Apparatus 200 for extracting a variable from two quadrature signals which are functions of the variable is disclosed and claimed. The apparatus is particularly suitable for use with a minimum configuration open-loop fiber optic gyroscope 100 to provide a signal (V.sub.out) proportional to the Sagnac phase shift, which is proportional to the rotation rate .OMEGA. of fiber loop 20. The apparatus comprises a trigonometric transformation circuit 30, a dynamic control circuit 32, a feedback loop 33, an adder and a feedforward loop 32.1. The adder, in use, adding an output signal of the dynamic control circuit and a signal in the feedforward loop to provide the signal (V.sub.out), with improved dynamic response. The apparatus also comprises a reset circuit 34 for extending the angular range of the apparatus. An adaptive reset circuit for improving the dynamic range of the apparatus is also disclosed.