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—y'
—x'
—cos(2nAvt)
— l.l sin(2nAvt)
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:
real FID = Mx(1) +My(2) —Mx(3) —My(4) = 4.2 sin(2nAvt) imaginary FID = My(1) —Mx(2) —My (3) +Mx(4) =— 4.2 cos(2nAvt)
Now the two parts of the FID are perfectly balanced, regardless of the matching of gain of the two receiver channels. This technique is an example of phase cycling, a general way of eliminating artifacts by subtraction in the sumtomemory as a number of scans are acquired.
The trick of directing the Mx and My components of net magnetization to different data tables in the sumtomemory (real and imaginary sums) is a way of changing the reference phase (also called the receiver phase or the observe phase). If we just add Mx to the real sum and My to the imaginary sum in the sumtomemory, we say that the receiver phase is —/, and magnetization that starts on the y' axis will give rise to a positive absorptive peak in the spectrum. If instead we subtract Mx from the real sum and subtract My from the imaginary sum (as in scan 3 above), we say that the receiver phase is +/, and magnetization that starts on the +/ axis will give rise to a positive absorptive peak. But we can also "swap" the channels: If we add My to the real sum and subtract Mx from the imaginary sum (as in scan 2 above), we say that the receiver phase is +X, and net magnetization that starts on the +X axis will give a positive absorptive peak. Finally, if we subtract My from the real sum and add Mx to the imaginary sum (as in scan 4 above), we have receiver phase —x', and magnetization that starts on —x! will give a positive absorptive peak. Thus, another way of describing the phase cycle above is
Scan No. 
l 

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