# How is zero order phase correction applied?

As I understand it "zero order phase" is like this:

Where $\theta$ is the phase between the two lines.

If I have two lines on a graph which are both exponentially decreasing sine waves (in my instance, real and imaginary data from an NMR experiment), and I want to apply a "zero order phase correction", what am I meant to do?

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I think the question is probably poorly phrased. This is the answer I was looking for (and consequently found!):

The signal from an NMR experiment is usually represented as a stream of complex numbers.

You can imagine a complex number like this:

where x is the real value and y is the imaginary value. This means that the magnitude of the number is $\sqrt{x^2 + y^2}$ and a phase is $\arctan{(y / x)}$.

In NMR, experimenters want the beginning of the return signal to be at maximum for the real part, and zero for the imaginary.

However the reading could start before the maximum, so to correct this the phase is changed and the magnitude kept the same.

To do this the new values for x and y are calculated thus:

$\ x = magnitude.cos \theta$
$\ y = magnitude.sin \theta$

Where $\theta$ is the new phase you want the data to have. This calculation is applied across all points in the signal.

This is known as adjusting the zero order phase.

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Normally when you get a NMR signal it is somehow phase distorted, means a mixture of dispersive and absorptive signals. With a zero order phase correction you (virtual) turn your detector such that you only get absortive ones. As your picture indicates you shift your signal such that you get a $\cos (\omega t)$. Try this!

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