converter circuit design.[4]Template:R/superscript Measurements of the true inter-sample peak levels are notated as dBTP or dB TP (decibels true peak).[5]Template:R/superscript[6]Template:R/superscript

RMS levels

Since a peak measurement is not useful for qualifying the noise performance of a system,[7]Template:R/superscript 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 for sinusoidal signals is 3Template:NnbspdB below the peak value, while others choose the reference level so that RMS and peak measurements of a sine wave produce the same result.[8]Template:R/superscript[9]Template:R/superscript[10]Template:R/superscript[11]Template:R/superscript[12]Template:R/superscript

dBFS is defined in AES Standard AES17-1998,[13]Template:R/superscript IEC 61606,[14]Template:R/superscript and ITU-T Recs. P.381[15]Template:R/superscript and P.382,[16]Template:R/superscript such that the RMS value of a full-scale sine wave is designated 0Template:NnbspdB FS. This means a full-scale square wave would have an RMS value of +3Template:NnbspdB FS.[17]Template:R/superscript[18]Template:R/superscript This convention is used in Wolfson[19]Template:R/superscript and Cirrus Logic[20]Template:R/superscript digital microphone specs, etc.

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 0Template:NnbspdBov.[21]Template:R/superscript[22]Template:R/superscript All possible dBov measurements are negative numbers, and a sine wave cannot exist at a larger RMS value than −3 dBov without clipping.[21]Template:R/superscript This unit can be applied to both analog and digital systems.[21]Template:R/superscript This convention is the basis for the ITU's LUFS loudness unit,[23]Template:R/superscript and is also used in Sound Forge[10]Template:R/superscript and Euphonix meters,[24]Template:R/superscript and Analog Devices digital microphone specs[25]Template:R/superscript (though referred to as "dBFS").

Dynamic range

The measured dynamic range (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. This is usually modeled as a uniform random fluctuation between −Page Template:Fraction/styles.css has no content.1⁄2 LSB and +Page Template:Fraction/styles.css has no content.1⁄2 LSB. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.)[26]Template:R/superscript

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):

DR=SNR=20log10(2n32)≈6.0206n+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 −98.09Template:NnbspdBFS relative to a full-scale sine wave:

DR=SNR=20log10(21632)≈6.0206⋅16+1.761≈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,[27]Template:R/superscript[28]Template:R/superscript[29]Template:R/superscript and the term "dBFS" has been used since 1977.[30]Template:R/superscript

Although the decibel (dB) is permitted for use alongside units of the International System of Units (SI), the dBFS is not.[31]Template:R/superscript

The CD-DA Red Book (1980) standard defined the maximum loudness should be 0 dBFS.

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:[32]Template:R/superscript[33]Template:R/superscript[34]Template:R/superscript

See also

References

  1. ^ Page Module:Citation/CS1/styles.css has no content.M. Thurston, A; H. Pearce, T; D. Higman, M; Hawksford, Malcolm (1993-01-01), Bandpass Sigma Delta A-D Conversion, Springer, pp. 259–281, ISBN 9781441951311, retrieved 2018-07-27, In all cases the reference power level used for measurements will be the overload point of the converter in question, and figures will be quoted in dBO.
  2. ^ Page Module:Citation/CS1/styles.css has no content.Price, Jim. "Understanding dB". Professional Audio. Retrieved 2007-03-13.
  3. ^ Page Module:Citation/CS1/styles.css has no content.Nielsen, Søren H.; Lund, Thomas. "0dBFS+ Levels in Digital Mastering" (PDF). TC Electronic A/S. Denmark. Archived from the original (PDF) on 2019-05-02. Retrieved 2018-07-27. inter-sample peaks may be considerably higher than 0dBFS.
  4. ^ Page Module:Citation/CS1/styles.css has no content.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 on 2010-08-16. Retrieved 20 November 2010.
  5. ^ Page Module:Citation/CS1/styles.css has no content."BS.1770-4 (10/2015): Algorithms to measure audio programme loudness and true-peak audio level". International Telecommunication Union. Retrieved 2018-07-27. Meters that ... use an oversampled sampling rate of at least 192 kHz, should indicate the result in the units of dB TP [which] signifies decibels relative to 100% full scale, true-peak measurement.
  6. ^ Page Module:Citation/CS1/styles.css has no content."Terminology for Loudness and Level dBTP, LU and all that - BBC R&D". BBC. January 2011. Retrieved 2018-07-27. As can be seen from the figure, if the peak sample values are 0 dBFS, the true peak will be higher than 0 dBTP.
  7. ^ Page Module:Citation/CS1/styles.css has no content.Davidson, J. (1961). "Average vs RMS meters for measuring noise". IRE Transactions on Audio. AU-9 (4): 108–111. doi:10.1109/tau.1961.1166333. ISSN 0096-1981. the conclusion is reached that the meaningful quantities are found by rms measurements. ... At this point it may be objected that other measurements, peak, or peak-to-peak voltage measurements in particular, are also significant. This is true, but not from the standpoint adopted here. Such measurements are applicable only to the field of nonlinear response, such as dielectric breakdown, etc.
  8. ^ Page Module:Citation/CS1/styles.css has no content."RMS Settings" (PDF). Adobe Audition – User Guide for Windows. Adobe. 2003. Archived from the original (PDF) on 2007-01-27. Retrieved 2007-03-16. - Allows "0dB = FS Sine Wave" or "0dB = FS Square Wave"
  9. ^ Page Module:Citation/CS1/styles.css has no content."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"
  10. ^ a b Page Module:Citation/CS1/styles.css has no content.Katz, Robert (2000-10-28). "Zero dBFS Defined". Digital Domain. Retrieved 2017-06-11. This method yields a result of -3dB for a full scale sine wave and 0dB for a full scale square wave. Sound Forge uses this method.
  11. ^ Page Module:Citation/CS1/styles.css has no content."A/85 – Techniques for Establishing and Maintaining Audio Loudness for Digital Television — ATSC". ATSC. Retrieved 2018-07-27. many software programs indicate level on virtual meters by means of a conventional RMS calculation, leading to a full scale sine wave reading -3.01 dB FS, which is incorrect in the context of this document.
  12. ^ Page Module:Citation/CS1/styles.css has no content."LUFS, dBFS, RMS... WTF ?!? How to read the new loudness meters - Production Advice". Production Advice. 2013-01-08. Retrieved 2018-07-27.
  13. ^ Page Module:Citation/CS1/styles.css has no content."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. ^ Page Module:Citation/CS1/styles.css has no content."IEC 61606-3:2008 Audio and audiovisual equipment - Digital audio parts - Basic measurement methods of audio characteristics - Part 3: Professional use". International Electrotechnical Commission. 2008. Retrieved 2018-07-27. the r.m.s. amplitude of a ... 997 Hz sinusoid whose peak positive sample just reaches positive digital full-scale ... is defined as 0 dB FS
  15. ^ Page Module:Citation/CS1/styles.css has no content."P.381 (03/17): Technical requirements and test methods for the universal wired headset or headphone interface of digital mobile terminals". International Telecommunication Union. 2017. Retrieved 2018-07-27. 0 dBFS represents the root mean square (RMS) level of a full-scale sinusoidal
  16. ^ Page Module:Citation/CS1/styles.css has no content."P.382 (07/16): Technical requirements and test methods for multi-microphone wired headset or headphone interfaces of digital wireless terminals". International Telecommunication Union. Retrieved 2018-07-27. 0 dBFS represents the root mean square (RMS) level of a full-scale sinusoidal signal
  17. ^ 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"
  18. ^ Page Module:Citation/CS1/styles.css has no content."10 Audio Recording". Tonmeister. 23 October 2011. Retrieved 30 January 2016.
  19. ^ Page Module:Citation/CS1/styles.css has no content."WM7216E datasheet" (PDF). May 2016. Note that, because the definition of FSR is based on a sine wave, it is possible to support a square wave test signal output whose level is +3dBFS.[permanent dead link]
  20. ^ Page Module:Citation/CS1/styles.css has no content."CS7250B datasheet" (PDF). Note that, because the definition of FSR is based on a sine wave, it is possible to support a square wave test signal output whose level is +3 dBFS.
  21. ^ a b c Page Module:Citation/CS1/styles.css has no content."G.100.1 (06/15): The use of the decibel and of relative levels in speechband telecommunications". International Telecommunication Union. Retrieved 2018-07-27. The level of a tone with a digital amplitude (peak value) of xover is therefore L= –3.01 dBov.
  22. ^ Page Module:Citation/CS1/styles.css has no content.Zopf, Robert (2002). "Real-time Transport Protocol (RTP) Payload for Comfort Noise (CN)". tools.ietf.org. doi:10.17487/RFC3389. 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
  23. ^ Page Module:Citation/CS1/styles.css has no content."BS.1770-4 (10/2015): Algorithms to measure audio programme loudness and true-peak audio level". International Telecommunication Union. 2015. Retrieved 2018-07-27. If a 0 dB FS, 1 kHz ... sine wave is applied to the ... input, the indicated loudness will equal −3.01 LKFS.
  24. ^ Page Module:Citation/CS1/styles.css has no content."Application Note 1: System 5 Metering: Peak vs. Average" (PDF). January 2002. On a logarithmic dB scale, the difference between a sine wave's peak and RMS average level is 3 dB. Euphonix bases its metering on the Audio Precision measurement system, which adheres to the RMS average technique.
  25. ^ Page Module:Citation/CS1/styles.css has no content."Understanding Microphone Sensitivity". Analog. Retrieved 30 January 2016. so a digital microphone's output must be scaled from peak to rms by lowering the dBFS value. For a sinusoidal input, the rms level is 3 dB (the logarithmic measure of (FS√2) below the peak level ... A 94 dB SPL sinusoidal input signal will give a –26 dBFS peak output level, or a –29 dBFS rms level.
  26. ^ Page Module:Citation/CS1/styles.css has no content.Watkinson, John (2001). The Art of Digital Audio 3rd Edition. Focal Press. ISBN 978-0-240-51587-8.
  27. ^ Page Module:Citation/CS1/styles.css has no content.Automatic Control. Reinhold Publishing Corporation. 1957-01-01.
  28. ^ Page Module:Citation/CS1/styles.css has no content.Hewlett-Packard Journal. Hewlett-Packard Company. 1962-01-01.
  29. ^ Page Module:Citation/CS1/styles.css has no content.The General Radio Experimenter. General Radio Company. 1969-01-01.
  30. ^ Page Module:Citation/CS1/styles.css has no content.Robert, Talambiras (1977-05-01). "Some Considerations in the Design of Wide-Dynamic-Range Audio Digitizing Systems". Journal of the Audio Engineering Society. 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
  31. ^ Taylor 1995, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811
  32. ^ http://wiki.ibs.org.uk/faq/index.php?title=dBFS#dBFS[permanent dead link]
  33. ^ Page Module:Citation/CS1/styles.css has no content.Eberhard Sengpiel. "Decibel (dB) level conversion to volt". Sengpiel Audio. Retrieved 30 January 2016.
  34. ^ http://www.broadcastpapers.com/whitepapers/paper_loader.cfm?pid=393[permanent dead link]

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