A signal-processing tool adapted to the periodic biphasic phenomena: the Dynalet transform

Area of Science:

• Mathematical Physics
• Biophysics
• Signal Processing

Background:

• Linear functional analysis, including Fourier, Laplace, and Wavelet transforms, has been pivotal in physics and engineering.
• Classical pendulum-based transforms may not be optimal for all applications, especially in biology where models differ.
• Developing new functional transforms tailored to specific problem domains is crucial for accurate signal analysis.

Purpose of the Study:

• To introduce and describe the Dynalet transform, an extension of Fourier analysis.
• To demonstrate the utility of the Dynalet transform for analyzing biological signals.
• To provide a method for robust approximation of signals from periodic biphasic organs.

Main Methods:

• Development of the Dynalet transform, building upon Fourier analysis principles.
• Analysis of the relationship between physical/biological problems and orthogonal/non-orthogonal basis functions.
• Application of the Dynalet transform to model relaxation signals in human physiological systems.

Main Results:

• The Dynalet transform provides a new mathematical framework for functional analysis.
• Robust approximated results were achieved for relaxation signals of periodic biphasic organs.
• The approach highlights the importance of basis selection in signal approximation.

Conclusions:

• The Dynalet transform offers a powerful extension to existing functional analysis techniques.
• This novel transform is particularly effective for analyzing complex biological signals.
• The study underscores the need for problem-specific basis functions in signal processing.