In this paper, we evaluated comprehensively the structure and operation of open-loop interferometric optical fiber gyroscopes (IFOG). To complete the previous works, a digital approach to derive the rotation angle in optical fiber gyroscopes is investigated theoretically. Results are simulated by the MATLAB software; therefore we could compare the results in simulated area with the values derived from theory. Also, feedback Erbium-doped fiber amplifier (EFDA) FOGs, called FE-FOG, is categorized in closed-loop IFOGs. The procedure of finding the Sagnac shift for open-loop and closed-loop IFOG have been studied and compared to one another. The signal processing in the open-loop IFOG was simulated using Matlab software and for the closed-loop IFOG by PSCAD. In the open-loop IFOG the analogue formulation of the IFOG in order to extract the phase shift is analyzed. A novel and promising method for derivation of Sagnac phase shift based on digital finite impulse response filtering is proposed. Based on our simulation results, the reliability and accuracy of the method is determined. In the closed-loop IFOG, the shift was derived through frequent use of Sagnac loop. The output signal is injected in the input again as feedback. The shift phase between clockwise and counterclockwise waves in each complete route, including primary and feedback route, is identified as Sagnac shift phase.