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Author Topic: Digital summing saturation = myth?  (Read 11535 times)

Hanjong Ko

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Digital summing saturation = myth?
« on: February 27, 2009, 08:24:21 am »

I know that this issue has been discussed to death all over many forums, and always thought that it was a myth.  That digital summing is just summing of numbers.  However, there are also many people who believe in this theory of lots of tracks will saturate digital bus and cause degradation of audio quality), even many professionals.  Could someone PLEASE explain why this is a myth or not?

Thanks and please no bullshit.
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compasspnt

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Re: Digital summing saturation = myth?
« Reply #1 on: February 27, 2009, 08:43:24 am »

I can't "do the match," but I personally think there *might* be a little something to it.

I do believe that any "digital problems" can be mitigated, and to a large extent, by keeping levels reasonably lower.

If you haven't yet, do read the "DAW...Desks" Sticky thread here above, and the "Digital tracking...low levels" Sticky at the top of Whatever Works.

This all leads me to believe, again not from mathematical expertise, but rather from empirical observation, that numbers are intrinsically involved.

I would venture to *guess* therefore that, the more tracks you have, the lower the levels should actually be...?
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Hanjong Ko

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Re: Digital summing saturation = myth?
« Reply #2 on: February 27, 2009, 12:07:50 pm »

Hmm I wonder if anyone actually knows.  I had an ironic experience when testing power cables.  I thought they weren't supposed to make much difference in sound theoretically(not sure if this is valid tho), my experience differed.  I found them not to be transparent so I came back to cheap power cables, but I am really curious.
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Andy Peters

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Re: Digital summing saturation = myth?
« Reply #3 on: February 28, 2009, 05:10:33 pm »

Hanjong Ko wrote on Fri, 27 February 2009 06:24

I know that this issue has been discussed to death all over many forums, and always thought that it was a myth.  That digital summing is just summing of numbers.  However, there are also many people who believe in this theory of lots of tracks will saturate digital bus and cause degradation of audio quality), even many professionals.  Could someone PLEASE explain why this is a myth or not?


Of course digital summing can overload, in the same way an analog mix bus overloads -- too much signal.

You can overload an analog summing bus by mixing lots of tracks too.

Now the smart DSP engineer can ensure that a digital mix bus does not overload for a reasonable number of tracks by appropriate scaling and such. But the smart analog circuit engineer can ensure that an analog mix bus does not overload for a reasonable number of tracks by appropriate scaling and such.

If the person mixing insists on running a hundred tracks, each at Full Tilt Boogie, the mix bus will overload. Regardless of whether the mix is digital or analog. And both will sound like ass.

-a
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Hanjong Ko

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Re: Digital summing saturation = myth?
« Reply #4 on: February 28, 2009, 08:52:10 pm »

So regardless of how many tracks are used on a digital bus, as long as not clipping, there isn't quality loss?  Because there are people who says "When you mix digitally in your PC, you can lose information and sound quality."  I am actually quoting that from Dangerous 2-BUS product overview on their website.
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Andy Peters

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Re: Digital summing saturation = myth?
« Reply #5 on: February 28, 2009, 10:36:57 pm »

Hanjong Ko wrote on Sat, 28 February 2009 18:52

So regardless of how many tracks are used on a digital bus, as long as not clipping, there isn't quality loss?  Because there are people who says "When you mix digitally in your PC, you can lose information and sound quality."  I am actually quoting that from Dangerous 2-BUS product overview on their website.


It's the same thing as mixing in analog.

At some point, if you want to mix two or three or four dozen inputs (depending on console design), you need to keep the channel faders down so that you don't overload the summing amps. It really is as simple as that.

Dangerous just wants to sell you their little mixer. Excuse me, "summing bus."

-a
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Hanjong Ko

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Re: Digital summing saturation = myth?
« Reply #6 on: March 02, 2009, 11:03:25 am »

I think I understand now.  Thanks all!  Some really good threads here.
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Ian Visible

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Re: Digital summing saturation = myth?
« Reply #7 on: March 19, 2009, 10:04:48 am »

How does "in the box" or digital summing work?

I can imagine how it works in the real world in air but I can't get my head round digital summing...or I'm trying to make it more complicated than it is.

jimmyjazz

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Re: Digital summing saturation = myth?
« Reply #8 on: March 19, 2009, 02:41:20 pm »

It's arithmetic, but unlike arithmetic with a pencil and paper, arithmetic in a computer has a maximum allowable value, since numbers have a finite length (# of bits) in that world.  Add too many numbers together and exceed that length?  Clippage.  

Imagine going to the grocery store with $200, but you take $210 worth of groceries to the cashier.  You ain't getting that 12-pack of Sierra Nevada, and consequently, you distort.

(I am actually ashamed of my simplistic explanation and my lousy metaphor, but hey, I'm watching college basketball and this was all I could muster.)
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Steve Hudson

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Re: Digital summing saturation = myth?
« Reply #9 on: March 22, 2009, 10:52:41 am »

jimmyjazz wrote on Thu, 19 March 2009 13:41

Imagine going to the grocery store with $200, but you take $210 worth of groceries to the cashier.  You ain't getting that 12-pack of Sierra Nevada, and consequently, you distort.


Brilliant analogy. And my favorite beer.
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Tomas Danko

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Re: Digital summing saturation = myth?
« Reply #10 on: March 23, 2009, 05:43:52 am »

Steve Hudson wrote on Sun, 22 March 2009 14:52

jimmyjazz wrote on Thu, 19 March 2009 13:41

Imagine going to the grocery store with $200, but you take $210 worth of groceries to the cashier.  You ain't getting that 12-pack of Sierra Nevada, and consequently, you distort.


Brilliant analogy. And my favorite beer.



But which one? Smile

Pepperwood Sierra Nevada Pale Ale Clone
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Andy Peters

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Re: Digital summing saturation = myth?
« Reply #11 on: March 28, 2009, 02:32:12 am »

Ian Visible wrote on Thu, 19 March 2009 07:04

How does "in the box" or digital summing work?

I can imagine how it works in the real world in air but I can't get my head round digital summing...or I'm trying to make it more complicated than it is.


It's really quite simple.

As in, simple addition.

With attention paid to overflow and word size.

-a
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Jon Hodgson

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Re: Digital summing saturation = myth?
« Reply #12 on: April 01, 2009, 07:10:02 pm »

Right now I hate Waves, since I'm typing half of this behind their advert.

Since programming DSP is something I do for a living, I think I'm reasoably qualified to answer this question.

There are two reasons why a digital summer might saturate, the first is a hardware limitation in the numerical format, the second intentioal.

Let's deal with the first one, the numerical format. There are three main ways of storing numbers in digital form, integer, fixed point, and floating point. Now for the purposes of this discussion we can lump integer and fixed point together (in fact integer is a special case of fixed point really).

In the case of a fixed point addition, the range of numbers that can be stored in n bits is +/- 2^(n-1)  (well the positive range is one less than that if anyone wants to be pedantic).

If you exceed that range then depending on the way the adder is implemented it will either saturate, or wrap (really nasty). Avoiding this is conceptually not that different from analogude design, you can reduce signal levels at certain points to prevent saturation, but the more you do that the less signal to noise you will get, so it's a tradeoff, or you can use double words which give you masses more headroom with no quality loss, but that uses much more processing power (think of that as a bit like an analogue designer having the option to use super-duper-mega-high quality components but them being very expensive).

But actually there aren't many systems which use fixed point processing that I know of. The only ones that spring to mind are Pro-Tools, which these days uses 48 bit words in the mix buss (that's what they introduced when they started calling it Pro Tools-HD) and SAW on the PC, which I think uses 64 bits in interim calculations and 32 bits for storage and busses (note that 32 bits lets you add 256 24 bit signals before you could possibly reach clipping in the worst case).

Most systems on computers use floating point, and in the case of floating point the numbers that can be stored are huge, so you're not going to get accidental saturation.

So that leaves us with the intentional saturation. The thing is that your final output format, be it a DAC or a CD/DVD, is going to have a limited range, so the numbers that are fed to that are going to have to be kept within that range, but avoiding that is just a case of setting your output level correctly.

All of the above basically adds up to the following...

in modern DAWs, so long as you don't see any clipping lights, you shouldn't have anything to worry about.
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compasspnt

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Re: Digital summing saturation = myth?
« Reply #13 on: April 01, 2009, 08:19:34 pm »

Jon, what would you say the trade off is in using floating point?  Or is it a Free Lunch?
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Jon Hodgson

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Re: Digital summing saturation = myth?
« Reply #14 on: April 01, 2009, 09:04:10 pm »

compasspnt wrote on Thu, 02 April 2009 01:19

Jon, what would say the trade off is in using floating point?  Or is it a Free Lunch?



It's not free, but it's generally pretty cheap these days.

You have two issues, accuracy and cost.

Now the accuracy part is a bit swings and roundabouts, for a given word size fixed point can hold the results of calculations with greater accuracy if they fall with a given range, but will be less accurate outside that range.

Personally I would say that it's usually (but not always) easier to get it right with floating point, even though in some cases you could theoretically get it "more" right with the same word width in fixed point.

The cost part is down to the fact that floating point calculations require more things to be done to the bits, so you need more logic circuitry and/or more processing time. This has become less of an issue over time (some people may remember when the floating point coprocessor was an extra cost option in a PC, these days you can't buy an x86 processor that doesn't have a couple of 80 bit floating point units AND a SIMD 32/64 bit unit on each core.

The reduced cost of processing as a whole means that these days the option of using double width for calculations in both formats is a lot more viable.

Basically this stuff is an issue for me when I'm tryinng to implement an AAC decoder on a low power DSP with 40,000 gates... but much less of an issue if I'm working with a desktop processor with a few 100 million gates.
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