I'm trying to scale wave amplitude (0-1) to perceived loudness (still 0-1). The decibel scale seems to be unbounded. For my audio, the amplitude 1 represents a decibel $d$ - i.e. the audio is being played at volume $d$. But what would the decibel be for 0 amplitude? I know 0dB is the minimum a human can hear, but what's the actual minimum. If I can obtain this, then I can successfully convert wave amplitude to perceived loudness (while staying between 0 and 1)
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http://www.sengpielaudio.com/calculator-db.htm – Juha P Aug 08 '20 at 17:56
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Remember that decibels are a ratio, fundamentally, on a log scale. As a ratio, there are no inherent bounds, and there is no inherent reference.
When you say that 0 dB is the lowest amount we can hear, you really mean 0 dB SPL (Sound Pressure Level). In this case, 0 dB is the ratio "1" (1:1, for instance), times a defined reference intensity for SPL that is nominally the threshold of hearing.
Your 0-1 range can map to anything, but let's say 1 maps to 0 dB. This is common in audio DSP, because of a gain of 1 x is synonymous with a gain of 0 dB (again, simply ratio 1:1, not referenced to anything). But at the other end, 0 maps to minus infinity, because it's a log scale.
Again, this is simply a ratio, or gain factor. "Bob has twice as much money today as he had yesterday"—we don't know if Bob can afford a \$3 beverage. When coupled with a reference, as with dBV, dBm, or dB SPL, then you actually have measurable levels. "Bob has twice the reference quantity of money, which is defined as $100."
Nigel Redmon
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Do all dB scales use the same log base (which would make the reference DB the only parameter to convert to a real level)? – Tobi Akinyemi Aug 11 '20 at 19:41
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One scale, but you'll see two different calculations depending on whether you're using power (energy) or field (amplitude). For power, it's 10 * log10(x/xref), for amplitude (voltage, for instance), it's 20 * log10(x/xref). For an audio signal or samples, you'd use the latter, and xref is 1 for most things, so a gain factor of 2 would yield 6.02 (we usually just say +6 dB), gain of 1 is 0 dB, a gain of 0.5 is -6.02 dB. But that only tells us the relative change in the signal. If you need to know the actual amount, you need to reference it to something with units...that's where dB SPL/m/V... – Nigel Redmon Aug 12 '20 at 20:41
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@TobiAkinyemi For audio DSP, you'll mostly care about levels relative to full scale, or to the signal you're working with. For instance, you may generate a sine wave at full scale and output it to a DAC. How loud is it? Well, we don't know—it depends on how far up the fader is on your mixer, the setting of the control room level knob, and how much power and how efficient your powered monitors are. Typically, that's not your problem. But if it is—maybe you've created a loudness meter (SPL), or you designed the mixer and want to ensure standard voltage levels (dBm, dBV) to send to monitors. – Nigel Redmon Aug 12 '20 at 20:49
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As a physically realizable metric, the dB value for zero is anything less than Plank energy, or 1.96×109J, as the would be statistically unmeasurable.
hotpaw2
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