The aim of this research was to develop an improved analysis and synthesis model for utilization in speech synthesis. Conventionally, linear prediction has been used in speech synthesis but is restricted by the requirement of an all-pole, minimum phase model. Here, cepstral homomorphic deconvolution techniques were used to approach the problem, since there are fewer constraints on the model and some evidence in the literature that shows that cepstral homomorphic deconvolution can give improved performance. Specifically the spectral root cepstrum was developed in an attempt to separate the magnitude and phase spectra. Analysis and synthesis filters were developed on these two data streams independently in an attempt to improve the process. It is shown that independent analysis of the magnitude and phase spectra is preferable to a combined analysis, and so the concept of a phase cepstrum is introduced, and a number of different phase cepstra are defined. Although extremely difficult for many types of signals, phase analysis via a root cepstrum and the Hartley phase cepstrum give encouraging results for a wide range of both minimum and maximum phase signals. Overall, this research has shown that improved synthesis can be achieved with these techniques.