We propose a four-parameter adaptive signal decomposition method and related adaptive time-frequency distribution, which is positive, cross-term interference-free energy distribution and yields better time and frequency resolution. The elementary functions are dilations, translations,rotations and modulations of single Gaussian window function, which are obtained by successively matching the signal local natures. So the coefficients and parameters, obtained from the decomposition process, can provide an interpretation of signal structure and can be used for the analysis and synthesis of signals.