# Signal demodulation

In practice the signal deduced in the previous section is not visualised as it is, but instead the NMR or MRI instrument eliminates the frequency offset $\omega_0$ by demodulating the signal. It is done by multiplying the signal with harmonics of frequency that is close to the Larmor frequency . That is, . In this way a complex signal is created: the real part will be when the sign is multiplied with , and the imaginary part arises as the multiplication of the signal and .

The real part of the demodulated signal (often called as the "real channel") will be:

(1)

After the multiplication the part with frequency is removed with a lowpass filter, and the remaining low-frequency term forms the real channel of the signal.

(2)

The imaginary channel is quite similar. After the multiplication with and the lowpass filtering:

(3)

So the detected signal managed as complex is:

(4)