The frequency shift method multiplies the vibration signal with a reference sine wave to shift a signal of interest down to a DC signal. For example, assume the that signal of interest is f(t) = A * cos(w *t) and we have a reference signal r(t) = cos(w *t). Then using basic trig identities (or complex math) we have f(t) * r(t) = (A/2) + (A/2)cos(2 w t). Now, if we apply a low pass filter, we get rid of the 2*w component and leave only the DC component. This method is shown schematically in figure 35
This method has the advantage that it is relatively easy to do in real time. So-called ``lock-in amplifiers'' use this method for real-time tracking. A disadvantage is that only one frequency is available. For example, if you wanted both a signal and it's second harmonic, you need to do the calculation twice. With some of the other methods, higher harmonics are available ``for free''.
