Signal fluctuation extraction method combining hadamard matrix and mathematical morphology

Abstract

The application discloses a signal fluctuation extraction method combining a Hadamard matrix and mathematical morphology, and comprises the following steps: determining the order m of the Hadamard matrix and the specific number l of rows to be selected according to signal characteristics and sampling accuracy; taking the lth row of the selected Hadamard matrix as a structure element g to perform mathematical morphology operation on an input signal f to obtain a signal fluctuation part and complete the extraction operation. According to the application, a certain row in the Hadamard matrix is selected as the structure element according to signal characteristics, and the order of the matrix is determined; the characteristics that the Hadamard matrix only takes values of 1 and -1 are utilized; the fundamental component in the signal is suppressed through the morphological operation; and the fluctuation part is extracted. The orthogonality of the Hadamard matrix is fully utilized, the Hadamard matrix is used as the structure element for the morphological transformation, the signal can be processed simply and quickly, and the characteristic information is extracted. The application of the mathematical morphology can accurately analyze the signal in the time domain.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method for extracting signal fluctuations that combines Hadamard matrix and mathematical morphology. Background Technology

[0002] Currently, methods for extracting abnormal fluctuations in signals are mainly divided into frequency domain methods and time domain methods.

[0003] Among them, the frequency domain method transforms the signal into the Fourier domain for analysis. By combining it with filters, the frequencies of normal signals are filtered out, thereby extracting and processing fluctuation components such as faults. The frequency domain method can more accurately distinguish the type of fluctuation components based on the frequency band range. However, this type of method is computationally complex, time-consuming, and it is difficult to determine the characteristics of fluctuation components in the time domain. In addition, it is not effective in extracting random disturbances.

[0004] In actual production, it is often necessary to extract and process fluctuations in the time domain. Time-domain methods, represented by mathematical morphology, identify the timing and amplitude of fluctuation components by processing the time-domain portion of the signal. Summary of the Invention

[0005] This invention addresses the shortcomings of traditional mathematical morphology methods by proposing a signal fluctuation extraction method that combines Hadamard matrix and mathematical morphology, which can effectively extract abnormal parts of signals.

[0006] To achieve the above objectives, the technical solution provided by this invention is as follows: a signal fluctuation extraction method combining Hadamard matrix and mathematical morphology. This method addresses the difficulty in extracting fluctuation components from one-dimensional stationary signals by using Hadamard matrix instead of traditional morphological structural elements. After signal processing, it can effectively extract abnormal fluctuation components, including the following steps:

[0007] 1) Determine the order m of the Hadamard matrix and the specific number of rows l to be selected based on the signal characteristics and sampling accuracy;

[0008] 2) Using the l-th row of the selected Hadamard matrix as the structuring element g, perform mathematical morphological operations on the input signal f to obtain the signal fluctuation part, thus completing the extraction operation.

[0009] Furthermore, in step 1), the Hadamard matrix is ​​defined as follows:

[0010]

[0011] In the formula, k = 1, 2, ..., H1, H2 and Representing first-order, second-order, and 2 respectively k 1st order Hadamard matrix.

[0012] Furthermore, in step 1), the order m of the Hadamard matrix H is determined by the characteristics of the input signal and the sampling accuracy.

[0013] Furthermore, in step 2), the l-th row of the m-order Hadamard matrix is ​​selected as the structuring element g to participate in mathematical morphology operations, which include erosion, dilation, opening, and closing operations.

[0014] Furthermore, in step 2), the length of the input signal f is n, which includes a sinusoidal periodic signal x and an unknown disturbance signal y, satisfying the following condition:

[0015] Δx=x i+1 -x i

[0016] Δy=y i+1 -y i

[0017] In the formula, Δx and Δy are the differences between adjacent sampling points of x and y, respectively, and x i x i+1 y i and y i+1 These are adjacent sampling points, i = 0, 1, ..., n-1. As the sampling accuracy increases, Δx → 0.

[0018] Furthermore, in step 2), the l-th row of the m-order Hadamard matrix is ​​selected as the structuring element, with a length of 2. m The value of the qth position is e. q (1 or -1).

[0019] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0020] To better identify wave components in the time domain, this invention uses mathematical morphology to process the signal. Various mathematical morphological operations can be modified according to different signal characteristics. By adjusting the structuring elements, the start and end times of the wave components can be identified, and the amplitude changes of the wave components can be extracted.

[0021] To effectively suppress the fundamental frequency and fully extract the wave components, this invention uses the Hadamard matrix as the structuring element. The Hadamard matrix is ​​a common matrix in image processing and communication fields due to its orthogonality. The Hadamard matrix only takes the values ​​1 and -1, and through morphological operations, it can reduce the fundamental frequency components of adjacent sampling points while amplifying the wave components.

[0022] In summary, this invention uses mathematical morphology as the basic operational form. By adjusting the structuring element, it can accurately identify the wave components of a signal in the time domain. This invention uses the Hadamard matrix as the structuring element, making full use of its orthogonality and the characteristic of taking only the values ​​1 and -1, to suppress the fundamental wave component through morphological operations. This invention can be extended to two-dimensional image processing and has good application prospects. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the logic flow of the present invention.

[0024] Figure 2 This is a schematic diagram illustrating the effect of the present invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0026] like Figure 1 As shown, this embodiment provides a signal fluctuation extraction method that combines the Hadamard matrix and mathematical morphology, which includes the following steps:

[0027] 1) Input the signal to be processed, f, such as Figure 2 As shown, the signal to be processed consists of an ideal sine wave and an added disturbance.

[0028] 2) Generate the Hadamard matrix.

[0029] The Hadamard matrix H is defined as follows:

[0030]

[0031] In the formula, k = 1, 2, ..., H1, H2 and Representing first-order, second-order, and 2 respectively k 1st order Hadamard matrix.

[0032] 3) Determine the order m of the Hadamard matrix and the specific number of rows l to be selected based on the signal characteristics and sampling accuracy.

[0033] 4) Take the l-th row of the selected Hadamard matrix as the structuring element g, and perform mathematical morphological operations on the input signal f.

[0034] The signal f to be processed has a length of n, which includes a sinusoidal periodic signal x and an unknown disturbance signal y, and satisfies the following conditions:

[0035] Δx=x i+1 -x i

[0036] Δy=y i+1 -y i

[0037] Where Δx and Δy are the differences between adjacent sampling points of x and y, respectively, and x i x i+1 y i and y i+1 These are adjacent sampling points, i = 0, 1, ..., n-1. As the sampling precision increases, Δx → 0.

[0038] The l-th row of the m-order Hadamard matrix is ​​selected as the structuring element, with a length of 2. m The value of the qth position is e. q (1 or -1). The following section uses erosion in mathematical morphology as an example to introduce the specific steps for wave extraction.

[0039] The signal sequence obtained by the erosion operation is [Γ i ,Γ i+1 ,…],in:

[0040]

[0041] In the formula, e i and e i+1 These are the values ​​at positions i and i+1 of the selected Hadamard matrix, respectively.

[0042] As sampling accuracy increases

[0043] When y does not exist, the erosion result of f is 0; when y exists, the result of the erosion operation of f approaches the result after eroding the perturbation signal y. Similarly, the results of other mathematical morphological operations of f will also approach the result after processing the perturbation signal y.

[0044] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A signal fluctuation extraction method combining Hadamard matrix and mathematical morphology, characterized in that, This method addresses the difficulty in extracting the fluctuation component from one-dimensional stationary signals. It uses the Hadamard matrix instead of traditional morphological structural elements, and after signal processing, effectively extracts anomalous fluctuation components. The method includes the following steps: 1) Determine the order m of the Hadamard matrix and the specific number of rows l to be selected based on the signal characteristics and sampling accuracy; The Hadamard matrix is ​​defined as follows: In the formula, k = 1, 2, ..., H1, H2 and Representing first-order, second-order, and 2 respectively k Hadamard matrix of order 1; The order m of the Hadamard matrix H is determined by the characteristics of the input signal and the sampling accuracy. 2) Using the l-th row of the selected Hadamard matrix as the structuring element g, perform mathematical morphological operations on the input signal f to obtain the signal fluctuation component, thus completing the extraction operation, as follows: The l-th row of the m-order Hadamard matrix is ​​selected as the structuring element g to participate in mathematical morphology operations, which include erosion, dilation, opening, and closing operations. The input signal f has a length of n, and includes a sinusoidal periodic signal x and an unknown disturbance signal y, satisfying the following condition: Δx=x i+1 -x i Δy = y i+1 -y i In the formula, Δx and Δy are the differences between adjacent sampling points of x and y, respectively, and x i x i+1 y i and y i+1 These are adjacent sampling points, i = 0, 1, ..., n-1. As the sampling accuracy increases, Δx → 0. The l-th row of the m-order Hadamard matrix is ​​selected as the structuring element, with a length of 2. m The value of the qth position is e. q That is, 1 or -1.

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