Signal modeling and parameter estimation for 1/f processes using scale stationary models

In our previous work, we proposed two classes of self-similar models for 1/f processes which we referred to as scale stationary and p-self similar models. We introduced a new mathematical framework and several new concepts, such as periodicity, autocorrelation, and spectral density function to analyze scale stationary and p-self similar processes. In particular, we introduced a family of finite parameter scale stationary models, similar in spirit to ARMA models by which any scale stationary processes can be approximated. In this work, we utilized the framework of scale stationary processes and introduced novel methods of 1/f signal modeling and parameter estimation techniques. These include a sampling theorem, a mathematically consistent estimator for the self-similarity parameter, an unbiased estimator for the scale autocorrelation function and a maximum likelihood estimator for scale stationary autoregressive models. Results from our study suggest that scale stationary processes provide a powerful framework for practical 1/f signal processing problems.