Fundamental wave and harmonic wave detecting method based on three-coefficient Nuttall windowed interpolation FFT

A harmonic detection and coefficient technology, applied in complex mathematical operations, spectral analysis/Fourier analysis, etc., can solve problems such as the inability to directly calculate the interpolation coefficient, the inability to calculate the interpolation coefficient, the absence of an effective solution to the equation, etc. Stability, small amount of calculation, the effect of reducing the amount of calculation

Inactive Publication Date: 2010-05-05

ZHEJIANG UNIV

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Problems solved by technology

[0004] The deficiencies of the prior art are that the windowing interpolation FFT method based on a window function with a small number of items has a small amount of calculation, and has an explicit calculation formula for interpolation coefficients, but the analysis accuracy is low; the windowing method based on a window function with a large number of items The interpolation FFT method has high analysis accuracy, but it needs to solve multiple equations, and the interpolation coefficient cannot be directly calculated through an explicit expression, and the calculation amount is large

For example, the Hanning window is a two-term coefficient cosine window, and its interpolat...

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Abstract

The invention discloses a fundamental wave and harmonic wave detecting method based on three-coefficient Nuttall windowed interpolation FFT. The method comprises the following steps of: obtaining a sampling data of a detected signal by an analog-to-digital converter; carrying out a three-coefficient Nuttall windowed FFT calculation on the sampling data; searching for a largest spectral line and an adjacent second largest spectral line of an amplitude spectral line for the fundamental wave and each harmonic in an FFT spectral line, according to the amplitude ratio of adjacent spectral peaks and an explicit formulation, directly calculating interpolation coefficients of the fundamental wave and each harmonic; and finally, obtaining the frequency, the amplitude and the phase of the fundamental wave and each harmonic by the interpolation calculation. The invention provides the three-coefficient Nuttall windowed interpolation FFT fundamental wave and harmonic detecting method for directly calculating the interpolation coefficients based on the explicit formulation. The invention has advantages of providing the windowed interpolation FFT fundamental wave and harmonic wave detecting method thereof with small calculated amount and high analysis precision.

Application Domain

Spectral/fourier analysisComplex mathematical operations

Technology Topic

Spectral lineAnalog-to-digital converter +2

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Examples

Experimental program(1)
Effect test(1)

Example Embodiment

[0040] Example 1

[0041] Taking the current harmonic detection of an electrical appliance as an example, the current expression of the electrical appliance is The set value is shown in Table 1. The fundamental wave and harmonics detection method based on Nuttall window interpolation FFT of the present invention is applied to measure the fundamental wave and the 2-9th harmonic (but the present invention is not limited to the 2-9th harmonic). In this embodiment, Matlab simulation software to illustrate its implementation process.

[0042] (1) Obtain the sampling data of the electrical current through the analog-to-digital converter, where the analog-to-digital converter uses MAX125CEAX integrated circuit chip, the sampling frequency f s = 10kHz, data length N = 2048. Matlab software adds 80dB Gaussian white noise to the original signal to represent its measurement noise.

[0043] (2) Construct a 2048-point three-term coefficient Nuttall window, add a window to the sampled data, and perform 2048-point FFT transformation to obtain 1024 FFT spectral lines, denoted as X(0), X(1),..., X( 1023).

[0044] (3) For the fundamental wave and each harmonic, search for the largest and adjacent large spectral lines of the amplitude spectral line in the spectral line FFT, and obtain: k 1 =10, k 2 =20, k 3 = 30, k 4 = 40, k 5 = 51, k 6 = 61, k 7 = 71, k 8 = 81, k 9 =91; Calculate the interpolation coefficients of the fundamental wave and each harmonic according to formula (2), and get: δ 1 =0.2195、δ 2 =0.4398、δ 3 = 0.6585, δ 4 =0.8777、δ 5 =0.0977、δ 6 =0.3167、δ 7 =0.5363、δ 8 =0.7565、δ 9 = 0.9757.

[0045] (4) Finally, the frequency, amplitude and phase of the fundamental wave and each harmonic are obtained through interpolation formulas (3), (4) and (5). The results are shown in Table 1.

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Small amount of calculation
Improve operational stability

Fundamental wave and harmonic wave detecting method based on three-coefficient Nuttall windowed interpolation FFT

AI-Extracted Technical Summary

Problems solved by technology

Abstract

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Examples

Example Embodiment

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Description & Claims & Application Information

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