The Orthogonal Decomposition Algorithm for Speech Signals in Reproducing Kernel Space

An orthogonal decomposition method and implementation algorithm for speech signal processing are proposed in this paper. In the reproducing kernel function of Hilbert space ] , [ 1 2 b a W , a set of normalized orthogonal function system n j x 1 * )} ( {φ is generated, and speech signals can be orthogonally decomposed in ] , [ 1 2 b a W according to the basis n j x 1 * )} ( {φ , the orthogonal decomposition coefficients can be computed by a fast algorithm based on the properties of reproducing kernel function. This approach mapped the speech signals represented by discrete samples to continuous functions which is different from the canonical form represented by series of triangle functions, and the inner product computation in Hilbert space was transformed into function evaluation problem only at some discrete points.