Definitions

# DBFS

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.

• 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.

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.

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

dBFSD is an abbreviation for the standard digital audio level measurement scale. It is measured in decibels referenced to Full Scale Digital, which is the loudest possible digital audio sample value.

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.)....