MID-SIDE vs SUM-DIFFERENCE

[Scodiddly]

If you take a coincident-diaphragm LR stereo pair of cardioid microphones and sum them to mono, you end up with the same signal you'd get with a single cardioid microphone pointed straight - so that's how Mid = L + R works.

Not exactly, wouldn't the combined coincident pair give you a wider pickup pattern that the single cardoid mic (assuming all the "cardiod" patterns are the same)? Unless the two were both pointed straight ahead of course.

Nope - where the pickup patterns overlap you get extra gain from the summing. When you add everything up and then remove a few dB to compensate for the extra gain, you end up with the same width cardioid pattern. I wrassled with this concept a lot trying to figure out if I could use M/S processing to produce a variable-width mic in live sound with a mono PA. Short answer, no.

[Scodiddly]

This article on the UA website promulgates the above-described misunderstanding, by stating that Mid=(L+R)/2. (L+R)/2 is actually the SUM, and still contains all the stereo info, albeit combined into mono.

http://www.uaudio.com/webzine/2007/june/index7.html

It's not M = (L+R)/2, it's "M = L+R/2". In the formula, then, Mid and the Sides are 1/2 the original stereo signal volume. (IOW, "(M = L+R)/2".)

I think that "L+R/2" is not to be taken, necessarily, as math, like you are adding popsicle sticks.

None too sure about your equations there, especially "(M = L+R)/2" which is malformed. But with respect to "M = L + R/2", are you saying that the right channel should be reduced in gain compared to the left channel?

[jhharvest]

Part of my question remains unanswered - Do these processors, such as the DrMS plug-in and the Avenson Mid-Side box, go through extra "steps" to remove the information contained in the "side" signal from the "mid" signal (which I figure can be done with a few more stages of combining, panning, and polarity manipulation) or are they really SUM - DIFFERENCE processors?

You could test it.

Take a signal and pan it hard left, centre and hard right. You should see the following:
hard left: mid channel at a lower level, side channel positive phase.
centre: mid channel at normal level, side channel no signal.
hard right: mid channel at lower level, side channel negative phase.

This should tell you how your plugin works. If you get identical mid channel with all pannings then it's the same as if you had an MS mic setup with an omni mid mic. The actual level drop in the panned cases would depend on what kind of imaginary polar pattern is used.

[vvv]

None too sure about your equations there, especially "(M = L+R)/2" which is malformed. But with respect to "M = L + R/2", are you saying that the right channel should be reduced in gain compared to the left channel?

With "M = L + R/2", I am quoting the cited uaudio.com article.

And your difficulty with "my equations" there is, I think, exemplary of all of our difficulties with those.

That's because they are "equations by analogy", to the extent that they tell you "Mid" is the same as "L+R", and then remind you with the the "/2" that you need to halve the total volume to remain at the same volume of the original stereo track that the "L" and the "R" are derived from. (He also fails to distinguish between log and equal-power Sine panning.)

The issue is in the application of the "/2" which I argued is to both the "Mid" and the "L+R" part of the "equation", which "equation" is representative at best in that it speaks first of what "Mid" is, and then compares it (makes analogy to ) the aforesaid volume issue.

To quote the above-cited uaudio.com article, 'You might be wondering what the ?/2? means. It simply means ?divided by two,? because when you sum the left and right tracks, the result will be louder.'

jhharvest: That sounds cool, and if it bears out (I think it will), your analysis might be brilliant! I note that the test is what the OP wrote in his second post in this thread, altho' he skipped mentioning (and I was too stupid to fill in) the subsequent application of the M/S processing. (He also fails to distinguish between panning laws, ex., log and equal-power Sine panning, etc., when he speaks of "reinforcement".)

[Scodiddly]

With "M = L + R/2", I am quoting the cited uaudio.com article.

And your difficulty with "my equations" there is, I think, exemplary of all of our difficulties with those.

Actually I think that the linked article has the equations wrong!
L + R/2 means that the L signal is full strength, the R signal is half strength.
(L + R) / 2 means that the two signals are summed equally and then the sum divided by 2, which is what seems to be described in the text.
The usual rules of mathematical precedence are still in effect!

But that aside, we are dealing with math directly here and not allusions to math. Audio summing in a circuit is straightforward math, and you can build a fairly simple circuit to do that. Doing it with plugins does involve more steps, but you can still boil it down to the math involved.

[leigh]

But that aside, we are dealing with math directly here and not allusions to math.

Yes, I was going to point that out as well. These equations are not "math as metaphor" - they describe the exact process that an MS-Matrix is performing, whether in the analog or digital realm.

I put those equations right on the face of the MS encoder plug-in I made:
http://www.refusesoftware.com/products/feature/10

Part of my question remains unanswered - Do these processors, such as the DrMS plug-in and the Avenson Mid-Side box, go through extra "steps" to remove the information contained in the "side" signal from the "mid" signal (which I figure can be done with a few more stages of combining, panning, and polarity manipulation) or are they really SUM - DIFFERENCE processors?

No, they do not go through extra steps. They are really sum-difference processors.

I know what you mean that calling L + R = "Mid" is kinda bullshit, in an intuitive sense. By summing those signals, you didn't "get rid of" any side information. You did, I would note, reduce purely side information by about 6dB relative to purely centered information (since you halve the amplitude of both L and R when you add them together).

M = (L+R) / 2 = L/2 + R/2

But again, you didn't "eliminate" side information through that process.

To think of it another way, the process of stereo -> MS conversion is reversible, right? That is, you can convert stereo -> MS, apply processing (EQ, comp, whatever) to M and S separately, and then convert back MS -> stereo. And you know that L = (M+S) and that R = (M-S). You also know that Side is difference, i.e. S = (L-R)/2. So, the only way for all that math to work out, and have a reversible process, is to make M = (L+R)/2.

Leigh

PS: That equation in the Universal Audio is written incorrectly, as per the usual order of operations. That is just a formatting error, since they explain the process correctly in their following paragraph as "decrease them by 6 dB each" (emphasis mine).

[vvv]

My use of the phrase "math as metaphor" refers to the inaccurate formula presented at the uaudio.com site, (and some others here, probably including me); altho' I think I might be OK saying, "(Mid=L+R)/2" is more accurate, I stand by my statement that, as presented, the uaudio.com formula is an "equation by analogy" in that it assumes you know the significance of the "/2" as related to the volume of the original track - that is why I also said it is "representational".

(Mebbe I shoulda said "formula as metaphor", but that lacked the sexy alliteration. )

Again, I said earlier, and I hope I got this correct, an explanation of what is represented is,
"Level of Mid (Mid=L+R) = 2x original Stereo level".

That said, I have neither affinity nor affection for math or formulae, - "order of operations" = WTF? - and I love that I can learn this unpleasant (to me) but necessary stuff here!

[Scodiddly]

As Leigh pointed out, M = (L+R)/2 is the same as M = L/2 + R/2.

You could actually make an analogy out of that, if it helps.
M = (L+R)/2 would be described as "Sum L and R together, then pull the output fader down 6dB".
M = L/2 + R/2 would be described as "Sum L and R together, with each input fader down 6dB".

In both cases you're reducing by 6dB, it's just a matter of where you do it.

[groover]

Leigh, thank you for validating my analysis!

I am trying to create a matrix in PT to output a true mid-only signal, but so far my success is restricted to the theoretical realm. Not sure what I'm doing wrong here. But stubbornness is my primary asset, so I'll keep trying.

[Galen Ulrich Elfert]

Intuitively, think of this: You have only two speakers. Unless you have a third, central speaker, what you hear as being in the "middle" is "that which is coming out of both speakers at the same time". There is no separate stream of mid information.

[leigh]

Leigh, thank you for validating my analysis!

I am trying to create a matrix in PT to output a true mid-only signal, but so far my success is restricted to the theoretical realm. Not sure what I'm doing wrong here. But stubbornness is my primary asset, so I'll keep trying.

Stubbornness can be a good asset, but I don't think you'll find your way to a solution, because I don't think it can be done. Maybe it could be with some advanced Fourier transform processing (I haven't worked that out yet), but not with simple mixer matrices.

Earlier in this thread, this point was raised:

Once you've extracted the side-only information into a single mono track, it's a simple matter of subtracting that information from the mono L+R mix to leave you with the mid-only information.

Which seems intuitively right, but actually doesn't work. Do the math with the L's and the R's, and you'll see...

Leigh

[groover]

in response to G.U.E. - however there is a category of information that is present in both L+R channels equally, which can be considered a separate category from information that differs between the L+R channels. Admittedly this is a case of "fuzzy" lines and gradation between the two.

[Scodiddly]

in response to G.U.E. - however there is a category of information that is present in both L+R channels equally, which can be considered a separate category from information that differs between the L+R channels. Admittedly this is a case of "fuzzy" lines and gradation between the two.

The perfect microphone does not exist.

On the upside, that means that just using the processing to do tweaking on existing stereo signals can have greater effect than a microphone array would provide.

[vvv]

As Leigh pointed out, M = (L+R)/2 is the same as M = L/2 + R/2.

You could actually make an analogy out of that, if it helps.
M = (L+R)/2 would be described as "Sum L and R together, then pull the output fader down 6dB".
M = L/2 + R/2 would be described as "Sum L and R together, with each input fader down 6dB".

In both cases you're reducing by 6dB, it's just a matter of where you do it.

Aiight! I finally understand my mental block here, I think.

I was looking at "Mid" as being the result of the process of combining the tracks, period; I stopped short of including the volume adjustment, I know not why.

Well, it could have to do with my antipathy towards formulas and all things mathematical ...

Thanx for your patience!

[jhamburg]

Sadly my math is pretty rusty these days as I'd be able to explain this clearly when I was younger and smarter.

Both MS micing and sum-difference processing deal with what is known as correlation. There is a very specific mathematical definition of what it means for things to be correlated but here's an easy(ish) way to think of it.

We hear in "stereo" because we have two ears. When a sound reaches our ears the waves arrive at different times because of the different distances from the source to each ear. Our ears and skull are also shaped in a way which accentuates the ability of the brain to discern these different arrival times. Our brain uses the difference to determine the spatial location of sounds. This explains why it's much harder to tell where bass is coming from (the wavelengths are longer than the distance between our ears so there is no timing difference).

Stereo micing fakes this sort of response. When you record a spaced pair, all of the stereo information is contained in the "difference" between the two channels just as it is when it enters the two channels of your ears. The sameness between the two signals is called correlation.

Dual mono signals are 100% correlated because the are the same ! Flip the phase one one channel and you will here nothing.

A perfectly un-correlated stereo signal contains no common information between the channels. Imagine panning a bass hard left and a violin hard right. Flip the phase on one channel and you probably won't notice too much of a difference.

In mid-side recording, the mid mic is the part of the signal that is common to both mics (the mono part) The side mic is the part of the signal that is different between both mics (the stereo part). The MS matrix simply combines the info and distributes them to the two speakers.

A sum-difference processor simply takes a regular stereo signal and then splits the correlated parts (the mono, sum or mid) from the un-correlated parrs (the "stereo", difference or side). This can be done in the analog or digital domain.

ok, enough thinking for today

joel