Real and imaginary FIDs

Now we can construct a perfectly balanced real and imaginary FID from these signals by combining all the sine functions into a real FID and all the cosine functions into an imaginary FID ... 

Where X and Y are the real and imaginary FIDs coming out of the ADC. Thus, we can speak of the receiver phase as the point of view from which we view the FID signal in the rotating frame of reference. If the receiver phase is shifted by 90° (from x to y axis), we mean that the real channel has been shifted counterclockwise by 90° from the x axis to the y axis, and the imaginary channel has been shifted counterclockwise by 90° from the y axis to the -x axis. With this 90° shift, for example, a coherence of Iv would be observed as Ix, and in a four-scan phase cycle with Ar = 90°, we would observe a four-scan sequence of coherences lx, y, —Ix, —Iy as 4IX in the sum-to-memory. To keep track of these phase shifts, a shorthand notation is often used where 0 stands for a 0° phase shift (real part of receiver on the x axis), 1 stands for a 90° phase shift (receiver on the y axis), 2 stands for a 180° phase shift (receiver on the —x axis), and 3 stands for a 270° phase shift (receiver on the —y axis). In this notation, the four-scan receiver phase cycle with A
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