Frequency-Domain Resampling for Irregular Time Series Signals
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Solution Overview
Problem
Existing time series signal resampling methods in the time domain are computationally intensive and lack accuracy, particularly when dealing with sensors that have varying sampling rates and irregular intervals.
Innovation Solution
A frequency-domain resampling system that generates a power spectrum to identify prominent frequencies, builds dictionaries of phase factors, and uses these factors to resample time series signals to a target sampling rate without converting to the time domain, thereby improving accuracy and reducing computational overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If time domain interpolation methods are used for resampling, then the resampling process is straightforward to implement, but the computational overhead is high and accuracy is poor
Solution Approach 1:
The patent replaces time-domain interpolation methods with frequency-domain processing. Instead of performing complex time-domain calculations, the system transforms signals to the frequency domain, applies spectral analysis, and reconstructs resampled signals through inverse transformation. This substitution fundamentally changes the computational approach, reducing overhead while maintaining accuracy.
Solution Approach 2:
The patent changes the domain parameter from time to frequency. By representing signals in the frequency domain rather than time domain, the resampling operation becomes more computationally efficient. The system identifies prominent frequencies, manipulates spectral components, and reconstructs signals, achieving better accuracy and lower computational cost than time-domain methods.
2Ease of manufacture
If time domain interpolation methods are used for resampling, then the implementation is simple, but the accuracy of resampled signals is poor
Solution Approach 1:
The patent replaces time-domain interpolation with frequency-domain spectral analysis. By transforming to the frequency domain, identifying prominent frequencies through power spectrum analysis, and reconstructing signals from selected spectral components, the system achieves superior accuracy. This substitution allows selective retention of informative frequency components while filtering noise, which time-domain methods cannot accomplish effectively.
Solution Approach 2:
The patent extracts and retains only the prominent frequencies from the power spectrum that carry meaningful signal information. By identifying and selecting these key frequency components and discarding others (including noise), the system achieves accurate resampling. This extraction principle allows the system to focus computational resources on the most informative parts of the signal spectrum.
3Loss of information
If all frequency components are processed in resampling, then complete signal information is preserved, but computational burden increases significantly
Solution Approach 1:
The patent extracts only the prominent frequencies from the complete spectrum that contain meaningful signal information. By performing power spectrum analysis and selecting frequencies with significant power levels, the system identifies the subset of frequency components that carry essential signal characteristics. This extraction approach preserves necessary information while eliminating redundant and noisy components, reducing computational burden significantly.
Solution Approach 2:
The patent segments the frequency spectrum into prominent (informative) and non-prominent (noise or redundant) components. By dividing the complete frequency spectrum and processing only the prominent segments, the system achieves efficient resampling. This segmentation allows selective processing of frequency components, maintaining signal fidelity where needed while reducing computation in less critical areas.
Data Source
AI summary
Systems, methods, and other embodiments associated with frequency-domain resampling of time series are described. An example method includes generating a power spectrum for a first time series signal that is sampled inconsistently with a target sampling rate. Prominent frequencies are selected from the power spectrum. Sets of first phase factors that map the prominent frequencies to a frequency domain at first time points are generated. Coefficients are identified that relate the sets of first phase factors to values of the first time series signal at the first time points. Sets of second phase factors that map the prominent frequencies to a frequency domain at second time points are generated. A second time series signal that is resampled at the target sampling rate is generated by generating new values at the second time points from the coefficients and sets of second phase factors.