Abstract: Based on the principle of adaptive signal decomposition,a method of analyzing the speech signal's subtle time-frequency structure using Local cosine bases is proposed. Firstly, the algorithm of fast dynamic programming is used to decompose the signal into Local-cosine atoms which can cover the time-frequency pane accurately; then the Heisenberg boxes, from which the speech signal's effective time-freq-uency characters are extracted,can be obtained. In order to get more subtle time-frequency structures, the MP method is used to get WVD of these Local cosine bases,Simulation result has shown that the later method not only has higher time-frequency resolution,but also has the corresponding restriction effect on the cross-term interference in quadratic time-frequency representation.