DBFS

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. 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 maximum 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.

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.

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.)

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):

...
Wikipedia