Reconstruction of missing formants based on spectral power series expansion

In this paper, we investigated spectrum estimation for vowels using power series expansion. In general, sound signals can not keep their characteristics when the spectral peaks and dips are missing. Consequently, the missing spectral peaks and dips are estimated by using power series expansion. First, vowels are divided into cycle by cycle. Second, the one-cycle vowels are converted into frequency by FFT. Third, damaged spectra were made for demonstrating spectrum estimation. Fourth, we estimated missing spectral peaks and dips using power series expansion. In our spectrum estimation, the differential coefficients for power series expansion were calculated from nearby spectrum of missing spectrum. In this experiment, the estimated spectrum was almost the same compared with the original spectrum in the case of approximation by power series expansion on the rank of 6. The spectrum is restored about the range of 180 Hz using nearby 10-Hz samples. Consequently, power series expansion can estimate spectral peaks and dips for recovering spectrum.