Gaussian Window Phasor Measurement Spectral Leakage
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Solution Overview
Problem
Existing waveform analysis methods face challenges in achieving high precision, particularly in determining phasor components of periodic waveforms, due to limitations in sample window selection and noise suppression, which affects the accuracy of frequency domain measurements.
Innovation Solution
The use of a Gaussian window function with a spill level adjustment and a discrete Fourier transform, allowing for precise estimation of frequency peaks by fitting a Gaussian function to consecutive frequency bins, thereby suppressing noise and enabling accurate measurement of close-lying frequencies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional rectangular window function is used in FFT analysis, then the calculation is simple and fast, but the spectral leakage is high and measurement precision deteriorates
Solution Approach 1:
The patent changes the window function parameter from rectangular to Gaussian, which fundamentally alters the spectral characteristics. The Gaussian window function provides exponential decay in the time domain, resulting in significantly reduced spectral leakage and higher frequency measurement precision while maintaining acceptable calculation performance.
Solution Approach 2:
The patent applies local quality by using Gaussian weighting that concentrates energy locally around the center of the window while exponentially suppressing edges. This local concentration of energy reduces spectral leakage and improves frequency resolution for close-lying frequency components.
2Measurement precision
If very long sampling records are used to improve accuracy, then measurement precision improves, but measurement time increases
Solution Approach 1:
The patent changes the window function from rectangular to Gaussian, which fundamentally alters the spectral characteristics. The Gaussian window function provides exponential decay in the time domain, resulting in significantly reduced spectral leakage and higher frequency measurement precision while maintaining acceptable calculation performance.
Solution Approach 2:
The patent replaces the mechanical approach of extending sampling duration with a mathematical approach using Gaussian windowing. Instead of increasing record length to improve precision, the Gaussian window function achieves high precision through its optimal spectral concentration properties, substituting time extension with functional optimization.
3Measurement precision
If balanced sampling is used to achieve integer periods, then frequency analysis accuracy improves, but adaptability to unknown frequencies deteriorates
Solution Approach 1:
The patent changes the window function from rectangular to Gaussian, which fundamentally alters the spectral characteristics. The Gaussian window function provides exponential decay in the time domain, resulting in significantly reduced spectral leakage and higher frequency measurement precision while maintaining acceptable calculation performance.
Solution Approach 2:
The patent introduces dynamic adaptability by using Gaussian windowing that automatically provides optimal spectral concentration regardless of the signal frequency. This dynamic approach eliminates the need for pre-synchronization to integer periods, as the Gaussian window's exponential decay characteristics inherently minimize spectral leakage for any frequency component.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach achieves measurement accuracy within parts per million in laboratory settings and 0.01% in electrical grid measurements, providing a synergistic effect in approximating frequency peaks with high precision.
Implementation Method 1
The frequency spectrum is determined by means of a frequency transform, utilizing a Gaussian window function
Implementation Method 2
The frequency spectrum is determined by means of a frequency transform, utilizing a Gaussian window function
Data Source
Figure 1~2
Figure 3a~3b
Figure 4~5
AI summary
The present disclosure relates to a method of determining phasor components of a periodic waveform, wherein the method comprises: a) sampling the periodic waveform, b) determining a frequency spectrum of the sampled periodic waveform by means of a frequency transform utilizing a Gaussian window function, wherein a ratio np defined by the duration (T0) of the sampling of the periodic waveform divided by the width parameter (tw) of the Gaussian window function is at least 5, c) selecting a region of the frequency spectrum containing a frequency peak defined by a group of consecutive frequency bins each being defined by a frequency value and a magnitude value, and d) determining phasor components of the periodic waveform based on the group of consecutive frequency bins.