From Audio Precision's "Audio.tst" newsletter May 1994:

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To our knowledge, the unit "dBFS" (decibels with respect to digital full scale) was first used in System OneDual Domain. This terminology and its exact definition was later standardized by the Audio Engineering Society as AES 17-1991 AES standard method for digital audio equipment - Measurement of digital audio equipment.

It specifies zero dBFS as the rms level of a sinewave signal calibrated so that peaks reach the positive full scale of the digital word.

The real-time meters and the graphs of all System One FFT-based programs are calibrated according to this definition.

This definition has some interesting attributes when:

- non-sinusoidal signals are measured, or
- when any digital signal is viewed in the time domain (oscilloscope mode).

If a squarewave is adjusted until its peaks just reach full scale of the digital word, the amplitude will be displayed as +3.01 dBFS.

At first thought, this may be confusing: "How can a signal exceed full scale in a digital system?"

In fact, a signal, including squarewave signals, of course cannot exceed full scale. The apparent conflict lies in the fact that a squarewave has a crest factor of one; its peak and rms values are equal. A sinewave has a crest factor of 3.01 dB. All other typical signals (music, voice, IMD test signals, etc.) have still higher crest factors.

The AES definition

__is based on the __**RMS value**, which is normally desired since it is power-related and independent of waveshape. A squarewave, and perhaps a heavily-clipped sinewave, are the only waveforms with crest factors less than a sinewave and which therefore can give rms readings greater than full scale.

Note that some competitive digital domain analyzers have not been designed and calibrated in accordance with the AES measurement standard and will display all digital domain signals with a -3.01 dB error.

Time domain (oscilloscope display) of a digital domain signal brings up essentially the same issue and potential confusion.

__The AES measurement standard __**does not address** time domain displays .

System One Dual Domain FFT program graphs are calibrated so that 100%FS corresponds to the definition stated above.

On these graphs, a

__sinewave__ whose rms value is 0 dBFS (100 %FS) will have

**peak samples** in the time domain which reach

__+3.01 dBFS__, which is 141.4%FS.

__This is a direct analogy to time domain display of an analog signal__. A one Volt rms sinewave has peaks which reach 1.414 Volts peak, as any oscilloscope will display.

The

__real-time amplitude meters__ at the top of the FFT-based program panels

**are peak-sensitive** (rather than rms) meters and respond to both positive and negative peaks, whichever is larger.

These meters are furnished

__to help users avoid overloads__, rather than to be used for quantitative measurements. On these meters, 0 dBFS or 100 % FS indicate a signal whose positive and/or negative peaks are just touching full scale,

**regardless of waveform**.

If both GENANLR and an FFT program could be simultaneously monitoring a digital signal whose peaks touch full scale:

- They would both read 100 %FS (0 dBFS) if the signal is a sinewave.
- The real-time meters would continue to read 100 %FS on all other full-scale waveforms.
- The rms-responding meters would read less than 100 %FS on waveforms whose crest factor is greater than a sinewave and, as noted above, more than 100 %FS with a squarewave since its crest factor is 1.00.

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Hope this helps.