Frequency Encoding Reduces Signal
INCORRECT. The signal does fade away according to T2* decay, but this is not the result of applying the frequency encoding gradient.
INCORRECT. Magnetic field gradients never rotate magnetisation. (This is what oscillating magnetic fields do—RF pulses.)
The frequency encoding gradient dephases the signal (as well as encoding it)
CORRECT. You may have noticed that a signal oscillation (the echo) with frequency encoding is highly dampened compared to the echo (the "free induction decay") without frequency encoding. This is because the frequency encoding gradient, whilst doing the business of encoding our signal, is also causing dephasing of the net magnetisations of signals from within imaging voxels. As a result, the signal from each voxel in the slice decays away more quickly than it otherwise would. This process is unavoidable!
However, there is something we can do about it. By deliberately dephasing the signal before measuring it with the frequency encoding gradient switched on, we can make the echo rephase and then dephase during the measurement period. Overall, we'll get a better signal readout.
A rephasing gradient can also be added after the slice selection gradient to "undo" its dephasing effects. (In fact, the phase encoding gradient is the only gradient in which the phase changes caused are actually what we want.)
Deliberate dephasing in the opposite direction (-Gf) before the signal is recorded causes the first half of the frequency encoding gradient to rephase the signal in our favour. A rephasing gradient (-Gs) is also seen.
It may be helpful to remember that the three magnetic field gradients used in MRI (slice selection, frequency encoding and phase encoding) all do the same thing to spins in a patient; they simply change the Larmor frequency in the direction they are applied, for the duration for which they are applied. How we use each gradient is all to do with the timing of each gradient—simultaneously or after certain RF pulses, during signal measurement, et cetera.