Abstract: An new orthogonal decomposition method and implementation algorithm for speech signals is proposed in this paper.From the reproducing kernel function of Hilbert space W₂¹ a,b,a set of normalized orthogonal functions φ_j^*(x)₁ⁿ are generated.Based on φ_j^*(x)₁ⁿ,speech signals can be orthogonally decomposed,and the orthogonal decomposition coefficients can be computed by a fast algorithm based on the properties of reproducing kernel function.This method transforms the discrete problem to continuous function space and convert the inner product computation problem in Hilbert space into function evaluation problem in some discrete points.The experiment results indicate that it can be applied to the reconstruction and feature extraction of speech signals.