GoldWave Inc.

In Removing vocals, it is observed that if reverse difference signal is available, we can recover both right channel and left channel signals. In addition, if both difference and reverse difference signals are available, we can recover vocals by simply mixing these two signals (Diff+ Rev Diff).

It follows that if we made available all three equivalent signals(sum, difference, and reverse difference), then we can always recover their original signals(left, right, and vocal). But if we left out reverse difference signal, then we can only recover one( say,left) channel signal, the other (say, right ) channel signal and vocal will be lost.

Sounds good in theory, but it doesn't work that way. No combination of simple addition or subtraction using the left and right channels will yield the vocals. There is no reverse difference, only a negative difference. More complex processing is required to extract the vocals.

Chris

Chris, can you tell me what kind of signals are available for recovering vocals? I'm not familiar with current recovering technology. Can we assume sum and difference are available? What do you mean by negative difference? Can we assume it is also available? Where can we get some references on this subject? Is it in the GoldWave manual, for example?

Can anyone explain the past attempts to manipulate the L+R, L-R, Left-only, or Right-only signals to remove or extract signals. Their assumptions, successs, failure and conclusion.

Using basic math you end up with 2 equations and 3 unknowns. All you are given is the left channel, L and the right channel, R. The left channel contains the left music, ML plus the vocals, V. The right channel contains the right music, MR plus the vocals, V.

You have two equations:
L =ML + V
R = MR + V

ML, MR, and V are the three unknowns.

By subtracting the two equations, you can cancel out V, but you end up with mono audio:
L - R = ML + V - (MR + V) = ML - MR

By adding the equations, you can double the vocals, V, relative to the music:
L +R = ML + V + MR + V = ML + MR + 2V

There is no way to solve for V using these equations. The fact that a solution does exist appears to defy conventional math, but none of the above equations factor in time and frequency.

Chris

How about if we introduce the third equation: RD=MR-ML+V by assuming RD is available which can be generated when we add the vocal
We now have 3 equations with 3 unkowns
Sum(S) L+R = ML + MR + 2V
Difference(D) L-R= ML-MR
Reverse Diff (RD) RD= MR-ML+V

The availability of RD will guarantee the solution exists and is unique.

The solution is then given by
V=D+RD
ML=(S+D)/2-V=(S-D)/2-RD
MR=(S-D)/2-V=(S-3D)/2-RD

Not only we recover vocals, we also successfully recover the original left and right channel music.

The problem is that RD is not available and cannot be calculated from L and R, which are the only known values.

Chris

If you are a song creator and when you add vocals, you can certainly generate RD when you generate L and R signals knowing that it is an absolutely essential piece of info. In other word, you don't calculate RD from L and R, you generate all three.

The point I try to make is this: when you add vocal, it is changing the signal contents from 2 signals to 3 signals. So to make the process revesible,you can't just keep only 2 signals R and L . You'll need another auxiliary signal RD.

Mathematically, the set{ ML,MR,V}, {L,R, RD} ,or {Sum, Diff,RD} are all equivalent. So knowing one set implies knowing the other and vice versa.

If you are a song creator and have the vocals, V, then none of this is necessary. There is no need to generate RD when you can just keep a copy of V. The point is that you cannot generate RD unless you have V. If you already have V, then you have everything you need.

Chris

The problem is not due to song creators but lack of info by the end users or whoever needs to process the signals. The song creators may have complete knowledge of V but the end users don't. Why can't they pass that piece of info to the end users whether explicitly( in terms of V) or implicitly (in terms of RD)?

It seems to me that the recovering will not be an issue if the person who holds key info is willing to help!

It seems to me that the recovering will not be an issue if the person who holds key info is willing to help!

I’m sure Madonna would be happy to email you a vocal-only track from her latest CD.

Look. The artists don’t want you messin’ with their work! They don’t want us copying their music, much less copying and altering it. “Look, I removed your vocals. Isn’t that cool… I replaced them with my voice.”

There was a court case (here in the USA) recently about censoring DVDs. The movie studios won the case by arguing that the censoring company did not have the right to alter their creative content. (You could send a DVD to the company, and they would make you a censored copy and drill a hole in the original DVD to so that there was not unauthorized “extra” copy made.) I was shocked by that court ruling.

It seems if they had their way, they would take away our bass & treble controls, and the color adjustments on the TV. They would probably even take away the volume control!!! “It needs to be at a certain volume to get the correct effect desired by the director”

Thanks, DougDbug, for your great insight!

I never thought about copyright issue has played such an impotant role until you pointed out!