Speech is the primary means of communication between people. Speech synthesis, automatic generation of speech waveforms has been under development for several decades [1, 2]. Recent progress in speech synthesis has produced synthesizers with very high intelligibility but the sound quality and naturalness still remain a major problem. The goal of this work is to develop a new speech synthesis system, which is based mainly on the fractal dimension to create natural sounding speech. Our initial work in this area showed that by careful use of the fractal dimension together with the phase of the speech signal to ensure consistent intonation contours and natural-sounding speech synthesis was achievable with word level speech. In order to extend the flexibility of this framework, we focused on the filtering and compression of the phase to maintain and produce natural sounding speech.