dBFS means "decibels full scale". It is an abbreviation for decibel amplitude levels in digital systems which have a maximum available level (like PCM encoding).

Clipping of a digital waveform.

0 dBFS is assigned to the maximum possible level.^[1]

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 derive the characteristic level of the waveform from its peak amplitude value, while others use its RMS amplitude value.^[2][3][4]

• 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.
• 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.

The measured dynamic range of a digital system is the ratio of the full scale signal level to the RMS noise floor. The theoretical dynamic range of a digital system is often estimated by the equation

\mathrm{DR} = \mathrm{SNR} = 20 \log_{10}(2^n) \approx 6.02 \cdot n \,

The value of n equals the resolution of the system in bits or the resolution of the system minus 1 bit (the measure error). This comes from a model of quantization noise equivalent to a uniform random fluctuation between two neighboring quantization levels. Only certain signals produce a uniform random fluctuations, so this model is not always accurate.^[5]

However, a signal that fluctuates randomly between two neighboring 16-bit quantization levels will measure at ?96.33 dBFS when the full-scale square wave convention is used.

Although the decibel (dB) is permitted for use alongside SI units, the dBFS is not.^[6]

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".

dBFSD

digital audio meters in the Metric Halo application, called SpectraFoo

The image shown is of a digital audio meter in the Metric Halo application, called SpectraFoo. It is using the K-System meter scale, calibrated for K-14. This shows both the current signal level, as well as indicating how much of the prescribed 14 decibels of headroom remain beneath -0 decibels Full Scale Digital. Too many full scale digital samples in a row (e.g., >3) implies that the reconstructed waveform is illegal, since it would have exceeded the full scale of amplitude, were it not "flattened" by the constraint of the format. (The K-System was invented by mastering engineer, Bob Katz, of Digital Domain (mastering studios), in Altamonte Springs, Florida.)

See also

• Full scale

References

1. ↑
2. ↑
3. ↑
4. ↑
5. ↑
6. ↑ Taylor 1995, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811

External links

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

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