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1

I have thought about some points which could help find the answer: 1- I think there might be something related to $\operatorname{arctan}(x)$ which is continuous in $(-\pi/2 \ \ \pi/2 )$ but I am not sure how. 2- We almost always work with phase DIFFERENCE rather than the absolute phase itself. Phase difference could be both positive and negative. So, it ...


0

It has to do with the unit circle in the i vs Re plane - instead of going counterclockwise by 360 degrees, we could equivalently go +/- 180 degrees. In my experience with audio, this thought process allows one to minimize phase delay. For example, let's say I've got a L and R audio signal arriving at some listening point in space, where (arbitrarily) the L ...


5

First, when you're talking angles, in DSP pretty much all angles are $\mod 2\pi$. So $2\pi \equiv 0$. Usually it's more convenient to keep angles on the interval $\left [-\pi, \pi \right )$, because we're usually most interested in angles around $0$. You don't have to do this, however -- if your problem at hand is easier to solve if your angle lies on $[-...


5

It is just a convention, but it is useful in some cases. For example, the phase of the DFT of a real discrete-time signal is odd only if the angles are expressed in the range $[-\pi, \pi)$. Sometimes you just have to adapt to the convention used by your tools -- for example, MATLAB functions like angle and atan2 return angles in $[-\pi, \pi)$. Note that the ...


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