Matlab function for calculating phase of complex number

Hello and good day to all,

Matlab has a built in function to calculate amplitude and phase of a complex number using abs(number) and angle(number) funstions. I have a question regarding phase part. Lets suppose we have a complex number in the form z=x+jy (x being your real and y your imaginary part). When you want to calculate the phase of this number the formula is phase=arctan(y/x). In addition to this formula we have to take care of sign's of real and imaginary part (especially real part)and correspondingly we add (+/-) pi to the calculated value. Does matlab "angle function" consider this thing because all examples I saw have only positive real parts. Thank you

Answer 1

[John D'Errico]

Actually, the formula is

atan2(y,x)

atan2 handles the problem properly, working in all 4 quadrants. If you don't believe me, just look in the angle function itself. There you will find only one line of code:

p = atan2(imag(h), real(h));

Yep.

angle(-1-0.5i)
ans =
       -2.67794504458899

[ehtisham asghar]

Thanks it saved alot of time for me

[John D'Errico]

A virtue of atan2 is it also always works even when x==0. atan works there too, at least it does in MATLAB.

I think just about every computer language seems to have an atan2 function, that takes the two arguments, instead of the ratio. That ratio screws things up, because it yields only a two quadrant solution. It can be repaired without TOO much effort. We have a simple identity:

atan2(y,x) == atan(y./x) + (x<0)*pi - (x<0 & y<0)*2*pi

That seems to work for all quadrants. I can probably write it more simply.

[Walter Roberson]

That would not work correctly for (0,0) because the 0/0 would give rise to NaN and atan(NaN) is NaN which would pollute the rest of the calculation.

[John D'Errico]

True. 0/0 will be a problem.