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A process of speech synthesis from diphones stored in a dictionary as waveforms, for text-to-speech conversion, comprises supplying a sequence of phoneme codes and respective prosodic information, and, for each phoneme, analyzing and synthesizing each phoneme, and then concatenating the synthesized phonemes. For each phoneme, two diphones are selected among the stored diphones and the presence of voicing is determined. For voiced phonemes, the respective waveforms of the two diphones constituting the phoneme are filtered by a window which is centered on a point of the selected waveform representative of the beginning of a pulse response of vocal cords to excitation thereof. The window has a width substantially equal to twice the greater of the original fundamental period and the fundamental synthesis period and has an amplitude progressively decreasing from the center of the window. The signals resulting from the filtering and obtained for each diphone are time shifted so as to be spaced apart by a time equal to the fundamental synthesis period. Synthesis is achieved by adding the displaced overlapping signals.