# Mathematically what does phase reverse do on a signal?

In a stereo sound, phase reverse one channel and add it to another channel, we will cancel out those centered components.

Mathematically what does phase reverse do on a signal? Can you explain that in terms of Fourier transformation?

Does "Effects->Inverse" in Audacity mean phase reverse?

In the simplest case, Fourier analysis probably won't help understand this. You can think of it arithmetically. (L - R) subtracts the right channel from the left channel, so as you noted, those parts they have in common -- those that are correlated -- will cancel. The amount of correlation determines the amount of cancellation.

Now, if you want a much deeper analysis, check out the Wikipedia article on autocorrelation. You'll find examples of using the FFT there.

A recording of a sound wave is a pattern of samples. Those samples have positive and negative values, which correspond to the compression and rarefaction of the source sound.

As I understand it, "reversing the phase" means inverting these. Each sample is its same magnitude, but if it was positive it is now negative, and vice versa.

This is why reversing one channel of a stereo sound causes cancellation - there's generally a lot of overlap between the two channels, so the negation of one causes them to appear canceled when heard together.

It's worth mentioning that in most stereo recordings, the two channels aren't exactly the same, so it's not 100% cancellation. But there's usually a fair bit in common.

• This is true, which is why technically it should be called a polarity reversal, since phase is really a temporal difference, not a positive to negative switch. But common usage of "phase reversal" is too strong a force to for the purists like me to overcome. – Todd Wilcox Jun 29 '15 at 19:44
• Is phase reversal on a signal simply to put a negative sign in front of the signal? – Tim Jun 29 '15 at 19:46
• No. Assuming a digital signal, every sample must be multiplied by "-1". This results in positive sample become negative and negative samples become positive. – Bit Depth Jun 30 '15 at 8:47
• @BitDepth Isn't "put a negative sign in front" just non-math speak for "multiply by -1"? Based on that interpretation, I'd say the answer to Tim's question here is "Yes". – Todd Wilcox Jun 30 '15 at 11:51
• No. Putting a minus sign in front of the samples only changes them to all negative. You need to change the sign: if sign + then change to - and if - change to +. He did ask for the mathematical operation. – Bit Depth Jun 30 '15 at 12:19