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In this paper short-time homomorphic analysis and the harmonic representation of voiced speech are explored with the result of a mixed-phase homomorphic vocoder of somewhat higher quality than its minimum-phase counterpart. A theoretical framework is presented for unwrapped phase estimation from harmonic spectra through smoothing real and imaginary spectral components. The short-time harmonic model leads to pitch adaptive duration and alignment requirements on time-domain windowing. The underlying phase envelope is consequently preserved so that cepstral windowing can he applied. In addition, two alternative vocoders with mixed-phase are considered: the first is based on linear interpolation of complex harmonic peaks, and the second on Lim's spectral root deconvolution scheme.