A method for determining the time-frequency characteristics of localized impulse components in continuous signals

Abstract

Background: We propose a method for analyzing the dynamics of signals of different nature. The method aims to find the time-frequency characteristics of the local impulse components for continuous signals. Thereby, we separate the information about the impulse shape from the time of its appearance. The method is based on a mathematical model of invariant pattern recognition by a visual system combined with a wavelet analysis method. Here we use Krawtchouk functions to model the response of the receptive fields of the lateral geniculate nucleus and, in addition, as the mother wavelet. Results: The inclusion of saccades in the model of the visual system allows us to extract invariant features of the signals. In addition, a parameter is included in the model that controls the front-to-back ratio of the basis functions. This means that the signal decomposition is not solely based on one particular set of basis functions, but on a family of basis functions parametrized by the shift transformation and an asymmetry parameter, which allows a better approximation of asymmetric impulse components. Conclusion: Our method makes it possible to study both the time of emergence of the impulse components of continuous signals and their spectral characteristics, which in turn can be used for their identification. Applying the method to biological signals of various nature, we could identify and localize a blinking, a muscle response due to emotions and find times of changes in a driver’s stress state, etc. Potentially, other applications of nonstationary signals with impulse components can also be considered.

Synchronization of Airflows at Varying Heights

“…. , 2) [15]. The calculated spectrograms of airflow velocities at heights of 20, 40, 60 and 80 meters using wavelet analysis for localization give high accuracy in resolving energy events within the frequency domain and demonstrate precise time localization.…”

“…In [15] we introduced a wavelet analysis method for localization, intended for analyzing the dynamics of signals of diverse natures. The method aims to find the time-frequency characteristics of local impulse components within continuous signals.…”