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How does summing (analog)signals in the digital domain affect sound quality?
Old 16th February 2007
  #1
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How does summing (analog)signals in the digital domain affect sound quality?

An a/d samples an analog (voltage) signal and outputs a digital signal that is 24bit unsigned. The range 2^24 bits accomodates the analog signal's amplitude range. The (known) quatization errors that occur during this conversion will be propagated to any future digital processing of that signal.

What happens when you convert that 24 bit *signal* to a 32 or 64 bit floating point *number* in a DAW?

One would think that floating point is as precise, or better, (a holder of data) as 24bit unsigned because it's mantissa alone has 24 bits,
thus yielding the same precision
as 24bit plus the extra "headroom" of the 7bit exponent. But, in reality the distribution of values in floating point
is such that as a signal gets larger there are less possible combinations (less precision) to represent it. The problem affects *mostly* operations like adding two numbers where one is much larger than the other. The effects, though, are devastating and that's one of the reason many professionals prefer the otb sound signature. Check out this link:
http://www.cs.princeton.edu/introcs/91float/

and this link:
http://docs.python.org/tut/node16.html

and this link for more enlightment:
http://en.wikipedia.org/wiki/Fraction_%28mathematics%29


The combination of inaccuracy and imprecision in floating point dsp computations is what leads to what I would call "digital harmonics". These digital harmonics result in a sound that is unpleasing to the ear, in the same way and order of magnitude as a soundwave that is reproduced as an electric signal. REPRODUCTION

It would be interesting to see what are the pitfalls of fixed point systems aka pt. Meanwhile I'll take the analog route and try to figure out a way to make those fractions work in the daw domain. Hey, wordlengths are limited as is, we don't have to mess up the arithmetic
Old 16th February 2007
  #2
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Nobody walks down the road whistling a mantissa ...

Interesting reading though - good ammunition against the "it's just zeros and ones" apologists.

But analog isn't accurate either. Shouldn't it worry you that your perfect analog analog waveform is being pushed through a bunch of resistors and capacitors with perhaps a 1% accuracy tolerance (if you are very lucky)? Or that the DC voltage to the transistors has 10mVrms ripple (if you are lucky)?
Old 16th February 2007
  #3
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Capstan Cappy's Avatar
 

numbers numbers,
0.1 % distortion by accuracy of components all together at the ouput are not even audible , speakers alone do about 2 to 3%
well built equipment have minimal phase shifts of 1 degree, so no, does not worry me personally at all
Old 16th February 2007
  #4
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I agree that analog also introduces nonlinearities to a signal, but one thing to remember is that in an analog system the signals at least are continous, they haven't been quantized, so any operation of the signal/s will also result in a continous signal. I was thinking about the following mental experiment: take any number of analog signals, record them to individual tracks digitally. Then, output each signal to its own amplifier/speaker. Place the speakers in a room in such a way as to create the soundstage desired (ie sum the soundwaves in a room). Record the result using a stereo miking technique. How would this sound compared to summing itb or otb? I'll call it "summing in the room". How about summing using transformers? Or maybe mixing in water? Or how about sythesizing the digital signals using the wavelet transform?
Old 16th February 2007
  #5
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Quote:
Originally Posted by boxymoron View Post
The combination of inaccuracy and imprecision in floating point dsp computations is what leads to what I would call "digital harmonics". These digital harmonics result in a sound that is unpleasing to the ear, in the same way and order of magnitude as a soundwave that is reproduced as an electric signal. REPRODUCTION
I've found that certain types of white noise, when frequency shaped and added to the mathematical stream with just the right multiple, can actually act as a DIGITAL HARMONICS FILTER, resulting in a more enjoyable listening experience for all, the increased enjoyment of which is directly proportional to the magnitude of the electrical signal reproduction.

-R
Old 16th February 2007
  #6
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Ahh, I forgot about dithering. Dithering is used to mask the quantization errors in a digital system by adding noise to the low bits in the system. We are effectively raising the "noise floor" to mask the distortions.
Old 16th February 2007
  #7
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Quote:
Originally Posted by boxymoron View Post
I was thinking about the following mental experiment: take any number of analog signals, record them to individual tracks digitally. Then, output each signal to its own amplifier/speaker. Place the speakers in a room in such a way as to create the soundstage desired (ie sum the soundwaves in a room).
What would be even cooler is if you had two acoustic dead identic rooms with 8 identic speakers with 8 amplifiers in each room. Then play back 16 tracks spread out thrugh the 16 speakers and mic'd up by two identic microphones, one in each room!

Anyone want to try?
Old 16th February 2007
  #8
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Quote:
Originally Posted by boxymoron View Post
Ahh, I forgot about dithering. Dithering is used to mask the quantization errors in a digital system by adding noise to the low bits in the system. We are effectively raising the "noise floor" to mask the distortions.
How very analog of you.

-R
Old 16th February 2007
  #9
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Quote:
Originally Posted by Cojo View Post
What would be even cooler is if you had two acoustic dead identic rooms with 8 identic speakers with 8 amplifiers in each room. Then play back 16 tracks spread out thrugh the 16 speakers and mic'd up by two identic microphones, one in each room!

Anyone want to try?
I've done that right here in my room wiith my 5 LSR 28's. Great way to listen to bluegrass.

At that point is the music being summed in the room or in my brain?

-R
Old 17th February 2007
  #10
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Quote:
Originally Posted by RKrizman View Post
I've done that right here in my room wiith my 5 LSR 28's. Great way to listen to bluegrass.

At that point is the music being summed in the room or in my brain?

-R
heh
Old 17th February 2007
  #11
Gear Maniac
 
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Quote:
Originally Posted by RKrizman View Post
How very analog of you.

-R
Yes, in analog there is also a noise floor, which affects low level detail, but at least the summing of signals is even even across the entire range? In a floating point system there is a skewing of precision from top to bottom. I guess the same happens in analog when summing large signals (running out of headroom leads to distortion/clipping). It would be interesting to make an accuracy/precision comparison btw the two at both extremes.
Old 17th February 2007
  #12
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Numbers are fun, but the fact is that I have heard great sounding all digital mixes and really ****ty sounding all analog mixes, so what's up with that?

Anyway, like it or not, we are a digital society. The current generation of earbud wearing mp3 listening folks don't have an issue with digital. It's all relative. the phasing distorted sound of an MP3 is the accepted norm. The consumer doesn't care about the math.

But....I still mix OTB heh
Old 18th February 2007
  #13
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http://www.oreilly.com/catalog/mindh...ter/hack33.pdf

I found this article, I think it relates to how we hear too.
Old 18th February 2007
  #14
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Quote:
Originally Posted by Sizzleboy View Post
Numbers are fun, but the fact is that I have heard great sounding all digital mixes and really ****ty sounding all analog mixes, so what's up with that?

Anyway, like it or not, we are a digital society. The current generation of earbud wearing mp3 listening folks don't have an issue with digital. It's all relative. the phasing distorted sound of an MP3 is the accepted norm. The consumer doesn't care about the math.

But....I still mix OTB heh


To me MP3s being the norm makes it even more important to get the biggest, fattest, punchiest, and most phenomenal sound possible. Why ? Because if this is where your mixes are going to end up at the end of the day, they sure as hell better be nothing short of spectacular sounding in your CR and then finally at the mastering house!

For this reason IMO great analog processing has become even more important today than it was in the past with vinyl. That's why dedicated outboard mic pres have grown so much in popularity in the last decade. Not hard to see why, when MP3 has become the standard.
Old 18th February 2007
  #15
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Quote:
Originally Posted by RKrizman View Post
I've done that right here in my room wiith my 5 LSR 28's. Great way to listen to bluegrass.

At that point is the music being summed in the room or in my brain?

-R
Unless you have 5 ears, I would suggest the room ...

Summing is easy, and it's easy to prove that DAW's can sum multiple sinewaves and still end up with a sinewave that can be phase inverted and nulls one of the original sinewaves. In other words, the summing is mathematically perfect and phase coherent. And you can check this for any frequency you care to try.

I don't believe an analog desk can do this (I haven't tried, but logically each channel will have it's own imperfections). I believe it's the imperfections that make analog sound good - and to a great extent you can model these with digital if you want to.
Old 18th February 2007
  #16
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So the reason digital does'nt sound good is that it isn't accurate enough as opposed to analog ? Funny that,i always thought it was the other way around.
Digital is too precise.It does'nt add or take away nearly as much as analog equipment does.

As for the summing issue. The thought that analog summing is more exact than digital beacause digital does'nt have enough bits to do exact calculations is of course complete nonsense. That isn't even a theoretical issue. Imparting analog inaccuracies in the signal path is were the (supposed ) magic is.
Old 18th February 2007
  #17
Gear Maniac
 
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Was looking through the akm5394a a/d datasheet and found the following:

dynamic range = 120 dB
s/n ratio = 120 dB
highest sample value = EFFFFF
full scale input +/- 2.4 vpp

"The output is EFFFFFhex for input above a positive full scale"
"800000hex for input below below negative full scale"
"000000hex for no input signal"


So, this particular a/d should be able to resolve a signal as small as 1/(2^23/4.8) 0.000000572203 volts. But the stated DR is 120 dB, which means that the noise floor uses up the first 3 bits, so the effective bit depth is 20 bits. (that's why ppl say there are no real 24 bit converters). So the converter can actually resolve 1/(2^20/4.8) = .000005 volts or 5 microvolts, which doesn't seem like a lot of precision when compared to the human ear.

Now my question is the following: Say you want to sum two signals, one is 2.4 volts and the other is .000005 volts (the two extremes). How can we quantify the difference in the result btw summing those signals in the digital domain(in floating point) vs in the analog domain?

In the decimal world (mathematically), the answer would be 2.400005.

Using an online ieee754 converter I found that 2.4dec-> 2.3999999 and .000005 ->4.9999999e-6.
Furthermore, the correct answer 2.400005dec can be represented as 2.4000049 in floating point.
But, 2.3999999dec + 4.9999999e-6dec = 2.4000048999999.
The difference is, 2.400005 - 2.4000048999999 = 0.0000001000001 and the error is 0.0000001000001/2.400005 = .000000041666 or about 4 millionths of a percent (.0000041666%).

Can the human ear detect such error? It doesn't matter. What does matter is that in a floating point system errors like these keep compounding themselves, especially when dealing with tens of signals and all those nasty plugins.

Could someone corroborate these results? What would be the error when summing these two signals in an analog circuit?
Old 19th February 2007
  #18
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Quote:
Originally Posted by boxymoron View Post
Can the human ear detect such error? It doesn't matter. What does matter is that in a floating point system errors like these keep compounding themselves, especially when dealing with tens of signals and all those nasty plugins.
If the human ear can't detect it, then it doesn't matter.

-R
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