Exact compression of waveform data

This thesis studies techniques for lossless compression of one dimensional waveform data. Linear predictive coding is investigated as a means of pre-processing the data in order to reduce waveform redundancy. Much of the previous work in computing linear predictors is based on the least-squares criterion where predictor coefficients are chosen to minimise the squared sum of resulting prediction errors. Observing that the distribution of prediction error data is well approximated by the Laplacian distribution it is expected that the least-absolute-deviations criterion will be more effective in modelling this data. In the context of compression the optimal predictor is one which minimised the entropy of the resulting prediction error distribution. The IRLS algorithm is used to compute predictors based on the least-entropy and least-absolute-deviations criteria. Results are presented to show that the least-squares criterion is in general not optimal and often performs poorly in the presence of outliers in the data. The least –absolute-deviations criterion is shown to be very close to optima in most cases. It is shown how the IRLS algorithm may also be used to compute predictors which minimise the entropy of quantized prediction errors in the context of lossy compression. […]