Signal processing for low-finesse fiber-optic Fabry-Perot sensors based on white-light interferometry is investigated. The problem is demonstrated as analogous to the parameter estimation of a noisy, real, discrete harmonic of finite length. The Cramer-Rao bounds for the estimators are given, and three algorithms are evaluated and proven to approach the bounds. A long-standing problem with these types of sensors is the unpredictable jumps in the phase estimation. Emphasis is made on the property and mechanism of the "total phase" estimator in reducing the estimation error, and a varying phase term in the total phase is identified to be responsible for the unwanted demodulation jumps. The theories are verified by simulation and experiment. A solution to reducing the probability of jump is demonstrated. (C) 2013 Optical Society of America