There is an increasing need for everyday communications to be both secure and resistant to external perturbations. We have, therefore, created an experimental implementation of the coupling-function-based secure communication protocol in order to assess its robustness to channel noise. The transmitter and receiver are implemented on single-board computers, thereby facilitating communication of the analog electronic signals. The information signals are encrypted at the transmitter as the time-variability of nonlinear coupling functions between dynamical systems. This results in a complicated nonlinear mixing and scrambling of the information. To replicate the channel noise, analog white noise is added to the encrypted signals. After digitization at the receiver, the decryption is performed with dynamical Bayesian inference to take account of time-varying dynamics in the presence of noise. The dynamical Bayesian approach effectively separates the deterministic information signals from the perturbations of dynamical channel noise. The experimental realization has demonstrated the feasibility, and established the performance, of the protocol for secure, reliable, communication even with high levels of channel noise.

The usefulness of the information contained in biomedical data relies heavily on the reliability and accuracy of the methods used for its extraction. The conventional assumptions of stationarity and autonomicity break down in the case of living systems because they are thermodynamically open, and thus constantly interacting with their environments. This leads to an inherent time-variability and results in highly nonlinear, time-dependent dynamics. The aim of signal analysis usually is to gain insight into the behavior of the system from which the signal originated. Here, a range of signal analysis methods is presented and applied to extract information about time-varying oscillatory modes and their interactions. Methods are discussed for the characterization of signals and their underlying nonautonomous dynamics, including time-frequency analysis, decomposition, coherence analysis and dynamical Bayesian inference to study interactions and coupling functions. They are illustrated by being applied to cardiovascular and EEG data. The recent introduction of chronotaxic systems provides a theoretical framework within which dynamical systems can have amplitudes and frequencies which are time-varying, yet remain stable, matching well the characteristics of life. We demonstrate that, when applied in the context of chronotaxic systems, the methods presented facilitate the accurate extraction of the system dynamics over many scales of time and space.

In signal processing applications, it is often necessary to extract oscillatory components and their properties from time–frequency representations, e.g. the windowed Fourier transform or wavelet transform. The first step in this procedure is to find an appropriate ridge curve: a sequence of amplitude peak positions (ridge points), corresponding to the component of interest and providing a measure of its instantaneous frequency. This is not a trivial issue, and the optimal method for extraction is still not settled or agreed. We discuss and develop procedures that can be used for this task and compare their performance on both simulated and real data. In particular, we propose a method which, in contrast to many other approaches, is highly adaptive so that it does not need any parameter adjustment for the signal to be analyzed. Being based on dynamic path optimization and fixed point iteration, the method is very fast, and its superior accuracy is also demonstrated. In addition, we investigate the advantages and drawbacks that synchrosqueezing offers in relation to curve extraction. The codes used in this work are freely available for download.