A first study of speech processing via a novel mode decomposition based on the fourier sine spectrum and spectrogram

An approximate mode decomposition method based on the Fourier sine spectrum and spectrogram is purposed and applied to decompose a vocalization of "hello". It seems that the combination of modes involving one of these two modes can partially recover the voice quality whose original meaning can be recognized by an adult. If three and more than three modes are examined, most voice quality can be recovered. If a mode is considered as the mother mode and the other mode(s) are reconstructed by performing the frequency shift which preserves the original modulus variation with respect to time, the resulting combination may partially recover the voice. However, by considering the pitch as the mother mode, there is no effective two-mode-combinations but only one three-mode- combination, say the 0-12 case. By considering the 1^st or 2^nd harmonic as the mother mode, there are many effective combinations. Although results of the test are derived from a typical vocalization, it seems that the proposed mode decomposition and reconstruction are new tools to look into details of a complicated time series data string. A promising extension will be to shift a complicated data string to the human ear\´s frequency range as will be shown in an upcoming paper.