Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time-frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.