The phrase "dB below full scale" has appeared in print since the 1950s, and the term "dBFS" has been used since 1977. This removes the effects of non-uniform quantization error, but increases the minimum noise floor. In any real converter, dither is added to the signal before sampling. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.) Īs 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):ĭ R = S N R = 20 log 10 ( 2 n 3 2 ) ≈ 6.0206 n + 1.761 This is usually modeled as a uniform random fluctuation between − 1⁄ 2 LSB and + 1⁄ 2 LSB. The theoretical minimum noise floor is caused by quantization noise. The measured dynamic range (DR) of a digital system is the ratio of the full scale signal level to the RMS noise floor. This convention is the basis for the ITU's LUFS loudness unit, and is also used in Sound Forge and Euphonix meters, and Analog Devices digital microphone specs (though referred to as "dBFS"). This unit can be applied to both analog and digital systems. All possible dBov measurements are negative numbers, and a sine wave cannot exist at a larger RMS value than −3 dBov without clipping. The unit dBov is defined in the ITU-T G.100.1 telephony standard such that the RMS value of a full-scale square wave is designated 0 dBov. This convention is used in Wolfson and Cirrus Logic digital microphone specs, etc. This means a full-scale square wave would have an RMS value of +3 dB FS. P.381 and P.382, such that the RMS value of a full-scale sine wave is designated 0 dB FS. The unit dB FS or dBFS is defined in AES Standard AES17-1998, IEC 61606, and ITU-T Recs. 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.Ī 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 for sinusoidal signals 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. Measurements of the true inter-sample peak levels are notated as dBTP or dB TP ("decibels true peak"). This can be prevented by careful digital-to-analog converter circuit design. Conventions differ for root mean square (RMS) measurements, but all peak measurements smaller than the maximum are negative levels.Ī 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. For example, a signal that reaches 50% of the maximum level has a level of −6 dBFS, which is 6 dB below full scale. The level of 0 dBFS is assigned to the maximum possible digital level. The unit is similar to the units dBov and decibels relative to overload ( dBO). The red lines indicate full scale, and the waveform is shown before and after hard clipping (grey and black outlines respectively).ĭecibels relative to full scale ( dBFS or dB FS) is a unit of measurement for amplitude levels in digital systems, such as pulse-code modulation (PCM), which have a defined maximum peak level. For other uses, see DBFS (disambiguation).
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