Interpreting the angle from the angle obtained by atan2 function

Hi, I have two signals(x,y) whose absolute phases i'm calculating by using the atan2 function.Then subtracting both i'm getting the relative phase between two signals.

Because the absolute phase is calculated by atan2,it's range is [-pi,pi]. Now the relative phasei got after subtracting the absolute phase, will its value still be in the range [-pi,pi] ? How do i convert this to [0,2pi] ?

My efforts:- On the final relative phase obtained by atan2.i'm doing this

if phase >= 0 then
phase = 360 - phase;
else
phase = abs(phase);
end

This is yielding good results & matching with the phase between signals x & y, except in the range from [0 to 10] & [350 to 360]

[Stephen23]

"will its value still be in the range [-pi,pi]"

Not necessarily: (-pi) - (+pi) is not in that range.

Answer 1

[Star Strider]

This has worked for me when I needed to use it:

D = load('Luffy matlab.mat');

Angles2pi = @(a) rem(2*pi+a, 2*pi);

X = D.X;
Y = D.Y;

X_2pi = Angles2pi(X);
Y_2pi = Angles2pi(Y);

If you want the angles in degrees, use the atan2d function instead, and then substitute this version of the conversion anonymous function:

Angles360 = @(a) rem(360+a, 360);

[Luffy]

Actually the method suggested above is same as the other two methods suggested in this question.

% Method 1
  abs(rad2deg(mod(phase1,2*pi) - mod(phase2,2*pi)))
% Method 2
  if rad2deg(phase1) >= 0
  phase1= 360 - rad2deg(phase1);
  else
  phase1= abs(rad2deg(phase1));
  end
Similarly do for phase2 & subtract

But all of these 3 methods have the same problem, if i'm giving initial phase difference as 1 & run the simulation for 1000 trials, i'm getting o/p as 357,359,1,5,8 etc... Why is it getting wrapped to 357,359 ?

And why are the other answers getting deleted ?

[Star Strider]

I’m not certain what the problem is.

Adding this to the end of my other code:

figure(1)
plot(X_2pi)
hold on
plot(Y_2pi)
plot(X_2pi-Y_2pi)
hold off
grid

seems to suggest that everything is as it should be.

People delete their Answers for many reasons. I delete mine if it seems obvious to me that they won’t be accepted, and I delete them if another answer is accepted and my answer isn’t voted.

[Luffy]

Before closing this thread, one final question. If signal 1 & 2 have a phase diff phi(which is in [0,2*pi] range). I do atan2d on 1 gives me X [in -180,180 range] I do atan2d on 2 gives me Y [in -180,180 range] So X - Y could be in the range [-2*pi,2*pi]. If I do this

    Angles360 = @(a) rem(360+a, 360);
    phase_diff_360 = Angles2pi(X-Y);

Will the phase_diff_360 be same as phi ?

[Star Strider]

My ‘Angles...’ functions don’t do radian-to-degree or degree-to-radian conversions, so this will not result in a degree result:

phase_diff_360 = Angles2pi(X-Y);

The result will be in radians if the angles are in radians.

Also, because rem and mod are nonlinear, these two are not equivalent:

Dif1 = Angles2pi(X) - Angles2pi(Y);
Dif2 = Angles2pi(X-Y);

The ‘Dif1’ assignment is mathematically correct for the angle differences. The ‘Dif2’ assignment is not correct. Again, the arguments would have to be in radian measure to use ‘Angles2p’ correctly.

Please only use radian arguments with ‘Angles2pi’, and only use degree arguments with ‘Angles360’. If you mix them, the results will be meaningless.