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In this paper, we present an extension of a novel continuous residual-based vocoder for statistical parametric speech synthesis. Previous work has shown the advantages of adding envelope modulated noise to the voiced excitation, but this has not been investigated yet in the context of continuous vocoders, i.e. of which all parameters are continuous. The noise component is often not accurately modeled in modern vocoders (e.g. STRAIGHT). For more natural sounding speech synthesis, four time-domain envelopes (Amplitude, Hilbert, Triangular and True) are investigated and enhanced, and then applied to the noise component of the excitation in our continuous vocoder. The performance evaluation is based on the study of time envelopes. In an objective experiment, we investigated the Phase Distortion Deviation of vocoded samples. A MUSHRA type subjective listening test was also conducted comparing natural and vocoded speech samples. Both experiments have shown that the proposed framework using Hilbert and True envelopes provides high-quality vocoding while outperforming the two other envelopes.