Femtosecond time-resolved signals often display oscillations arising from the nuclear and electronic wave packet motions. Fourier power spectrum is generally used to retrieve the frequency spectrum. We have shown by numerical simulations and coherent phonon spectrum of single walled carbon nanotubes (SWCNT) that the Fourier power spectrum may not be appropriate to obtain the spectrum, when the peaks overlap with varying phases. Linear prediction singular value decomposition (LPSVD) can be a good alternative for this case. We present a robust way to perform LPSVD analysis and demonstrate the method for the chirality assignment of SWCNT through the time-domain coherent phonon spectroscopy.