An efficient and precise method, which is called adaptive Fourier decomposition method, for decomposing given functions in Hardy spaces was proposed by Tao QIAN et al (2010). This typical method is based on the rational orthogonal system (Takenaka-Malmquist system) and can be considered as a variation of greedy algorithm. This thesis develops the above method to non-stationary speech signal synthesis, with modifying to ensure the effective numerical result. Finally, an experiment is proposed in this thesis with satisfying reconstruction. To prove the effectiveness of the new method, we also introduce the classic STFT (Short-Time Fourier Transform) synthesis method, and compare the results of the two methods. In Chapter 1, Section 1.1 introduces the classical description of signals and the general non-stationary signals. Section 1.2 shows why we have to develop a time-frequency representation of signals and has an overview of the former methods. In Chapter 2, a review of the classic STFT method is given in section 1, and to prepare for the final comparison, we introduce the discrete STFT and show a synthesis method named OLA based on STFT. In Chapter 3, the adaptive Fourier decomposition method is showed in details for the 𝐻2 (𝔻) case. Moreover, the corresponding algorithm is showed in section 2 as well. In Chapter 4, based on the results of numerical experiments, as well as a comparison with OLA method, the feasibility of the new method in synthesis is presented and some other conclusions are obt