Non-stable signal multi-fractal feature extraction method based on dual-tree complex wavelet transformation

Abstract

The invention discloses a non-stable signal multi-fractal feature extraction method based on dual-tree complex wavelet transformation. The steps include: performing integration processing on a non-stable signal to be analyzed; performing dual-tree complex wavelet transformation on the integrated signal, and using wavelet decomposition scale coefficients and detail coefficients to obtain fluctuation components of the signal under each scale; using the obtained wavelet coefficient of each scale to estimate the instantaneous frequency of each scale, and obtaining a time scale value of each scale; based on the scale values, performing segmentation on the fluctuation components under each scale; calculating a fluctuation function of each order of the signal, utilizing a double-logarithm relation of the fluctuation functions and the scale values, obtaining a generalized hurst index through least squares fitting, and obtaining scale index of each order; and utilizing legendre transformation to obtain a multi-fractal singular spectrum of the signal. The non-stable signal multi-fractal feature extraction method provided by the invention utilizes dual-tree complex wavelet transformation to perform signal decomposition, overcomes the problem that traditional wavelet transformation lacks translation invariance, ensures accuracy of multi-fractal feature extraction, the arithmetic speed is fast, and thus the method is in favor of 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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Problems solved by technology

[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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