DBFS

Clipping of a digital waveform.

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). 0 dBFS is assigned to the maximum possible level.

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.

• In the case of a FS square wave = 0 dBFS, all possible dBFS measurements are negative numbers. A sine wave of larger amplitude than −3 dBFS would be clipping by this convention.
• In the case of a FS sine wave = 0 dBFS, a FS 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 derived by the equation

$\mathrm {DR} =\mathrm {SNR} =20\log _{10}(2^{n})\approx 6.02\cdot n$

This comes from a model of quantization noise equivalent to a uniform random fluctuation between two neighboring quantization levels. For instance, 16-bit audio has a quoted dynamic range of 96.33 dB.

To make an equivalent measurement of a system's noise floor, the full-scale square wave convention is used. A signal which fluctuates randomly between two neighboring quantization levels will measure at −96.33 dBFS with this convention.

References

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