Sinusoidal Wave Tracking with Recursive FIR Noise Filtering
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Solution Overview
Problem
Current methods for tracking sinusoidal waves in noisy data face challenges such as accuracy, stability, dynamic response, and computational load, especially in short data windows and high noise conditions, and existing filters like IIR and FIR have limitations in real-time adaptation and efficiency.
Innovation Solution
The implementation of a low-pass FIR filter using a recursive sliding window technique with linear phase response and good numerical stability, allowing for on-line design with limited resources, and the ability to combine filters for more complex requirements, along with sinusoid trackers that estimate frequency, phase, and amplitude with low computational cost and high accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current methods are used for tracking sinusoids in noisy data, then sinusoidal tracking can be performed, but accuracy deteriorates in short data windows and high noise conditions
Solution Approach 1:
The patent introduces an intermediary filtering stage that processes the noisy signal before sinusoidal tracking. The filter separates the sinusoidal component from noise by exploiting frequency domain characteristics, providing a cleaned signal to the tracker and thereby improving accuracy in high noise conditions
Solution Approach 2:
The patent divides the signal processing into distinct stages: filtering to extract sinusoidal components, followed by separate tracking of amplitude, frequency, and phase parameters. This segmentation allows each stage to be optimized independently, improving overall tracking accuracy
2Stability of the object's composition
If current methods are used for sinusoidal tracking, then tracking can be performed, but stability deteriorates with respect to noise and parameter changes
Solution Approach 1:
The patent implements feedback mechanisms where tracking results are fed back to adjust the filter parameters and tracking algorithms in real-time. This adaptive feedback maintains stability when signal parameters change or noise characteristics vary, preventing divergence and maintaining consistent performance
3Speed
If current methods are used for sinusoidal tracking, then tracking can be performed, but dynamic response deteriorates with respect to parameter changes
Solution Approach 1:
The patent employs dynamic adaptation where filter order, window length, and tracking algorithm parameters are adjusted in real-time based on signal characteristics. This dynamic configuration allows fast response to parameter changes while maintaining reliability through adaptive thresholding and validation checks
4Adaptability or versatility
If multiple sinusoidal components are tracked simultaneously, then comprehensive signal analysis is achieved, but computational load increases
Solution Approach 1:
The patent segments the multi-component tracking problem by first identifying and extracting dominant sinusoidal components in sequential stages. Each component is tracked separately using optimized algorithms, reducing the overall computational burden compared to simultaneous tracking of all components
Solution Approach 2:
The patent implements partial tracking by focusing computational resources on tracking the most significant sinusoidal components that contribute most to the signal energy. Less significant components are tracked with reduced precision or omitted, achieving acceptable overall performance with lower computational load
5Reliability
If FIR filters are used to provide linear phase characteristics and numerical stability, then filtering performance is improved, but computational burden increases
Solution Approach 1:
The patent dynamically adjusts FIR filter parameters such as window length, filter order, and cutoff frequencies based on signal characteristics and performance requirements. This parameter adaptation allows the system to achieve necessary numerical stability and linear phase characteristics while minimizing computational burden by using the simplest adequate filter configuration
Data Source
AI summary
A system for tracking selected wave parameters from a received sinusoidal wave with noise and methods for making and using the same. The method includes performing a multi-track double integral analysis of the sinusoidal wave with noise and creating time dependent outputs. These time dependent outputs may be analyzed mathematically to determine the amplitude, frequency and/or phase of the wave with reduced noise. In one embodiment, the method may employ multiple passes through double integral analysis. The method advantageously can measure output sinusoidal wave parameters with reduced noise, measurements that are close to theoretical noise reduction limits.