Frequency-Domain Time Series Resampling for Uneven Signal Sampling
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Solution Overview
Problem
Existing time series signal resampling methods in the time domain are computationally inefficient and result in reduced accuracy due to the need for interpolation, especially when dealing with unevenly sampled data.
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 the time series at a target sampling rate, eliminating the need for time-domain interpolation.
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 computational overhead increases and accuracy decreases
Solution Approach 1:
The patent replaces time-domain interpolation mechanisms with frequency-domain processing. Instead of using computational algorithms to interpolate time-domain signals, the system transforms signals to the frequency domain using FFT, processes them there, and transforms back, substituting the mechanical interpolation process with a frequency-based approach that reduces computational overhead while maintaining or improving accuracy.
Solution Approach 2:
The patent changes the domain parameter from time-domain to frequency-domain processing. By transforming the resampling operation from time-domain interpolation to frequency-domain filtering and transformation, the system fundamentally changes the parameter space in which the resampling occurs, thereby reducing computational complexity and improving accuracy simultaneously.
2Ease of manufacture
If time-domain interpolation methods are used for resampling, then the implementation is simple, but measurement precision of the resampled signal decreases
Solution Approach 1:
The patent substitutes time-domain interpolation with frequency-domain processing methods. By using FFT-based transformation and frequency-domain filtering, the system replaces the simple but inaccurate time-domain interpolation mechanism with a more sophisticated frequency-based approach that preserves signal fidelity and improves measurement precision of the resampled signal.
Solution Approach 2:
The patent moves the resampling operation from the time dimension to the frequency dimension. By transforming the signal into the frequency domain, processing it there through filtering and transformation operations, and then transforming back, the system utilizes another dimension (frequency) to achieve more accurate resampling results while maintaining ease of implementation through standardized FFT algorithms.
3Loss of energy
If frequency-domain resampling is used, then computational overhead is reduced and accuracy is improved, but device complexity increases
Solution Approach 1:
The patent employs FFT-based frequency transformation that serves multiple functions: it enables efficient signal transformation, facilitates frequency-domain filtering, and supports various resampling operations. This universal approach using standardized FFT algorithms and frequency-domain processing techniques allows the system to achieve reduced computational overhead and improved accuracy without proportionally increasing device complexity, as the same core mechanisms serve multiple resampling needs.
Data Source
AI summary
Systems, methods, and other embodiments associated with frequency-domain resampling of time series are described. In an example method, a power spectrum is generated for an original time series that is sampled at original time points. Prominent frequencies are selected from the power spectrum. Input phase factors are generated that map the prominent frequencies to a frequency domain at the original time points. Coefficients are identified that relate the input phase factors to the original time series at the original time points. Output phase factors are generated that map the prominent frequencies to the frequency domain at new time points. The original time series is resampled in the frequency domain by generating new values at the new time points from the coefficients and output phase factors to produce a resampled time series that has the target sampling rate. And, an anomaly is detected in the resampled time series signal.