Signal singularity detection method based on sixth-order spline interpolation wavelet

A spline interpolation and spline wavelet technology, which is applied in special data processing applications, complex mathematical operations, instruments, etc., can solve problems such as unsatisfactory detection results, large amount of calculation, and difficulty in obtaining wavelet coefficients

Inactive Publication Date: 2019-01-01
UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Problems solved by technology

Since the discrete integral is only an approximate expression of the continuous integral, this method is difficult to avoid numerical calculation errors, not only has a large amount of calculation, but also is difficult to obtain accurate wavelet coefficients, resulting in unsatisfactory final detection results

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  • Signal singularity detection method based on sixth-order spline interpolation wavelet
  • Signal singularity detection method based on sixth-order spline interpolation wavelet
  • Signal singularity detection method based on sixth-order spline interpolation wavelet

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Embodiment Construction

[0059] The signal singular point detection method based on the sixth-order spline interpolation wavelet, the steps are as follows:

[0060] (1) From the sixth-order spline wavelet scaling function Get the sixth-order spline interpolation wavelet scaling function

[0061] The frequency domain expression of the sixth-order spline wavelet scaling function is as follows, where ω is the angular frequency:

[0062]

[0063] The frequency domain expression of the sixth-order spline interpolation wavelet scaling function is, where k is an integer:

[0064]

[0065] (2) Wavelet scaling function interpolated by the sixth-order spline Get low pass filter P s (ω):

[0066] Low-pass filter P corresponding to the sixth-order spline interpolation wavelet scaling function s (ω):

[0067]

[0068] (3) by the low-pass filter P s (ω) Get the high pass filter Q s (ω):

[0069] High-pass filter Q corresponding to the sixth-order spline interpolation wavelet scaling function s (w):

[0070]

[0071] Where i ...

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Abstract

The invention relates to a signal singularity detection method based on a sixth-order spline interpolation wavelet, which solves the problems of large calculation amount and low detection accuracy ofthe traditional method. The sixth-order spline interpolation wavelet scale function described in the description is obtained from the sixth-order spline wavelet scale function described in the description. The function described in the description yields the low pass filter Ps(omega), a high-pass filter Qs (omega) is obtained from the low-pass filter Ps (omega), a low-pass, high-pass filter Ps (omega), Qs (omega) obtains dual interpolation filters Gs (omega) and Hs (omega), the dual interpolation filter Gs (omega) is obtained, the coefficients of Fourier series of Hs (omega), input the signalto be tested and sample, The interpolation wavelet decomposition coefficients are obtained from the coefficients of the sampling value sequence and the dual interpolation filter Fourier series, The interpolation wavelet decomposition coefficients {an} and {bn} are normalized, and the obtained interpolation wavelet decomposition coefficients are processed by zero interpolation and threshold. The position of the maximum modulus point of the obtained interpolation wavelet decomposition coefficients is the position of the singularity point of the measured signal.

Description

Technical field [0001] The present invention relates to a method for detecting singular points of signals. Background technique [0002] The singularity of a signal means that the signal has discontinuities or its derivatives have discontinuities. The singularity detection of signals has very important theoretical significance and practical value. Fourier transform is a traditional tool for signal processing. It can detect the singularity of the signal through the speed of the signal Fourier transform towards zero. However, because the Fourier transform lacks the time-domain positioning function, the Fourier transform can only obtain the overall characteristics of the signal singularity, but cannot determine the specific spatial distribution of the signal singular points. Wavelet transform, as an emerging time-frequency analysis method, overcomes the limitations of the traditional Fourier transform. It can localize the signal in both the time domain and the frequency domain, so ...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06K9/00G06F17/14
CPCG06F17/141G06F17/148G06F2218/00
Inventor 张治国施博文
Owner UNIV OF ELECTRONICS SCI & TECH OF CHINA
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