Volume control
Digital volume control is multiplying the numerical value of the sample by a factor.
This factor is in general < 1 but not all of the time.
Volume levelling (replay gain) is an example where > 1 might be applied.
By design the audio is no longer bit perfect when digital volume control is applied.
One easy example is applying volume control. If you change the volume to 90% for example, the software will multiply all the digital audio data by 0.9. The result is rarely an exactly 16-bit word, just like dividing regular numbers often results in non-integer numbers. It usually has a remainder...which will require more bits (digits, or decimal places in regular numbers). If the data path is limited to 16-bit, the remainders will be truncated. That's analogous to dividing 10 by 3, and having a result of 3. With extra digits available, a more accurate result of 3.333... can be achieved.
Most DACs accept 16 or 24 bit words only.
No matter what kind of math is applied, the result must be rounded to a 16 or a 24 bit integer.
The remainder simple doesn’t fit in.
This is called quantization error.
This affect affects the LSB (Least Significant Bit) both in 16 and in 24 bits.
The LSB of a 16 bit word is -96 dBFS. Although very soft, it is audible. Dither must be applied to camouflage this artifact.
In case of a 24 bit word the LSB is at -144 dBFS. This is way below the noise floor of any gear.
Using a 24 bit DAC has an advantage.
A lot of audiophiles think digital volume control is bad.
They set the digital volume control to 100% and use analog device.
An analog volume control brings down the peak signal and noise simultaneously to preserve S/N down to low output levels.
| Level | Analog | Digital |
| 0 | 96 | 96 |
| -5 | 96 | 96 |
| -10 | 96 | 94 |
| -15 | 96 | 89 |
| -20 | 96 | 84 |
| -25 | 96 | 79 |
| -30 | 96 | 74 |
| -35 | 96 | 69 |
| -40 | 96 | 64 |
| -45 | 91 | 59 |
| -50 | 86 | 54 |
| -55 | 81 | 49 |
| -60 | 76 | 44 |
S/N ratio of volume control using a DAC with a -104dB S/N ratio, 16-bit/44.1 audio.
Already at -10 dBFS the analog volume control outperforms the digital in S/N ratio.
This is the consequence of the quantization noise.
| Level | Analog | Digital |
| 0 | 96 | 96 |
| -5 | 96 | 96 |
| -10 | 96 | 96 |
| -15 | 96 | 96 |
| -20 | 96 | 96 |
| -25 | 96 | 96 |
| -30 | 96 | 96 |
| -35 | 96 | 96 |
| -40 | 96 | 92 |
| -45 | 91 | 87 |
| -50 | 86 | 82 |
| -55 | 81 | 77 |
| -60 | 76 | 72 |
S/N ratio of volume control using a DAC with a -132dB S/N ratio, 16-bit/44.1 audio.
Now we have to go down to -40 dBFS to hear a difference.(Mark Mallinson [1]).
It is unclear how these numbers are obtained.
The correctness is questioned at the What’s Best Forum [2].
One thing is sure, digital volume control never wears, never crackles, never breaks.
- Digital vs. Analog Volume Control - Resonessence Labs
- Digital Volume Control - What's Best Forum