Spectral analysis of vowels and musical sounds by means of the fast Walsh transform
M. Yunik, Boyan Boyanov, Raymond MacDonald, Budi Rahardjo · 2003
Using the fact that short segments of voiced speech and musical sounds are periodic, it is shown that the Walsh transform can be used to analyze the harmonic structure of these signals. A procedure for spectral analysis is proposed which consists of: high-precision pitch detection; finding the separate pitch periods; separation of segments where the signal is periodic; and realization of spectral analysis over these segments by means of a modified fast Walsh transform (FWT) algorithm allowing computation of only half of the coefficients. The Walsh and Fourier spectra of vowels and tones from a violin were analyzed. It was found that the harmonics in Walsh spectra are similar to those in the Fourier spectra, although several additional peaks, not correlated with the harmonic structure, are present. This phenomenon is theoretically explained by the differences in the Walsh and Fourier transformation matrices.>