.We measured the hydrostatic pressure dependence of the birefringence and birefringent dispersion of a Sagnac interferometric sensor incorporating a length of highly birefringent photonic crystal fiber using Fourier analysis. Sensitivity of both the phase and chirp spectra to hydrostatic pressure is demonstrated. Using this analysis, phase-based measurements showed a good linearity with an effective sensitivity of $9.45\mathrm{nm}/\mathrm{MPa}$ and an accuracy of $\pm 7.8\mathrm{kPa}$ using wavelength-encoded data and an effective sensitivity of $-55.7{\mathrm{cm}}^{-1}/\mathrm{MPa}$ and an accuracy of $\pm 4.4\mathrm{kPa}$ using wavenumber-encoded data. Chirp-based measurements, though nonlinear in response, showed an improvement in accuracy at certain pressure ranges with an accuracy of $\pm 5.5\mathrm{kPa}$ for the full range of measured pressures using wavelength-encoded data and dropping to within $\pm 2.5\mathrm{kPa}$ in the range of 0.17 to $0.4\mathrm{MPa}$ using wavenumber-encoded data. Improvements of the accuracy demonstrated the usefulness of implementing chirp-based analysis for sensing purposes.