Sinusoidal Interference Removal via Eigenvalue Analysis
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Solution Overview
Problem
Conventional methods for noise measurement struggle with accurately identifying and removing sinusoidal interference signals from noise signals, particularly in high-precision spectral analysis, due to limitations in resolving closely spaced spectral lines and losing precise noise curve information, and lack the ability to selectively use subroutines based on measurement tasks.
Innovation Solution
A method utilizing a Fast Fourier Transform (FFT) filter bank to subdivide noise signals into frequency bands, applying eigenvalue analysis of autocorrelation matrices to identify and separate sinusoidal interference signals, and using deconvolution to recombine power levels across bands, with the option to adjust matrix dimensions and averaging for improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If graphic methods with threshold-value lines are used to identify spectral lines, then spectral lines can be recognised above the noise curve, but precise information about the noise curve in the region of identified spectral lines is lost due to interpolation
Solution Approach 1:
The patent extracts sinusoidal interference signals from the noise signal by analyzing eigenvalues of the autocorrelation matrix. The signal components correspond to large eigenvalues while noise components correspond to small eigenvalues, allowing separation without interpolating the noise curve and thus preserving precise noise information.
Solution Approach 2:
The patent introduces the autocorrelation matrix and its eigenvalue decomposition as an intermediary tool. This mathematical framework enables identification of spectral lines while maintaining the original noise curve information, avoiding the direct interpolation approach that causes information loss.
2Quantity of substance
If numerous spectral lines are present in the noise curve, then comprehensive interference signal information is available, but the graphic imprint of the spectrum curve is destroyed as a result of numerous interpolations
Solution Approach 1:
The patent extracts individual spectral line parameters (frequency, power level) directly from the eigenvalue analysis of the autocorrelation matrix, rather than using graphic interpolation methods. This allows handling of numerous spectral lines without destroying the overall spectrum curve graphic imprint.
3Ease of operation
If a constant threshold-value line is used for phase-noise curve analysis, then simple identification is achieved, but the monotonously descending phase noise curve requires a threshold line that is constant only in very small regions
Solution Approach 1:
The patent changes the approach from using a constant threshold-value line to using eigenvalue analysis with a significance threshold. This parameter change allows consistent application across the entire monotonously descending phase noise curve while maintaining measurement precision through statistical significance testing.
4Measurement precision
If high-resolution Fourier Transform is used to identify spectral lines, then spectral lines can be resolved, but the method does not allow separation between measurement, identification, and removal subroutines
Solution Approach 1:
The patent segments the noise analysis system into three independent subroutines: measurement subroutine (autocorrelation matrix calculation), identification subroutine (eigenvalue analysis and spectral line detection), and removal subroutine (spectral line elimination). This modular structure allows flexible combination and selective use of subroutines while maintaining high spectral resolution.
Solution Approach 2:
The autocorrelation matrix and its eigenvalue decomposition serve multiple functions: they enable both identification of spectral lines and provide the basis for their removal. The same mathematical framework supports measurement, identification, and removal operations, making the system versatile and adaptable to different analysis requirements.
Data Source
AI summary
An approach is provided for measuring, identifying, and removing at least one sinusoidal interference signal (Ak·ej(ω<sub2>k</sub2>t+φ<sub2>k</sub2>), Ak·ej(μ·ω<sub2>k</sub2>Δt+φ<sub2>k</sub2>)) in a noise signal (w(t), w(μ·Δt)). A frequency range to be measured is split into a plurality of frequency bands (ν) via a Fast Fourier Transform (FFT) filter bank. For each of the frequency bands (ν), an autocorrelation matrix ({circumflex over (R)}ν) is determined, wherein parameters of the autocorrelation matrices ({circumflex over (R)}ν) are variably adjusted based on whether the at least one sinusoidal interference signal (Ak·ej(ω<sub2>k</sub2>t+φ<sub2>k</sub2>), Ak·ej(μ·ω<sub2>k</sub2>Δt+φ<sub2>k</sub2>)) is to be measured, identified, or removed and further based on at least one averaging. The autocorrelation matrices ({circumflex over (R)}ν) are jointly utilized for one or more of measuring, identifying, or removing the at least one sinusoidal interference signal (Ak·ej(ω<sub2>k</sub2>t+φ<sub2>k</sub2>), Ak·ej(μ·ω<sub2>k</sub2>Δt+φ<sub2>k</sub2>)) in the noise signal (w(t), w(μ·Δt)).