Given that the intensity of a sound is perceived on a logarithmic scale (see [[loudness]]) it is frequently measured in [[deciBel]] (dB).
Decibel Full Scale (dBFS) is a unit of measurement used in digital audio systems to represent the maximum possible signal level before clipping occurs. It is typically used to quantify the dynamic range of a digital audio signal, with 0 dBFS representing the highest possible level without distortion. Negative values indicate levels below the maximum, while positive values indicate levels above the maximum and can lead to clipping or distortion.
If $v$ is the amplitude of the signal that we want to measure and $v_{0}$ a reference amplitude, the amplitude ratio in decibels is:
$
L_{dB} = 20 \log_{10}\left( \frac{v}{v_{0}}\right)
$
The measure of decibels relative to full scale (dBFS) assumes that $v_0$ is the maximum possible value for $v$ such that:
$
L_{dBFS}(v_{0}) = 0\ dB
$
When the amplitude is at 50% of the maximum level:
$
L_{dBFS}\left( \frac{v_{0}}{2} \right) \approx -6\ dB
$
Many signals resulting from an analog to digital conversion are represented in an amplitude range of $[-1,1]$, which means that $v_{0}=1$.
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