NumPy's Unwrap function __ function

This function is used to handle the phase angle recently, so here is a little space to record my understanding.

What is the unwrap function used for? It is used to solve the wound.

As for what is winding, the online statement is:

To calculate a system phase-frequency characteristics, it is necessary to use the inverse tangent function, the computer in the inverse tangent function, in the one or two quadrant angle is 0~PI, the three or four quadrant angle is 0~-pi.
If an angle from 0 to 2pi, but the actual result is 0~pi, and then by the-pi~0, in the w=pi of the jump, jump amplitude of 2pi, which is called phase winding.

As shown in the figure above, if the phase angle from the -0.99PI, counterclockwise rotation, through the negative axis of the x-axis, to reach the third phase, then by definition, at this point its angle will be directly from Pi to-pi, there will be a 2pi jump, so, if the rotation angle is drawn into the image, In fact, the image is discontinuous and, in order to correct the jump, there is a unwrap.

What the hell did unwrap do? It only detects adjacent two values A and B, and if ABS (A-b) > tol, then revise B to eliminate this sudden jump by adding or reducing 2pi to B, where Tol is actually a parameter to the unwrap function, The default is pi.

As an example:

OUT[196]: A = Np.array ([3.13, -3.12, 3.12, 3.13, -3.11]) in
[197]: A
out[197]: Array ([3.13, -3.12,  3.12,  3.13, -3.11]) in
[198]: Np.unwrap (a)
out[198]: Array ([3.13      ,  3.16318531,  3.12      ,  3.13      ,  3.17318531])

The code above, when the angle from 3.13 to 3.12, 3.13 + 3.12 > Pi, so to 3.12 to add a 2pi correction, changed to 3.16318531, then compare 3.16318531 and 3.12, do not fix, Continue to compare 3.12 and-3.11, add a 2pi to 3.11, change to 3.17318531, and complete the correction.

The only thing you need to pay special attention to with this function is not to use this function indiscriminately .
I didn't know the market before, often with a column of no rules can be said to do the winding, similar to:

IN[207]: Phase = Np.array ([2.67, -0.92, -1.37, -0.58, 0, 0,78, -2.94])
in[208]: np.unwrap (phase)
out[208]: 
Array ([2.67      ,  5.36318531,  4.91318531,  5.70318531,  6.28318531, 6.28318531,  8.88496162,  9.62637061])

See no, the above result is not very surprising, what ghost, incredibly appeared more than PI angle.

This is because, unwrap actually contains a premise (see from the operating mechanism also), these angles have time series. For the sequence [A,b,c], the object must first be a angle, then the b angle, and then the C angle.

Above, from the 2.67->-0.92, 0.92 plus a 2pi to make corrections, get 5.36 ..., 5.36 ... Compare with-1.37, 1.37 becomes 4.91 ..., 4.91 ... Compare with-0.58, 0.58 becomes 5.70 ..., 5.70 ... Compared with 0, 0 directly adds a 2pi to 6.28 ...,......

Overall, unwrap B is corrected by comparing the adjacent A and B, taking into account A's value.

So try not to use unwrap to the random angle of correction, meaningless.