Robust Peak Finder for Noisy Sampled Data
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Solution Overview
Problem
Existing peak detection methods for sampled data are prone to errors and biases, especially when dealing with noisy data, necessitating a robust peak finding method.
Innovation Solution
A method involving fitting a curve to the data using an orthonormal expansion, obtaining a differential curve to find roots, calculating corresponding values, and determining peak values and positions, with optional confidence interval estimation based on standard deviation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing peak detection methods are used on noisy data, then the detection process is simple, but the accuracy and reliability of peak detection deteriorates
Solution Approach 1:
The method segments the peak detection process into distinct stages: curve fitting using orthonormal expansion, differential calculation, root finding, and peak identification. This segmentation allows each stage to be optimized independently, improving overall accuracy while managing complexity through modular processing steps.
Solution Approach 2:
The patent introduces intermediate mathematical constructs (orthonormal expansion coefficients, differential curves, and root calculations) as mediators between the raw noisy data and the final peak detection. These intermediaries filter out noise while preserving peak information, thereby improving measurement precision without directly complicating the final detection step.
2Measurement precision
If curve fitting with orthonormal expansion is used, then peak detection accuracy improves, but computational complexity increases
Solution Approach 1:
The method transforms the peak detection problem by changing parameters from direct data point analysis to orthonormal expansion coefficients. This parameter transformation enables more accurate peak detection through mathematical properties of orthonormal functions while managing computational load through efficient coefficient calculation methods.
Solution Approach 2:
The patent replaces direct mechanical/numerical search methods for peak detection with analytical methods based on orthonormal expansion and differential calculus. This substitution reduces computational iterations and improves accuracy by using mathematical closed-form solutions where possible.
Data Source
AI summary
A method for determining a peak value of a histogram or a sequence of sampled data is disclosed. The method may include fitting a curve to the sequence of data, the curve being modeled based on an orthonormal expansion; obtaining a differential curve, the differential curve describing changes in slope of the curve fitted to the sequence of data; finding at least one root for the differential curve; for each of the at least one root for the differential curve, calculating a corresponding value on the curve fitted to the sequence of data; and determining the peak value of the sequence of data based on a maximum value among the corresponding value calculated for each of the at least one root.