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In Reply to: What's the math behind a digital volume control? posted by JayM on February 8, 2007 at 17:46:32:
Digital attenuation done with PCM truncates data. It is roughly 1 bit loss of resolution per 6dB attenuation. Some clever designs use dithering and wordlength expansion to minimize this effect, but it's still there.
Follow Ups:
What is meant by "truncation" in the digital attenuation context?
Is it literally chopping off the last bit(s) in the 16-bit word?
For a given number of digits in a data word, bits in this case,
attenuation, which is done by division or multiplication with a value less than 1, shifts the significant digits to the right and thus
out of the word.Example:
Imagine a 4 bit system, and you want to attenuate "1111" with 6dB,
which is *0.5."1111" * 0.5 = "0111.1", reduced to 4 bits only = "0111".
So you lost data, as only 3 of the original 4 '1' bits are left.
--
Now with CD's 16 bit standard there is a way of doing at least some
lossless digital attenuation: DAC chips exist with an effective resolution of 20 bits. That's 4 bits more than the 16 bits of the input channel, so you can tolerate up to 2^4 = 16 => 24dB of digital attenuation before really starting to lose data.So with 4 bits signal and a 6 bit DAC the unattenuated scenario
would be:source "1111" => no att. => DAC input "1111.00"
source "1111" => att. by 6dB => DAC input "0111.10"
Which still doesn't make it practical for the large amounts of attenuation required in music volume control.
As I write I am listening to a replay level of -24dBfs via a digital volume controlled DAC where a level of -20dBfs is stated to be the maximum attenuation before loss of resolution sets in (see also the various posts above). Frankly I cannot hear any difference (aside from one being quieter) between the two settings. However if I attempt to make the system as a whole comfortable to listen to within the recommended envelope set at the DAC of 0dBfs to -20dBfs by inserting a passive 10dB attenuator at the power amps input it still sounds worse than using no passive attenuator with a lower than recommended setting on the DAC. So much for passive attenuators.I guess that 1. one is perhaps less sensitive to resolution loss when listening at comparatively low levels (I guess peaks at around the upper 70dBs mark)and 2. I am still listening to only a 16 bit medium which allows greater tolerance even if upsampled (i.e there is no more actual information there). With highly compressed low sample rate digital radio I can set the digital volume control even lower without any apparent subjective losses.
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