  Degenerate pump-probe reflectivity experiments have been performed on a
single crystal of bismuth telluride (Bi$_2$Te$_3$) as a function of sample
temperature (3K to 296K) and pump intensity using $\sim$ 50 femtosecond laser
pulses with central photon energy of 1.57 eV. The time resolved reflectivity
data show two coherently generated totally symmetric A$_{1g}$ modes at 1.85 THz
and 3.6 THz at 296K which blue shift to 1.9 THz and 4.02 THz, respectively at
3K. At high photoexcited carrier density of $\sim$ 1.7 $\times$
10$^{21}$cm$^{-3}$, the phonon mode at 4.02 THz is two orders of magnitude
higher positively chirped (i.e the phonon time period decreases with increasing
delay time between the pump and the probe pulses) than the lower frequency mode
at 1.9 THz. The chirp parameter, $\beta$ is shown to be inversely varying with
temperature. The time evolution of these modes is studied using continuous
wavelet transform of the time-resolved reflectivity data.
