Anharmonic Signal Decomposition via Phase Parameterization
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Solution Overview
Problem
Existing methods for decomposing anharmonic periodic signals require a large number of Fourier coefficients, making them difficult to analyze and represent effectively, especially in systems with strong non-linear interactions, as they lack physical meaning and result in inefficient coding and synthesis.
Innovation Solution
A method that determines the phase equation and expresses the phase Φ(t) using a small number of parameters (r, Φ0, pk) to decompose anharmonic signals, allowing for a more compact and meaningful representation of the signal's dynamics and structure, using trigonometric polynomials and specific functions like h cos and h sin to reduce the number of parameters needed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Fourier series decomposition is used to represent anharmonic periodic signals, then any periodic signal can be decomposed universally, but a large number of coefficients are required which makes the coding inefficient and the parameters difficult to interpret physically
Solution Approach 1:
The patent transforms the signal representation from Fourier coefficients to a phase-based parameterization using only three parameters (amplitude A, phase offset φ0, and nonlinearity parameter ε). This parameter change allows the same universal decomposition capability while dramatically reducing the number of parameters needed, as the phase function Φ(t) captures the anharmonic behavior through a single nonlinearity parameter ε rather than requiring many Fourier coefficients
2Measurement precision
If many Fourier coefficients are kept to accurately represent anharmonic signals, then the signal synthesis accuracy improves, but the coding compactness deteriorates and the parameters lose physical meaning
Solution Approach 1:
The patent changes the parameter set from Fourier coefficients cn to physical parameters (A, φ0, ε) that have direct physical interpretations: amplitude, phase offset, and nonlinearity strength. This transformation maintains signal synthesis accuracy while restoring physical meaning to the parameters, as ε directly quantifies the deviation from harmonic motion in the phase dynamics
3Reliability
If Fourier decomposition is used for anharmonic signals, then complete signal representation is achieved, but the number of parameters increases making comparison and analysis of multiple signals difficult
Solution Approach 1:
The patent reduces the parameter set from infinite Fourier coefficients to three finite parameters (A, φ0, ε), making signal comparison and analysis straightforward. The nonlinearity parameter ε serves as a single metric to quantify and compare the degree of anharmonicity across different signals, while the simple phase function form maintains complete representation capability for the signal class considered
Data Source
AI summary
This method for decomposing an anharmonic periodic signal, the general form of which may be expressed as x(t)=x0+x1 cos(Φ(t)), wherein Φ(t) is the phase of the signal, is characterized in that it consists of:determining an expression of the phase equationF(Φ)=ⅆΦⅆt,determining an expression of the phase Φ(t) as a function of de parameters (r, rk, Φ1, pk) measuring the anharmonicity of the 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)rkkn.