In order to determine the angle of a shaft actuated by a hydraulic or electro-mechanical device, resolvers with windings mechanically coupled to the shaft of interest are commonly used. A resolver winding drive circuit provides an alternating current (AC) carrier as excitation for the resolver's primary winding on the shaft which stimulates a voltage in the resolver's fixed secondary windings. Usually, a resolver designed for precise shaft angle measurements has, at least, two secondary windings. One of the windings represents the sine function of the carrier's amplitude, the other represents the cosine function of the amplitude. It is preferred to consolidate the circuitry that receives and demodulates signals from the resolver output windings with the circuitry that interprets the amplitudes so that the circuitry can be used for a number of different resolvers. In order to accurately determine the angle of the shaft, it is necessary to amplitude demodulate each signal and compare the phase of the output winding signals with the phase of the drive signal to determine the polarity of their amplitudes. In many resolvers, this has been done by using special compensation windings which require complex supporting circuitry to precisely monitor or maintain the phase relationships. In resolvers that are not equipped with compensation windings, the resolver driver's phase is usually precisely monitored. One problem often faced in demodulating the resolver output winding signals is that they are contaminated with noise or transients that are either self-generated or coupled with other electrical devices such as motors and high-speed digital equipment. Filters are required to eliminate as much noise as possible and these filters have an undesirably long settling time. The settling time is particularly important if a number of different shafts are coupled to a single resolver circuit through a multiplexer because it increases the amount of time required to determine the angle of each shaft. The filters often require a large number of expensive high precision passive components.