Sinusoidal Interference Removal via Eigenvalue Analysis
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Solution Overview
Problem
Current methods for identifying and removing sinusoidal interference signals from noise signals are inefficient, particularly in high-precision spectral analysis, as they rely on graphic methods that require heuristic measurements and lose precise information due to interpolation, and struggle with multiple spectral lines and phase noise curves.
Innovation Solution
A method using a Fast Fourier Transform (FFT) filter bank to subdivide the frequency range into bands with white noise, applying eigenvalue analysis of autocorrelation matrices to separate signal and noise components, and employing deconvolution to recombine power levels across frequency bands, with plausibility criteria to ensure accurate power level determination.
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 is lost due to interpolation and numerous spectral lines destroy the graphic imprint
Solution Approach 1:
The frequency range is divided into multiple frequency bands using an FFT filter bank, where each band contains only a limited number of spectral lines. This segmentation prevents the destruction of the graphic imprint while maintaining identification accuracy in each sub-band.
Solution Approach 2:
Sinusoidal interference signals are extracted from the noise signal by analyzing eigenvalues of autocorrelation matrices in each frequency band. The eigenvalues associated with signal components are separated from noise component eigenvalues, enabling precise spectral line identification without interpolating the entire noise curve.
2Ease of operation
If a constant threshold-value line is used for phase noise curves, then identification is simplified, but the monotonously descending phase noise curve requires a complementary threshold course, making measurement only possible in a heuristic manner
Solution Approach 1:
The threshold is no longer a static constant line but becomes dynamic through the use of eigenvalue analysis. The threshold adaptively follows the noise characteristics in each frequency band, automatically adjusting to the monotonously descending phase noise curve without requiring manual heuristic adjustment.
Solution Approach 2:
The manual graphic method of drawing and adjusting threshold lines is replaced by an automated numerical method using eigenvalue analysis of autocorrelation matrices. This substitution eliminates the need for heuristic measurements while maintaining ease of operation through algorithmic processing.
3Measurement precision
If the entire frequency range is analyzed at once with high-resolution Fourier Transform, then spectral lines can be identified, but the computational complexity increases and practicable frequency resolution becomes difficult to achieve
Solution Approach 1:
The entire frequency range is segmented into multiple smaller frequency bands using an FFT filter bank. Each band is analyzed separately with eigenvalue analysis, reducing the computational complexity compared to analyzing the entire spectrum at once while maintaining high frequency resolution through the bank structure.
Solution Approach 2:
Results from multiple frequency bands are merged to form the complete spectral analysis. The FFT filter bank combines the results from individual band analyses, achieving high-resolution frequency analysis across the entire spectrum without the computational burden of processing all frequencies simultaneously.
4Measurement precision
If spectral lines are removed from the noise spectrum, then noise measurement accuracy is improved, but the identification of sinusoidal interference signals must be extremely accurate to avoid removing valid signal components
Solution Approach 1:
Sinusoidal interference signals are extracted and identified through eigenvalue analysis before removal. By separating signal component eigenvalues from noise component eigenvalues, the method ensures that only actual interference signals are removed while preserving valid signal components, thereby maintaining reliability.
Solution Approach 2:
The eigenvalue analysis provides feedback on the nature of each spectral component, allowing the system to distinguish between interference signals and valid signal components. This feedback mechanism ensures accurate identification before removal, preventing the accidental removal of useful signal information.
Data Source
AI summary
A method and a system for the detection and/or removal of sinusoidal interference signals in/from a noise signal transforms a measured signal (x(t), x(μ·Δt)) composed of a limited number of sinusoidal interference signals (Ak·ej(ω<sub2>k</sub2>t+φ<sub2>k</sub2>), Ak·ej(μ·ω<sub2>k</sub2>Δt+φ<sub2>k</sub2>)) and a white noise signal (w(t), w(μ·Δt)) into a subspace containing its white noise components and a subspace containing its interference signal components. Following this, the individual sinusoidal interference signals (Ak·ej(ω<sub2>k</sub2>t+φ<sub2>k</sub2>), Ak·ej(μ·ω<sub2>k</sub2>Δt+φ<sub2>k</sub2>)) are determined using an estimation method within the subspace containing the noise components. The entire frequency range is split into several frequency bands (ν), in which the measured signal (x(t), x(μ·Δt)) consists of a limited number (p(ν)) of sinusoidal interference signals (Ak·ej(ω<sub2>k</sub2>t+φ<sub2>k</sub2>), Ak·ej(μ·ω<sub2>k</sub2>Δt+φ<sub2>k</sub2>)) and a white noise signal (w(t), w(μ·Δt)).