Application of the linear prediction singular value decomposition method for studying the coherent phonon oscillations in single-walled carbon nanotubes

We report the analysis of coherent phonon oscillations of radial breathing modes (RBMs) in micelle-suspended CoMoCAT single-walled carbon nanotubes excited by the lowest E11 optical transition in the near-infrared from 1.23 to 1.71 eV. We compare two spectral analyses: fast Fourier transformation (FFT) and linear prediction singular value decomposition (LPSVD). In contrast to the FFT method, the LPSVD spectral analysis has the following advantages: excellent signal-to-noise ratio, no need for the data preprocessing, and a reliable table of frequencies, amplitudes, time constants and phases of each sinusoidal component in the signal. We also illustrate the full details of extracting a reliable set of sinusoidal signals to obtain resonance excitation profiles for coherent phonons. The LPSVD reveals the abundance of strong exciton-phonon coupling in cabon nanotubes with a 1-D structure.