Signal Modeling with Filtered Discrete Fractional Noise Processes

In this paper, we study filtered versions of fractionally differenced Gaussian noise (fdGn) processes. Fractionally differenced Gaussian noise is a discrete time equivalent of fractional Brownian motion. Filtered versions of such processes are ideally suited for modeling signals with different short-term and long-term correlation structure. We describe two iterative algorithms for estimating the parameters of filtered fdGn processes. The first technique is based on the expectation-maximization (EM) algorithm. It converges to a stationary point of the log-likelihood function corresponding to the parameters of the model. The second technique is a computationally efficient approximate approach. It is found to converge experimentally, but no proof of its convergence is given. The usefulness of filtered fdGn models and the performance of the proposed iterative algorithms are illustrated by fitting filtered fdGn models to speech waveforms and other data corresponding to natural phenomena.