The aim of the presented work was twofold: 1) To study whether the effect of the stochastic part of the glottal waveform can be replaced by a postprocessing of the synthesized signal when a mathematical excitation source is used and 2) To find a new way of representing the excitation signal for high quality synthesized speech with the properties of mathematical models which permits avoiding the problems related to prosody control by overlap add methods as used in PSOLA[1].