This article introduces a mathematical approach to extracting some statistical parameters from noise-like sounds. This approach could define a new spectral model or extend existing ones to analyze and synthesize such complex sounds. In the future, this method could also permit electro-acoustic composers to make musical transformations. We have performed several synthesis tests with synthetic and natural sounds using these parameters. The main assumptions is that analyzed sounds must not contain any transient or slow-varying deterministic component. The natural sounds resynthesized during our experiments sounds like the original ones even if some defects are perceptible because of the analysis limitations. We propose some initial solutions for future works.