I asked myself how to compute dBFS (dB full scale) from a value of sample between 1 and -1?
and in general?
It is really quite simple for values between 1 and -1:
valueDBFS = 20*log10(abs(value))
If you have values between another range, for example 16bit, then it's:
valueDBFS = 20*log10(abs(value)/32768)
(because 16bit signed has values between -32768 and +32767, e.g. 2^15=32768)
And so the general formula is:
valueDBFS = 20*log10(abs(value)/maxValue)
The code examples are given in MATLAB code.
All the standards define dBFS as an RMS measurement, relative to the RMS level of a full-scale sine wave, so the calculation is:
value_dBFS = 20*log10(rms(signal) * sqrt(2)) = 20*log10(rms(signal)) + 3.0103
The similar unit dBov is defined in relation to power ratios (so it's also an RMS measurement), such that full-scale DC or square wave is 0 dBov, so that calculation is:
value_dBov = 20*log10(rms(signal))