Thermal properties and transport control are important for many applications, for example, low thermal conductivity is desirable for thermoelectrics. Knowledge of mode-wise phonon properties is crucial to identify dominant phonon modes for thermal transport and to design effective phonon barriers for thermal transport control. In this paper, we adopt time-domain (TD) and frequency-domain (FD) normal-mode analyses to investigate mode-wise phonon properties and to calculate phonon dispersion relations and phonon relaxation times in bismuth telluride. Our simulation results agree with the previously reported data obtained from ultrafast time-resolved measurements. By combining frequency-dependent anharmonic phonon group velocities and lifetimes, mode-wise thermal conductivities are predicted to reveal the contributions of heat carriers with different wavelengths and polarizations.