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[Albert]

This thread is sort of an offshoot of the thread about digital attenuation. After reading about the issues regarding simple attentuation of a signal in the digital domain, I'm curious about what must be an even more involved process, that of mixing in the digital domain.

With mixing, not only do you have attenuation and gain, but you have things like fx plugins, sometimes sending and returning to external analog or digital processing boxes, and finally, very importantly, digital summing of all signals that have been through the previous processes.

The math involved in doing attenuation properly is staggering, based on what I read in the other thread. So what is really happening to a group of digital tracks in a DAW that must go through attentuation and gain, plugins, and summing? Is there anything left of the original track, meaning the original ones and zero's? I'm particularily interested in how the numbers work when summing digital tracks.

I apologize if this topic has already been covered here. Thank you in advance.

[danlavry]

Albert wrote on Thu, 23 December 2004 15:38

This thread is sort of an offshoot of the thread about digital attenuation. After reading about the issues regarding simple attentuation of a signal in the digital domain, I'm curious about what must be an even more involved process, that of mixing in the digital domain. With mixing, not only do you have attenuation and gain, but you have things like fx plugins, sometimes sending and returning to external analog or digital processing boxes, and finally, very importantly, digital summing of all signals that have been through the previous processes. The math involved in doing attenuation properly is staggering, based on what I read in the other thread. So what is really happening to a group of digital tracks in a DAW that must go through attentuation and gain, plugins, and summing? Is there anything left of the original track, meaning the original ones and zero's? I'm particularily interested in how the numbers work when summing digital tracks. I apologize if this topic has already been covered here. Thank you in advance.

This thread is sort of an offshoot of the thread about digital attenuation. After reading about the issues regarding simple attentuation of a signal in the digital domain, I'm curious about what must be an even more involved process, that of mixing in the digital domain.

With mixing, not only do you have attenuation and gain, but you have things like fx plugins, sometimes sending and returning to external analog or digital processing boxes, and finally, very importantly, digital summing of all signals that have been through the previous processes.

The math involved in doing attenuation properly is staggering, based on what I read in the other thread. So what is really happening to a group of digital tracks in a DAW that must go through attentuation and gain, plugins, and summing? Is there anything left of the original track, meaning the original ones and zero's? I'm particularily interested in how the numbers work when summing digital tracks.

I apologize if this topic has already been covered here. Thank you in advance.

This is a big question. I’ll try to make it reasonably short:

The math for gain and attenuation is not all that difficult. If you know where the noise floor is for a given track, than if you increase the gain by Xdb, the noise will rise by X dB. For attenuation it is a bit more difficult but not too bad…

In all cases, from a purist standpoint, the best you can do is to record each track with the music peaks as close to full scale as possible, but never to the point of clipping. That way, you utilize digital audio in the best possible way. That way you do not need to amplify signals (and with it amplify their noise floor). If you need to attenuate, you will end up about where you would be recording further down from the full scale, no real loss. A weak signal in digital audio is simply closer to the noise floor. Often you such signals have somewhat “masked” by a stronger signal within the mix.

Mixing digital is not so bad. Say you add 2 identical 1KHz tones (IN PHASE), each at say -1dBFS (dB from full scale) Say each has a -90dBFS noise. The added outcome is doubling of the signal. Double means +6dB so you now have +5dB signal. What happened to the noise? Unlike the signals – an addition of 2 identical waves, the noise of each channel is different. Say it is random, than the total noise will go up by only 3dB, to -87dBFS.  Of course a +5dBFS is over full scale. Say we attenuate it by 6dB. The signal is now again at -1dBFS, the noise went down to -93dBFS. This is an improvement.

This is not a typical case. How often do you add 2 identical signals? It is safer and more realistic to assume that  2 signals (at the same overall levels) are very un related to each (low correlation) and than the addition will not double, but increase the overall level by some amount, such as 3dB, just like the noise. So an addition and rescaling will not alter the signal to noise ratio. It is better than “attenuation only” because you not just attenuating, you are also adding a signal.

It does get a bit more complicated when the signals are to be mixed at unequal relative strength, but not impossible to comprehend. The best way to be safe is to have a reasonably low noise on the original track and a wide enough mix bus (bits).

Analog attenuation is cleaner than digital one. Analog gain is cleaner than a digital one. But analog mix bus (adding of signals) also has its own peculiar set of problems…

Regards
Dan Lavry

[Albert]

Okay, so far so good. But you have all these streams of 1's and 0's, each having started with a series of 1's and 0's in the original recording. They are then altered when attenuated or gain is applied, altered again by menas of plugins, and finally, these streams of numbers must be combined.

How does that combination take place? Let's say you have 24 tracks of digital audio, each track it's own distinct data stream. This is then reduced down to two data streams, the stereo mix. How is all the 24 channels of data combined into two? Is there numerical averaging going on, or are samples taken at the current bit rate?

I'm just curious how this mathematical process takes place, and why I don't like the sound of it as compared to an analog mix, or rather analog summing.

[Ethan Winer]

Albert,

> How does that combination take place? Let's say you have 24 tracks of digital audio <

It's really simple.

Seriously, mixing two tracks (or any number of tracks) is simple addition. At any given moment - the current sample for all tracks - the DAW software simply adds the numbers for all tracks together. The resulting number defines the loudspeaker's displacement, either moving outward (positive numbers) or inward (negative). Gain changes are also very simple, only in that case each track's sample number is multiplied by a constant amount instead of being added to other track sample numbers.

I also feel compelled to point out that the artifacts some people complain about during digital summing and gain changing are way overstated. What it really comes down to is distortion, and the added distortion with each math operation is really REALLY tiny in the grand scheme of things. Certainly many orders of magnitude below the distortion of any microphone or loudspeaker. Even after many such operations in a row.

--Ethan

[Albert]

Ethan, thanks for your response.

If it is simple addition, then why do the various DAW's sound different? Seems like they should all sound exactly the same.

Is there a book I can read on this subject?

[Barry Hufker]

A wonderful book on this subject is "Principles of Digital Audio" by Ken Pohlman.

Barry

[sdevino]

danlavry wrote on Thu, 23 December 2004 19:59

In all cases, from a purist standpoint, the best you can do is to record each track with the music peaks as close to full scale as possible, but never to the point of clipping. That way, you utilize digital audio in the best possible way. That way you do not need to amplify signals (and with it amplify their noise floor). If you need to attenuate, you will end up about where you would be recording further down from the full scale, no real loss. A weak signal in digital audio is simply closer to the noise floor. Often you such signals have somewhat ?masked? by a stronger signal within the mix.

Of course when doing this your analog front end is probably running with ver y high levels of gain pushing the analog clip limits and creating lots of distortion and noise. So this setup is purely a hypothetical best case for digital.

Quote:

Mixing digital is not so bad. Say you add 2 identical 1KHz tones (IN PHASE), each at say -1dBFS (dB from full scale) Say each has a -90dBFS noise. The added outcome is doubling of the signal. Double means +6dB so you now have +5dB signal. What happened to the noise? Unlike the signals ? an addition of 2 identical waves, the noise of each channel is different. Say it is random, than the total noise will go up by only 3dB, to -87dBFS.  Of course a +5dBFS is over full scale. Say we attenuate it by 6dB. The signal is now again at -1dBFS, the noise went down to -93dBFS. This is an improvement.

... and these idenetical issues exist in all analog mixing as well.

Quote:

Analog attenuation is cleaner than digital one. Analog gain is cleaner than a digital one. But analog mix bus (adding of signals) also has its own peculiar set of problems?

What do you mean by "cleaner" in this case Dan? Can you clarify?

My goal in commenting here was to clarify, not refute.

Steve

[RKrizman]

Albert wrote on Fri, 24 December 2004 15:44

If it is simple addition, then why do the various DAW's sound different? Seems like they should all sound exactly the same.

What makes you think they all sound different?  AFAIK,  they all sound the same if you just compare their summing and level change functions.

I mean, why wouldn't they?

-R

[Ethan Winer]

Albert,

> If it is simple addition, then why do the various DAW's sound different? <

I agree with RK. All DAWs do sound the same. If they don't then it's a coding error, or a sound card driver issue, or something else like that.

--Ethan

[Bob Olhsson]

RKrizman wrote on Sun, 26 December 2004 01:04

... What makes you think they all sound different?  AFAIK,  they all sound the same if you just compare their summing and level change functions. I mean, why wouldn't they? -R

They would all need to use the exact same math, precision, gain structure and dither!

Doing gain changes in a first class fashion reduces the number of possible features. Because most people (including too many misinformed developers) assume digital gain changes to be trivial, developers are inclined to spend their processing power elsewhere. Roger Lagadec presented a fascinating paper to the AES about the difficulty of creating a truly transparent digital volume control.

[Timeline]

This topic is one that I feel could be very useful to many of us. Here are some of my
questions I have wondered about for a long time.

1. Would mixing multiple track transient sources not be a reason to seek out systems with higher sample and or bit rates?   In-other-words, do complex waveforms actually require higher bandwidths to be properly reproduced compared to an individual track?  

2. If you record your tracks near the last bit possible, how might a digital mix buss then be an improved landscape for combining complex waveforms, i.e. mixing, of drums, percussion and all musical sources at once over analog? Compare digital combining to simply sending out instruments on an individual channels and mixing in analog where possible 'good sounding musical harmonics' are generated?

3. When your individually recorded multi-channel digital audio is reproducing itself at unity gain at the IO's output, are these levels in the analog devices of the IOs causing more problems in general to clarity due to slewing or lack of headroom? For instance MOTU has no facility to reduce it's OP levels in their IO's other than digitally reducing the level in the DAW. How may IO manufacturers have audio trims to solve this issue and have manufacturers really taken into consideration these higher OP levels for clean reproduction of sound?

Thanks

Gary Brandt
Producer/Engineer

[Bob Olhsson]

Every single one of these things is entirely a question of the implementation of specific equipment and software. While most people in music would love a simple formula for achieving high quality sound, the unpleasant reality is that there isn't any.

The closest thing I've found to a simple formula is investing in the very highest quality monitoring and D to A conversion you can put together. Only then does it become obvious how irrelevant most popular generalizations are to achieving truly great sounding audio.

[sdevino]

Timeline wrote on Sun, 26 December 2004 13:10

1. Would mixing multiple track transient sources not be a reason to seek out systems with higher sample and or bit rates?   In-other-words, do complex waveforms actually require higher bandwidths to be properly reproduced compared to an individual track?

The complexity of the transients does not effect required sample rate. ALl the transient information that makes up a 20 kHz bandwidth signal are within that 20kHz band. Transients that occur "between the sample points" represent frequency content that is higher than accepted audio frequencies.

So you have to settle the argument regarding audio bandwidth requirements before you can answer this question completely.

Steve

[ammitsboel]

Bob Olhsson wrote on Sun, 26 December 2004 18:32

The closest thing I've found to a simple formula is investing in the very highest quality monitoring and D to A conversion you can put together. Only then does it become obvious how irrelevant most popular generalizations are to achieving truly great sounding audio.

That was nicely put!

Best Regards,

[bobkatz]

Timeline wrote on Sun, 26 December 2004 13:10

1. Would mixing multiple track transient sources not be a reason to seek out systems with higher sample and or bit rates?   In-other-words, do complex waveforms actually require higher bandwidths to be properly reproduced compared to an individual track?

If all you are doing is mixing, it's not possible to create INTERSAMPLE peaks (additional peaks between the samples, or "higher bandwidth"). The material was prefiltered to the Nyquist rate when it was recorded, and you'll create nothing new there.

When the mixed material, which may include some equalization, for example, feeds the outside world, like a DAC, it's a good idea to use an oversampled peak meter, or, drop your levels to -3 dBFS measured on a simple, ordinary peak meter. Within the DAC, or any SRC, for that matter, the oversampling process, and filtering inside the DAC, can produce intersample peaks that are higher than what a simple digital meter reveals. But note: You do not have to worry about this "creation of extra bandwidth" UNTIL you SRC or until you feed a DAC.

What about processsing? Filters in your chain can produce higher output levels than their inputs (but not intersample peaks, so no worries there as long as you remain in the digital domain and your digital meter does not show an over).

However, non-linear processors like compressors can create serious distortion if left within "single" sample rate. So, if you're going to be compressing digitally, it's a good idea to think about using "double" sample rate to begin with! Some compressors internally double sample and then internally sample back down. If this is handled well (and it's a BIG CPU HOG!) then conceivably you can process and mix at the single sample rate (44 or 48); your mileage may vary depending on the quality of the digital compressor.

Quote:

2. If you record your tracks near the last bit possible, how might a digital mix buss then be an improved landscape for combining complex waveforms, i.e. mixing, of drums, percussion and all musical sources at once over analog? Compare digital combining to simply sending out instruments on an individual channels and mixing in analog where possible 'good sounding musical harmonics' are generated?

It's a tradeoff. Just make sure you're not fooling yourself because of level differences or anything else. Make tests at matched gain and decide for yourself. You're entering the world of noise, buzz, hum, hiss, distortion, and transparency loss. As well as (conceivably) perceived gain due to the quality of the distortion that is added, or the "softening" of the sound due to the loss of transparency. It's up to you to decide if the TOTAL "cure" sounds better than the "TOTAL" disease. Not every analog console you can dream up is a sonic winner in this regard, and it really pays to use superior converters with superior clocking as well, if you are going to be mixing analog.

I have a client who mixes through an SSL G or E, and he doesn't fool himself that there isn't a loss. In fact, for jazz music, there isn't much desirable "character" in the SSL that he or I can hear. He also bypasses the entire center section, which helps a lot. However, he loves the SSL automation, and as I said above, there are lots of advantages of using good ol' fashioned analog compressors once you've absorbed the hit of that first D/A conversion. (Perhaps this is a justification for compressing  in the analog domain while tracking, but that's another subject---I don't think you can hit on the nose how much compression you need while you are tracking not in the context of mixing)

Quote:

3. When your individually recorded multi-channel digital audio is reproducing itself at unity gain at the IO's output, are these levels in the analog devices of the IOs causing more problems in general to clarity due to slewing or lack of headroom? For instance MOTU has no facility to reduce it's OP levels in their IO's other than digitally reducing the level in the DAW. How may IO manufacturers have audio trims to solve this issue and have manufacturers really taken into consideration these higher OP levels for clean reproduction of sound?

I think you are hitting a few nails on the head here. Internal headroom in converters is often not well taken care of. That's why I recommended -3 dBFS peak maximum when converting, unless you have a well-designed converter.

HTH,

BK