Karhunen–Loeve method for data compression and speech synthesis

Abstract

The use of the Karhunen–Loeve (KL) method in speech data compression and synthesis using the Fourier-Bessel (FB) expansion coefficient of speech signal is described. Bessel functions seem to make a natural basis for speech signal decomposition. Sinusoidal functions are the eigenfunctions of vibrating strings. Bessel functions are the eigenfunctions of vibrating pipes. The vocal tract resembles an excited pipe rather than a vibrating string. Good quality intelligible speech signal can be reconstructed using only a small portion of the FB expansion coefficient. Further data compression is possible through KL transformation of the speech signal FB expansion coefficient for efficient speech coding and synthesis. The transformation is implemented by first forming a covariance matrix of the FB coefficients. Eigenvalues and eigenvectors of the covariance matrix are computed and ranked according to the eigenvalue magnitude. Speech signal is then reconstructed using only the feature corresponding to the larger magnitude eigenvalues of the covariance matrix.