Transients in speech and other acoustic signals are usually irregular and very difficult to analyze because of their short and nondeterministic duration. Therefore the traditional Fourier analysis technique does not give satisfying results. The classical Gabor technique uses a Gaussian waveform window. However, it is not numerically stable and it has slow convergence. In order to do time-frequency analysis of acoustic signals, a window transform is proposed that is derived from a Gaussian using the Zak transform. The resulting window possesses good locality properties in both the time and frequency domains. The computational procedure, which based on the FFT algorithm, is robust and fast. It will be shown that transform yields accurate estimates of onset and offset times for periodic and aperiodic signals as well as for vowel centers and the ramp frequencies of formant transitions.