In this study, the recent developments in the theory of linear time-frequency localization techniques are reviewed, and their applications to the analysis and synthesis of transient vibrations are investigated. Particular attention is given to the wavelet transform, wavelet frames and multiresolution concepts. The introduction of the basic wavelet theory and the related algorithms are followed by physical applications. In the first part, the continuous wavelet transform is employed as an analysis tool to study the propagation of transient structural and acoustic waves that are induced by impulsive forces. The time-scale representations generated by the wavelet transform are utilized to track the spectral evolutions of the transient wave interferences, and also to identify the characteristic signatures of the sources and the dispersive properties of the propagator. In the second part, the wavelet frame expansions and multiresolution concepts are utilized to construct the transient vibration response of a wide-band system. The forcing function is decomposed into multiresolution bands and convolved with the corresponding wavelet response functions. Then, the outputs generated at different resolution levels are combined together to form the system response. The examples demonstrate the effectiveness of the self-adjusting (zooming) window structure of the wavelet transform during both the analysis and synthesis of wide-band transient vibration responses.