Multifractal feature extraction method of non-stationary signal based on dual-tree complex wavelet transform
A dual-tree complex wavelet and non-stationary signal technology, applied in the direction of instruments, character and pattern recognition, computer components, etc., to achieve the effect of ensuring accuracy, fast operation speed, and fast algorithm
Active Publication Date: 2018-09-04
ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY
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[0004] In order to solve the above technical problems, the present invention provides a multi-fractal feature extraction method for non-stationary signals based on dual-tree complex wavelet transform, using wavelet transform to determine the trend and time scale of adaptive signals, using dual-tree complex wavelet Transformation overcomes the defect that the traditional wavelet does not satisfy the translation invariance, improves the adaptability and operation speed, and extracts the multifractal characteristics of non-stationary signals more accurately and quickly
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[0064] A multifractal feature extraction method for non-stationary signals based on dual-tree complex wavelet transform, for typical non-stationary signals p-model multiplicative cascaded signals, model parameters p 1 = 0.3 and p 2 = 0.7, signal length is 2 16 ,Such as figure 1 As shown, proceed with the following steps:
[0065] Step 1: Perform integrated processing on the signal, as shown in the following formula:
[0066] Wherein, x(k) is the original signal, k=1,...,t; is the mean value of the signal. The original signal and the integrated signal are as follows figure 2 with image 3 shown.
[0067] Step 2: Select the dual-tree complex wavelet filter, and the two tree decompositions in the first layer use (13, 19)-order approximately symmetrical biorthogonal filters, and the filter coefficients are:
[0068]
[0069] For the analysis of the remaining layers, a 14th-order linear phase Q translation filter is selected, and the filter coefficients are:
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The invention discloses a method for extracting multifractal features of non-stationary signals based on dual-tree complex wavelet transform. The steps are: performing integrated processing on the non-stationary signal to be analyzed; performing dual-tree complex wavelet transform on the integrated signal, and using wavelet to decompose scale coefficients and detail coefficients to obtain the fluctuation components of the signal at each scale; use the obtained wavelet coefficients at each scale to estimate the instantaneous frequency of each scale, and obtain the time scale value of each scale; combined with the scale value, the fluctuation components at each scale are calculated Segmentation; calculate the fluctuation function of each order of the signal, use the double-logarithmic relationship between the fluctuation function and the scale value, and obtain the generalized hurst index through least square fitting, and obtain the scale index of each order; use the legendre transformation to obtain the multi-fractal singular spectrum of the signal . The invention utilizes double-tree complex wavelet transform to decompose signals, overcomes the lack of translation invariance of traditional wavelet transform, ensures the accuracy of multi-fractal feature extraction, and has fast operation speed, which is beneficial to online application.
Description
technical field [0001] The invention relates to the technical field of non-stationary signal processing methods, in particular to a multi-fractal feature extraction method of non-stationary signals based on dual-tree complex wavelet transform. Background technique [0002] In the field of mechanical equipment status monitoring, turbulent flow analysis, ECG, EEG and other signal analysis fields, most of the processed objects are non-stationary signals. A key step in signal analysis is to extract the characteristics of the signal, and the fractal feature is an important one. one type. Compared with monofractal analysis, multifractal analysis is more suitable for non-stationary signals, and it can achieve a finer description of the local scale behavior of the signal, thus providing richer information for further analysis. [0003] The traditional multiple analysis tool is the box method, but when calculating the signal fluctuation function, its time scale is determined artific...
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IPC IPC(8): G06K9/00
CPCG06F2218/06G06F2218/08
Inventor 杜文辽巩晓赟谢贵重郭志强侯俊剑王良文王宏超孟凡念
Owner ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY