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Decibels 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. The unit is similar to the units dBov and decibels relative to overload (dBO).[1]
The level of 0 dBFS is assigned to the maximum possible digital level.[2] For example, a signal that reaches 50% of the maximum level has a level of −6 dBFS, which is 6 dB below full scale. Conventions differ for root mean square (RMS) measurements, but all peak measurements smaller than the maximum are negative levels.
A 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.[3] This can be prevented by careful digital-to-analog converter circuit design.[4] Measurements of the true inter-sample peak levels are notated as dBTP or dB TP ("decibels true peak").[5][6]
Since a peak measurement is not useful for qualifying the noise performance of a system,[7] or measuring the loudness of an audio recording, for instance, RMS measurements are often used instead.
A 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.[8][9][10][11][12]
The unit dB FS or dBFS is defined in AES Standard AES17-1998,[13] IEC 61606,[14] and ITU-T Recs. P.381[15] and P.382,[16] such that the RMS value of a full-scale sine wave is designated 0 dB FS. This means a full-scale square wave would have an RMS value of +3 dB FS.[17][18] This convention is used in Wolfson[19] and Cirrus Logic[20] digital microphone specs, etc.
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.[21][22] All possible dBov measurements are negative numbers, and a sine wave cannot exist at a larger RMS value than −3 dBov without clipping.[21] This unit can be applied to both analog and digital systems.[21] This convention is the basis for the ITU's LUFS loudness unit,[23] and is also used in Sound Forge[10] and Euphonix meters,[24] and Analog Devices digital microphone specs[25] (though referred to as "dBFS").
The measured dynamic range (DR) of a digital system is the ratio of the full scale signal level to the RMS noise floor. The theoretical minimum noise floor is caused by quantization noise. This is usually modeled as a uniform random fluctuation between −1⁄2 LSB and +1⁄2 LSB. (Only certain signals produce uniform random fluctuations, so this model is typically, but not always, accurate.)[26]
As 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):
The value of n equals the resolution of the system in bits or the resolution of the system minus 1 bit (the measure error). For example, a 16-bit system has a theoretical minimum noise floor of −98.09 dBFS relative to a full-scale sine wave:
In any real converter, dither is added to the signal before sampling. This removes the effects of non-uniform quantization error, but increases the minimum noise floor.
The phrase "dB below full scale" has appeared in print since the 1950s,[27][28][29] and the term "dBFS" has been used since 1977.[30]
Although the decibel (dB) is permitted for use alongside units of the International System of Units (SI), the dBFS is not.[31]
dBFS is not defined for analog levels, according to standard AES-6id-2006. No single standard converts between digital and analog levels, mostly due to the differing capabilities of different equipment. The amount of oversampling also affects the conversion with values that are too low having significant error. The conversion level is chosen as the best compromise for the typical headroom and signal-to-noise levels of the equipment in question. Examples:[32][33][34]
In all cases the reference power level used for measurements will be the overload point of the converter in question, and figures will be quoted in dBO.
inter-sample peaks may be considerably higher than 0dBFS.
Meters that ... use an oversampled sampling rate of at least 192 kHz, should indicate the result in the units of dB TP [which] signifies decibels relative to 100% full scale, true-peak measurement.
As can be seen from the figure, if the peak sample values are 0 dBFS, the true peak will be higher than 0 dBTP.
the conclusion is reached that the meaningful quantities are found by rms measurements. ... At this point it may be objected that other measurements, peak, or peak-to-peak voltage measurements in particular, are also significant. This is true, but not from the standpoint adopted here. Such measurements are applicable only to the field of nonlinear response, such as dielectric breakdown, etc.
This method yields a result of -3dB for a full scale sine wave and 0dB for a full scale square wave. Sound Forge uses this method.
many software programs indicate level on virtual meters by means of a conventional RMS calculation, leading to a full scale sine wave reading -3.01 dB FS, which is incorrect in the context of this document.
Because the definition of full scale is based on a sine wave, it will be possible with square-wave test signals to read as much as + 3,01 dB FS.
the r.m.s. amplitude of a ... 997 Hz sinusoid whose peak positive sample just reaches positive digital full-scale ... is defined as 0 dB FS
0 dBFS represents the root mean square (RMS) level of a full-scale sinusoidal
0 dBFS represents the root mean square (RMS) level of a full-scale sinusoidal signal
Note that, because the definition of FSR is based on a sine wave, it is possible to support a square wave test signal output whose level is +3dBFS.[permanent dead link ]
Note that, because the definition of FSR is based on a sine wave, it is possible to support a square wave test signal output whose level is +3 dBFS.
The level of a tone with a digital amplitude (peak value) of xover is therefore L= –3.01 dBov.
For example, in the case of a u-law system, the reference would be a square wave ... and this ... represents 0dBov
If a 0 dB FS, 1 kHz ... sine wave is applied to the ... input, the indicated loudness will equal −3.01 LKFS.
On a logarithmic dB scale, the difference between a sine wave's peak and RMS average level is 3 dB. Euphonix bases its metering on the Audio Precision measurement system, which adheres to the RMS average technique.
so a digital microphone's output must be scaled from peak to rms by lowering the dBFS value. For a sinusoidal input, the rms level is 3 dB (the logarithmic measure of (FS√2) below the peak level ... A 94 dB SPL sinusoidal input signal will give a –26 dBFS peak output level, or a –29 dBFS rms level.
It is convenient when working with A/D converters to define a 0 dB reference for a full-scale-to-full-scale sine wave. ... The quantizing noise in the Nyquist bandwidth for a 16 bit converter would be -98.08dbFS
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