by MMan » Sun Sep 06, 2009 1:57 pm
I have been
slowly working on a wiki page on the topic of volume leveling and general information on converting analog to digital. While it is not yet ready for prime time, here is an excerpt relating to the issue or dB measures generally as well as how they relate to digital audio. As you correctly point out, dB is a relative scale, also a logarithmic scale.
The harder the air gets pushed, the louder the sound. Although this is typically referred to as volume, in reference to acoustical energy, it is called Sound Pressure Level (SPL). The scale used to measure Sound Pressure Level is the Decibel scale, or dB SPL.
The intensity of sound is measured in a unit called the decibel (dB), which describes the relative intensity of a sound based on a logarithmic decibel scale containing values ranging from 0 to 194. Although a zero value on the decibel scale represents the weakest sound audible to humans and sound intensity increases in correspondence with numeric values, the relationship among the values on the decibel scale is not linear but logarithmic. Therefore, the simple assumption that a sound with a 50 dB level is twice as intense as a sound with a 25 dB level would be incorrect. Rather, in a perfect world, each three decibel increment affects a 50% change in sound pressure levels. Thus, a 3 dB drop reduces sound exposure by 50%, while a 6 dB drop reduces exposure by 75%. Though reducing the decibel level produced by a sound source from 80 to 77 may not seem like a major change, it would actually represent a 50% reduction in audible sound.
The intensity of a sound reaching a person’s ear depends not only on the intensity of the sound produced, but also on the person’s distance from the source of the sound. If you were standing one foot away from a loud machine, for instance, you would experience higher decibel level than if you were ten feet away, even though the intensity of the sound produced remains unchanged. This is so because the intensity of sound decreases as sound waves spread out over time and distance, a behavior demonstrated by the Inverse Square Law. The Inverse Square Law is a calculable equation proving that each time the distance between the source of a sound and its recipient doubles, the recipient will experience a 6 dB drop in sound intensity, assuming that no surfaces are present to create reflections that in real world situations would alter these results.
dBFS - dB Full Scale
So sound is measured in dBs and the higher the dBs the louder the sound and these are typically positive values. So why when we start talking about dBs in digital music, are the values negative? First, it is important to remember that a dB is not an absolute measure, it is a relative measure. In most instances, it is a logarithmic function of the ratio of one measure to a reference standard. In the case of normal sound, as discussed above, it is the log of the ratio of the SPL measure of the sound to the weakest audible signal for the human ear (the reference standard).
In the case of digital music, the reference standard is the highest possible level digital gear can record, or 0 dBFS. All other measurements expressed in terms of dBFS will always be less than 0 dB (negative numbers). 0 dBFS indicates the digital number with all digits ="1", the highest possible sample. The lowest possible sample is (for instance for 16 bit audio): 0000 0000 0000 0001, which equals -96 dBFS. Therefore the dynamic range for 16-bit systems is 96 dB. For 20-bit digital audio it is 120 dB. For 24 bit digital audio it is 144 dB. Full-scale input level is the analog input voltage level that will cause the A/D converter to just equal full scale with no clipping on either positive or negative peaks.
I have been [i][b]slowly[/b][/i] working on a wiki page on the topic of volume leveling and general information on converting analog to digital. While it is not yet ready for prime time, here is an excerpt relating to the issue or dB measures generally as well as how they relate to digital audio. As you correctly point out, dB is a relative scale, also a logarithmic scale.
[i][b][quote]The harder the air gets pushed, the louder the sound. Although this is typically referred to as volume, in reference to acoustical energy, it is called Sound Pressure Level (SPL). The scale used to measure Sound Pressure Level is the Decibel scale, or dB SPL.
The intensity of sound is measured in a unit called the decibel (dB), which describes the relative intensity of a sound based on a logarithmic decibel scale containing values ranging from 0 to 194. Although a zero value on the decibel scale represents the weakest sound audible to humans and sound intensity increases in correspondence with numeric values, the relationship among the values on the decibel scale is not linear but logarithmic. Therefore, the simple assumption that a sound with a 50 dB level is twice as intense as a sound with a 25 dB level would be incorrect. Rather, in a perfect world, each three decibel increment affects a 50% change in sound pressure levels. Thus, a 3 dB drop reduces sound exposure by 50%, while a 6 dB drop reduces exposure by 75%. Though reducing the decibel level produced by a sound source from 80 to 77 may not seem like a major change, it would actually represent a 50% reduction in audible sound.
The intensity of a sound reaching a person’s ear depends not only on the intensity of the sound produced, but also on the person’s distance from the source of the sound. If you were standing one foot away from a loud machine, for instance, you would experience higher decibel level than if you were ten feet away, even though the intensity of the sound produced remains unchanged. This is so because the intensity of sound decreases as sound waves spread out over time and distance, a behavior demonstrated by the Inverse Square Law. The Inverse Square Law is a calculable equation proving that each time the distance between the source of a sound and its recipient doubles, the recipient will experience a 6 dB drop in sound intensity, assuming that no surfaces are present to create reflections that in real world situations would alter these results.
dBFS - dB Full Scale
So sound is measured in dBs and the higher the dBs the louder the sound and these are typically positive values. So why when we start talking about dBs in digital music, are the values negative? First, it is important to remember that a dB is not an absolute measure, it is a relative measure. In most instances, it is a logarithmic function of the ratio of one measure to a reference standard. In the case of normal sound, as discussed above, it is the log of the ratio of the SPL measure of the sound to the weakest audible signal for the human ear (the reference standard).
In the case of digital music, the reference standard is the highest possible level digital gear can record, or 0 dBFS. All other measurements expressed in terms of dBFS will always be less than 0 dB (negative numbers). 0 dBFS indicates the digital number with all digits ="1", the highest possible sample. The lowest possible sample is (for instance for 16 bit audio): 0000 0000 0000 0001, which equals -96 dBFS. Therefore the dynamic range for 16-bit systems is 96 dB. For 20-bit digital audio it is 120 dB. For 24 bit digital audio it is 144 dB. Full-scale input level is the analog input voltage level that will cause the A/D converter to just equal full scale with no clipping on either positive or negative peaks.[/quote][/b][/i]