The objective of this work is to investigate new signal processing techniques for optical fiber sensors that utilize the phase information of the electromagnetic field. Research concentrated on Fourier transform spectroscopy as a means for capturing wavelength encoded information from the fiber sensor. Classical spectral analysis utilizing the Fourier transform as a mathematical foundation for relating a time or space signal to its frequency-domain representation was shown to be inadequate for mitigating the bias errors caused by harmonic distortions. A modified spectral estimation algorithm is presented to overcome some of the practical issues while maintaining the high spectral resolution characteristic of the classical technique. This research also showed that unlike in free-space propagation, an optical signal propagating through a fiber waveguide, even over short distances, can experience significant phase modulation noise. A number of chromatic distortion mechanisms including modal interference, mode coupling due to periodic perturbations such as microdeformation and macrobends, and mode field diameter variations are addressed. We treated these issues by employing both theoretical simulation and experimental data. Coupled-mode formalism based upon approximated field solutions is used in the theoretical analysis. An extensive error analysis was also performed to determine how waveguide and noise distortion affect the performance of the spectral estimation algorithm.