Sinusoidal Parameter Tracking with Prism Network Noise Suppression
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Solution Overview
Problem
Current methods for tracking sinusoidal waves in noisy data face challenges such as inaccurate performance, instability, high computational load, and difficulty in tracking multiple components simultaneously.
Innovation Solution
The use of a low-pass FIR filter with a recursive sliding window technique, combined with a Prism network that includes sequences of integration stage blocks with sine and cosine coefficients, allows for efficient tracking of sinusoidal wave parameters with linear phase response and good numerical stability.
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 measurement precision deteriorates especially for short data windows and high noise
Solution Approach 1:
The patent segments the sinusoidal tracking problem into multiple orthogonal components (sine and cosine basis functions at different frequencies). By decomposing the signal into orthogonal segments, the method can isolate and track individual sinusoidal components even in noisy environments with short data windows, thereby improving measurement precision while maintaining robustness against noise.
2Stability of the object's composition
If current methods are used for tracking sinusoids, then tracking can be performed, but stability with respect to noise and parameter changes deteriorates
Solution Approach 1:
The patent employs iterative optimization algorithms that use feedback from the residual error between the modeled signal and actual measurements. The algorithm continuously adjusts amplitude, frequency, and phase parameters based on this feedback, maintaining stable tracking even when noise or parameter changes occur. The orthogonal basis functions provide a stable framework that constrains the solution space and prevents divergence.
3Speed
If current methods are used for sinusoidal tracking, then tracking can be performed, but dynamic response with respect to parameter changes deteriorates
Solution Approach 1:
The patent uses adaptive algorithms that dynamically adjust their behavior based on the current signal conditions. The optimization process continuously updates parameter estimates in real-time, allowing the system to respond quickly to parameter changes. The orthogonal basis functions enable rapid computation of parameter updates, achieving fast dynamic response while maintaining tracking reliability through the constrained optimization framework.
4Adaptability or versatility
If current methods are used for tracking multiple sinusoidal components, then tracking can be performed, but device complexity increases
Solution Approach 1:
The patent creates a universal tracking framework using orthogonal basis functions that can handle any number of sinusoidal components simultaneously. The same mathematical framework and algorithm structure work whether tracking one component or multiple components, eliminating the need for separate specialized algorithms for each case. This multi-functional approach increases adaptability while keeping system complexity manageable through code reuse and unified processing.
5Measurement precision
If current methods are used for sinusoidal tracking, then tracking can be performed, but computational load increases
Solution Approach 1:
The patent transforms the tracking problem into a parameter optimization task where only amplitude, frequency, and phase parameters need to be estimated. By changing the problem formulation from direct signal processing to parameter space optimization, the computational load is reduced while maintaining or improving accuracy. The orthogonal basis functions enable efficient computation of parameter updates through simple inner products rather than complex signal transformations.
Data Source
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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.