Respiratory Signal Phase Analysis for Waveform Characterization
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Solution Overview
Problem
Current methods for analyzing respiratory activity signals are limited to determining frequency and amplitude, failing to effectively analyze the waveform, which is crucial for detecting respiratory abnormalities due to the non-linear nature of these signals, making Fourier decomposition unsuitable.
Innovation Solution
A method that extracts elementary signals from respiratory activity signals and expresses them using a phase equation and parameters (r, rk, Φ0, pk) to characterize anharmonicity and morphology, allowing for a compact representation of the signal's waveform.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Fourier decomposition is used to analyze respiratory activity signals, then frequency analysis is provided, but the analysis becomes complex and requires a large number of coefficients to characterize the non-linear signal
Solution Approach 1:
The patent transforms the signal analysis from frequency domain (Fourier coefficients) to waveform domain by introducing a phase function Φ(t) that directly characterizes the signal shape. This parameter transformation reduces the number of coefficients needed from many Fourier coefficients to a compact representation using phase function parameters, making the analysis simpler while maintaining accuracy for non-linear respiratory signals
Solution Approach 2:
Instead of decomposing the signal into frequency components (Fourier approach), the patent inverts the approach by directly modeling the phase evolution Φ(t) of the signal. This inversion from frequency-domain decomposition to phase-domain modeling provides a more efficient characterization of anharmonic respiratory signals with fewer parameters
2Device complexity
If only the first terms of Fourier decomposition are kept, then the analysis remains simple, but the signal cannot be efficiently characterized
Solution Approach 1:
The patent changes the parameter representation from Fourier coefficients to phase function parameters. This transformation allows the signal to be efficiently characterized using a compact set of parameters that directly describe the waveform morphology, achieving both simplicity and accuracy without needing to retain many terms
3Productivity
If respiratory activity signals are analyzed using conventional methods, then respiratory frequency and amplitude are determined, but waveform analysis is not performed
Solution Approach 1:
The patent extracts and focuses analysis on the phase function Φ(t) that encodes the waveform information. By isolating and analyzing this phase component separately from the amplitude, the method efficiently recovers waveform characteristics without redundant computation, maintaining productivity while preventing information loss
Solution Approach 2:
The patent adds a new dimension of analysis by introducing the phase function Φ(t) that describes the temporal evolution of the signal waveform. This dimensional extension from simple frequency-amplitude parameters to phase-based waveform parameters enables efficient waveform analysis without sacrificing computational efficiency
Data Source
AI summary
A method for analyzing the respiratory activity of a patient includes steps for acquiring at least one respiratory activity signal including at least one elementary signal corresponding to a respiratory cycle, the general form of which may be expressed by x(t)=x0+x1 cos(Φ(t)), wherein Φ(t) is the phase of the elementary signal, and for analyzing the respiratory activity signal. The analysis includes steps for extracting, from the respiratory activity signal, the elementary signal, for determining an expression of a phase equationF(Φ)=ⅆΦⅆtof the elementary signal and for determining an expression of the phase Φ(t) of the elementary signal as a function of parameters measuring the anharmonicity of the elementary signal and its morphology, from p cosn and p sinn functions defined by:pcosn(t,r)=∑k=1∞cos(kt)rkknandpsinn(t,r)=∑k=1∞sin(kt)rrkkn.