Digital pulse position modulation (PPM) has been shown to be attractive for implementation over the optical fibre channel when the laser transmitters are average power limited and the channel bandwidth is abundant. The synchronization requirements for optical fibre PPM however have not yet been addressed. We present an original mathematical formulation for the problem of spectral prediction and synchronization in PPM based on the cyclostationary properties of the format. Further we predict the conditions required to achieve and optimize both slot and frame synchronization. The major system parameters including the modulation index, data probability distribution and pulse shape are catered for and used in the analysis. A novel technique, capable of coping with the different PPM word sizes, is presented and used to achieve frame phase extraction directly from the PPM stream. Appropriate mathematical models are developed and used to predict the spectral properties at the output of the frame phase synchronizer. Original practical results measured on a PPM system are presented and shown to agree with the theoretical models and predictions to within 1 dB.>