Abstract: The formulas of discrete S-transform are derived , and the time-varying amplitude spectrum and time varying energy spectrum based on S-transform are given. A new procedure is presented to generate an accelerograms whose elastic response spectrum is compatible with a target spectrum by using actual earthquake records as parents. The time-frequency characteristics of Northridge wave, El-centro wave, Kobe wave and an artificial wave are analyzed through numerical example. The time-frequency characteristic spectrum which reflects the centralized degree of energy of earthquake ground motion is extracted from the time varying energy spectrum. It is showed that the time-frequency characteristic spectrum is related linearly to the elastic acceleration response spectrum. Finally, the approximate transformation equation between the time-frequency characteristic spectrum and the elastic acceleration response spectrum is established.