Why can't I isolate center-panned audio using inverse phase cancelling?

Question

In Audacity, you can split a stereo song to mono and invert the phase to remove center-panned audio (usually vocals).

Can someone explain why inverting the result and adding the original (in mono) doesn't result in an isolated vocal track?

Answer 1

Yeah it would appear to work that way, but the math reveals something else:

You have two channels, Left and Right, and you invert one, that is flip the sign on one channel and mix* them: Left + (- Right), or simply: L - R.

What you are doing here is essentially isolating the side channel. What was equal in both channels is now removed. What is different stays.

Now pay attention to the "formula" L - R. It will leave the original phase orientation of L intact and flip that of R. If you were to reverse it (which is just as good), R - L, the R orientation would be intact and L flipped.

So, you ask why mixing the inversed side channel equally back into the stereo mix will not produce the isolated center material:

The inverse side channel is equal to - (L - R)

Then we calculate new left and right channels:

Left = L - (L - R), or simply R. Right = R - (L - R), or simply 2*R - L.

So that is really not an attractive result ;-) It does not get better if you already mixed* left and right into a mono file:

(L + R) - (L - R), or simply 2*R.

And if the side were not inversed:

(L + R) + (L - R), or simply 2*L.

(source)

---

The best you can do is to mix L and R equally to double the volume of the center material. That is what we normally call the mid channel.

Moreover you can try some other things on the main LR stereo track:

• Reduce the active frequencies of the side channel (use an RTA or listen and attenuate with and EQ)
• Or boost the frequences of the mid/center material.
• "remove noise" using the side channel as noise profile.

---

*for the sake of simplicity mixing means adding here, attenuation has been left out.