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Speech contains important information in the nonstationary transitions between sounds. The Wigner-Ville distribution (WVD) allows a time-frequency representation of these transients, which convey acoustic cues or information about the sound identity, place of articulation, and speech anomalies. Speech has a complex spectral structure, which requires a careful choice of WVD analysis and time smoothing windows to attenuate spectral interferences. The smoothed WVD (SWVD) analysis of synthetic and real continuous speech transitions accurately shows the formant dynamics, glottal excitation, and energy variations. A simple classification experiment based on nasal consonant to front vowel transition SWVD spectra is presented.