This diagram shows the carrier signal and the modulation by a sine and cosine signal. The vertical line indicates sampling at signal maxima. Note the phase change in the sine signal at 0 and 180 degrees, and in the cosine signal at 90 and 270 degrees.
In the old days, it was common to excite the sin and cos windings with sinusoidal signals that were 90 degrees out of phase (sin and cos). Then when the shaft rotates, the rotor winding produces a fixed amplitude sine wave, whose phase shifts in proportion to the shaft angle. The control system must then resolve the phase angle of the rotor winding against a reference wave. This was a relatively easy thing to do with analog circuitry. The reference waveform could be the position command signal. The command signal to the actuator is then proportional to the phase error between the resolver rotor and the reference signal.
Switched-capacitor filters have a few disadvantages. They exhibit greater sensitivity to noise than their op-amp-based filter siblings, and they have low-amplitude clock-signal artifacts -- clock feedthrough -- on their outputs.