Random Sampling for Spectral Estimation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for spectral estimation with unevenly spaced or randomly spaced data, such as ARMA, DFT, and MF techniques, are inefficient due to high computation times and the need for large data sets, making them unsuitable for real-time applications like manufacturing environments.
Innovation Solution
A method of random sampling that determines a bounded sample timing interval and acquires samples at random times within this interval until a target signal-to-noise ratio is achieved, using a spectral estimator to compute the spectrum with a near-minimum number of samples through least-squares methodology.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If ARMA methods are used for spectral estimation with unevenly spaced data, then spectral estimation can be performed, but computation time becomes excessively high
Solution Approach 1:
The patent changes the fundamental parameter of sampling intervals from fixed/regular to variable/random. By using bounded variable sampling intervals instead of fixed intervals, the system achieves spectral estimation with reduced computation time while maintaining accuracy, directly resolving the contradiction between measurement precision and computation time
Solution Approach 2:
The patent introduces dynamic sampling where the sampling interval varies within bounded limits rather than remaining static. This dynamic approach allows the system to adapt sampling rates to signal characteristics, achieving accurate spectral estimation without the excessive computation time required by static ARMA methods
2Measurement precision
If DFT methods are used for spectral estimation, then spectral analysis can be performed, but extremely large sets of input data are required
Solution Approach 1:
The patent applies partial action by using a bounded variable number of samples rather than requiring extremely large data sets. The method achieves sufficient spectral estimation accuracy with a manageable number of samples by using least-squares spectral estimation with variable sampling intervals, eliminating the need for excessively large data requirements of DFT methods
3Measurement precision
If MF methods are used for spectral estimation, then spectral analysis can be performed, but measurement and computation times become excessively long
Solution Approach 1:
The patent changes the sampling interval parameter from fixed to bounded variable, enabling faster convergence of spectral estimation. This parameter change allows the system to achieve accurate spectral estimates in real-time manufacturing environments, directly improving productivity while maintaining measurement precision
Solution Approach 2:
The patent substitutes traditional iterative spectral estimation methods with a least-squares approach that operates efficiently with variable sampling intervals. This substitution eliminates the excessively long computation times of MF methods, enabling real-time operation in manufacturing environments
Data Source
AI summary
A method of random sampling a signal includes determining a bounded sample timing interval, and acquiring a sample of the signal at random sample times within the bounded sample timing interval. Sample acquisition is repeated until the signal to noise ratio of an estimated spectrum of the signal, produced from the acquired samples, achieves a target signal to noise ratio.