[opaqueice]

I'd like to get something straight on the subject of digital volume controls.  You very often hear people say (ar least on internet audio fora) that attenuating a digital signal is bad because of a loss of resolution.  This is justified on the grounds that when the volume is reduced some bits are filled in with zeros, and the smaller number of non-zero bits that remain can't store as high a resolution version of the signal as the original.

Now, strictly speaking all of that is correct.  But since you obviously need a volume control of some kind, the real issue is to compare digital attenuation to more conventional analogue volume controls (say a potentiometer).  And as far as I can see, there is no real difference.  You can forget everything about resolution - a digital volume control acts almost identically to an analogue one, at least in so far as signal degradation goes. 

Let me explain.  Suppose you start with a 16 bit digital signal, which is 96dB of range, and suppose the noise floor of the dac is at -90dB.  What that means is the last bit of those 16 bits is irrelevant, because changing it from 1 to 0 makes a difference at the -96dB level, below the noise floor.  But now think about digital attenuation for a second.  When you attenuate the signal, two things can reduce the resolution:

1) the signal to noise gets worse, because the signal is reduced but the noise stays the same, and

2) rounding errors and finite resolution effects from the reduced numbers of bits make the signal less accurate

But here's the thing - in my example above 2) is a total non-issue, because the attenuated signal is AT MOST off in the last bit - and that's below the noise floor.  And those numbers were not realistic - most digital devices I know of (the Logitech Squeezebox for example) actually do the volume control with 24 bits, which means the errors are -144dB down from the signal - and that's far below the noise floor of even SOTA devices.

Conclusion?  Digital volume control is no better or worse than analogue, all else being equal, and the stuff about "loss of resolution" is nonsense (unless you just mean decreased S/N, which will happen with analogue controls in just the same way).

Am I missing something?

[mcullinan]

If this is true, and its funny because Ive been looking around and deciding what to do because I have so much gain I cant turn my preamp 2 cm above zero, Id like to turn down my SB so I can more easily adjust my pre. I hate going from zero to ear bludgeoning, not fun. Let us know.
Mike

[PhilNYC]

One thought (a guess, actually)...how much of an audio signal uses the full 16-bits?  My assumption is that for the majority of a musical recording, the top end of the 16-bits are more times than not filled with 0's (especially in quiet recordings).  Because of this, bit-shifting and losing the lowest bit of data is generally a higher proportion of the data being played than your 16-bit/96db range example.  Possible?

[some young guy]

Alex Peychev from APL Hi-Fi designed an H-attenuator for his digital players. Here's his take on it:

"One of the problems with all digital attenuation is that the signal level drops but the noise floor remains, unlike analog attenuators where the signal and noise are equally attenuated. Of course, there are many other problems with analog attenuators. The steady noise floor with the all Digital attenuators is not a problem with low and average sensitive systems, but it creates problems with high sensitivity systems - like amplifiers with a lot of gain and high efficiency speakers, or both. For example, my amplifier has about 2-3 volts input sensitivity, my speakers are about 88 db efficient and I have no problems with noise. Many who have listened to my system were impressed by how low the noise floor is. I have the Denon with all Digital attenuator and NO power conditioning of any sort. I am running a pair of Power Chord cables from Audience plugged to a modified power strip which is connected to the wall.

The new H-Attenuator will be hybrid (this what the H means). The first 40 db of attenuation will be done in the analog domain by microprocessor controlled, laser trimmed precision resistor ladders. The rest will be taken from the DAC in the digital domain. Since 40 db covers normal listening levels the resistor ladder will be used most. This will decrease the noise level with 40 db and will also allow the DAC to work at full scale output and also "Direct DSD" mode with SACD."

[darrenyeats]

Just removed my previous two replies because they're a bit too rambling, incoherent and theoretical!! So third time lucky.

Digital might not be the end of the story if a source's output is not matched to the power amp's input sensitivity.

IF the source's output and power amp's input sensitivities are WELL MATCHED then opaqueice's assertion (that digital is like analogue, and for reasons of not being physical is actually better) holds true. This is because no *power amp* I know of has a 144db SNR anyway: it becomes moot whether a quiet CD sound (e.g. -90db) which is attenuated by say 50db looks better with a digital volume control or an analogue one. Such a small signal won't be resolved by the power amp anyhow.

If the mismatch of source's output and power amp's input sensitivities is bad enough, this situation could start to change. The reason is the source has effectively no longer a 144db SNR but less, because the maximum loudness the power amp can accept curtails the dynamic range of the source. If the mismatch is enough, you might start to notice the difference between correcting it digitally and in analogue. This is because a passive resistor attenuates both the noise and the signal, as some-young-guy pointed out just now. However, I think the argument doesn't rely on either the power rating of the power amp or the speaker sensitivity, in the sense that the argument would remain the same even for very loud PA systems or headphone set ups - absolute loudness isn't the issue, just SNR.

And another factor that might reduce the SNR of the source is DSP. Again, if this is within limits it may be moot but you have to calculate this in with sensitivity matching to see how it stacks up.
Darren