CN109088616B - Signal denoising method based on chaotic oscillator - Google Patents
Signal denoising method based on chaotic oscillator Download PDFInfo
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- CN109088616B CN109088616B CN201810973539.3A CN201810973539A CN109088616B CN 109088616 B CN109088616 B CN 109088616B CN 201810973539 A CN201810973539 A CN 201810973539A CN 109088616 B CN109088616 B CN 109088616B
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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- H—ELECTRICITY
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- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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Abstract
The invention discloses a signal denoising method based on a chaotic oscillator, which comprises the following steps: inputting a one-dimensional digital signal to be processed into a specific chaotic oscillator system, and solving a differential equation by a fixed-step-length four-order Runge Kutta method; and outputting the solved signal as an output signal of signal denoising. Compared with the existing mainstream signal denoising method, the method has better signal waveform reduction capability and high operation speed, is suitable for real-time signal processing, and can be widely applied to one-dimensional digital signal denoising.
Description
Technical Field
The invention relates to a signal denoising method, in particular to a signal denoising method based on a chaotic oscillator.
Background
At present, there are many methods for denoising digital signals, mainly including: filters, wavelet de-noising, blind separation, array signal de-noising, singular value decomposition, empirical mode decomposition, maximum likelihood estimation, and the like. The purpose of signal denoising is divided into two cases: one is to try to remove noise without precisely restoring the signal waveform; the other is to restore the signal waveform as accurately as possible. The two cases use different approaches and their nominal noise immunity is different. For the situation that the signal waveform needs to be accurately restored, the existing signal denoising method has the best performance by wavelet and singular value decomposition, and various improved methods are provided and are widely applied.
In recent years, chaotic vibrators are also applied in engineering, and are concentrated in the field of signal detection, and particularly, a periodic sine wave is detected by using a Duffing vibrator, so that the sine wave can be detected under the signal-to-noise ratio of-100 dB. However, no specific technique for applying the chaotic oscillator to signal denoising has been found so far.
Disclosure of Invention
The invention aims to provide a signal denoising method based on a chaotic oscillator, which can restore the original signal waveform as accurately as possible.
In order to achieve the above object, the present invention provides a signal denoising method based on a chaotic oscillator, comprising the following steps:
step 1, inputting a digital signal to be processed into a specific chaotic oscillator system, and solving a differential equation by a fixed-step-length four-order Runge Kutta method;
and 2, outputting the solved signal as an output signal of signal denoising.
Further, in step 1, the chaotic oscillator system is formed by coupling two Holmes-Duffing, and is specifically expressed as the following second-order ordinary differential equation:
in the formula, x1And y1Is a state variable, x, of the first vibrator2And y2And the state variable of the second oscillator is shown as xi, the damping coefficient of the oscillator is shown as alpha, beta are the coupling coefficient between the oscillators respectively, fcos (t) is a periodic driving force, f is the amplitude of the periodic driving force, and s (t) is a digital signal to be denoised.
Further, the output of the chaotic oscillator system is the difference value of oscillator state variables, namely the denoising result of the input signal s (t).
Further, a parameter xi in the chaotic oscillator system is 8, a parameter alpha is 3, a parameter beta is 0.5, and a parameter f is 0.2.
The invention has the beneficial effects that: the invention utilizes the chaotic oscillator system formed by coupling two Holmes-Duffing to carry out denoising processing on the signal, has better capability of restoring the signal waveform than the traditional mainstream signal denoising method, has very high operation speed and is suitable for real-time signal processing.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is an arbitrary waveform signal of the input of the present invention;
FIG. 3 is the signal of FIG. 2 after Gaussian white noise is added;
FIG. 4 is a denoising result of the method of the present invention for the signal of FIG. 3;
FIG. 5 is a denoising result of the discrete biorthogonal wavelet denoising method on the signal of FIG. 3;
FIG. 6 is a denoising result of the adaptive singular value decomposition method on the signal of FIG. 3;
FIG. 7 shows the comparison of the operation time of the three methods.
Detailed Description
As shown in fig. 1, the present invention provides a signal denoising method based on chaotic oscillator, which includes the following steps:
step 1, inputting a digital signal to be processed into a specific chaotic oscillator system, and solving a differential equation by a fixed-step-length four-order Runge Kutta method;
and 2, outputting the solved signal as an output signal of signal denoising.
Further, in step 1, the chaotic oscillator system is formed by coupling two Holmes-Duffing, and is specifically expressed as the following second-order ordinary differential equation:
in the formula, x1And y1Is a state variable, x, of the first vibrator2And y2And the state variable of the second oscillator is shown as xi, the damping coefficient of the oscillator is shown as alpha, beta are the coupling coefficient between the oscillators respectively, fcos (t) is a periodic driving force, f is the amplitude of the periodic driving force, and s (t) is a digital signal to be denoised.
Further, the output of the chaotic oscillator system is the difference value of oscillator state variables, namely the denoising result of the input signal s (t).
Further, a parameter xi in the chaotic oscillator system is 8, a parameter alpha is 3, a parameter beta is 0.5, and a parameter f is 0.2. The system can obtain the best denoising performance at this time. The value of the system parameter can have small fluctuation, and in addition, the initial value of the oscillator state variable does not influence the system performance.
The signal denoising comparison is carried out between the discrete biorthogonal wavelet denoising method provided by the patent method and the governing Wang in 2017 and the self-adaptive singular value decomposition method provided by Ashtiani, M.B. in 2014.
Fig. 2 shows a digital signal with an arbitrary shape, fig. 3 shows a signal of fig. 2 after the signal is interfered by a certain amount of additive white gaussian noise, fig. 4 shows a de-noising result of the signal of fig. 3 by using the method of the present invention (the solving step of the fourth-order lattice tata method is 0.2 seconds), fig. 5 shows a de-noising result of the signal of fig. 3 by the discrete biorthogonal wavelet de-noising method proposed by using the method of the present invention, and fig. 6 shows a de-noising result of the signal of fig. 3 by the adaptive singular value decomposition method proposed by Ashtiani, m.b. Comparing the results of the three methods for denoising the signals in fig. 3, it can be seen that the method of the present invention can better restore the tiny change details of some signals, while the other two methods can not restore the tiny change details of the signals. For example, where fig. 5 and 6 are marked by circles, the method of the present invention can better preserve the details of the signal, but the other two methods cannot. As can be seen from the comparison, the denoising performance of the method is superior to that of wavelet denoising and singular value decomposition. In addition, for the calculation time, the method utilizes the recursion of the initial value during the solution, and the algorithm is simple and quick, so the method is suitable for the real-time processing of signals. As shown in fig. 7, comparing the computation time of the three methods for denoising the signal in fig. 3, it can be seen that the method of the present invention has the fastest computation speed.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can modify and change the type of coupler to be applied to the denoising of one-dimensional digital signals, or extend the application to other fields within the technical scope of the present invention, and all such modifications and changes are intended to be included in the scope of the present invention.
Claims (3)
1. A signal denoising method based on a chaotic oscillator is characterized by comprising the following steps:
step 1, inputting a digital signal to be processed into a specific chaotic oscillator system, and solving a differential equation by a fixed-step-length four-order Runge Kutta method;
step 2, outputting the solved signal as an output signal of signal denoising;
in the step 1, the chaotic oscillator system is formed by coupling two Holmes-Duffing, and is specifically expressed as the following second-order ordinary differential equation:
in the formula, x1And y1Is a state variable, x, of the first vibrator2And y2And the state variable of the second oscillator is shown as xi, the damping coefficient of the oscillator is shown as alpha, beta are the coupling coefficient between the oscillators respectively, fcos (t) is a periodic driving force, f is the amplitude of the periodic driving force, and s (t) is a digital signal to be denoised.
2. The signal denoising method based on the chaotic oscillator of claim 1, wherein the output of the chaotic oscillator system is the difference value of oscillator state variables, that is, the denoising result of the input signal s (t).
3. The signal denoising method based on the chaotic oscillator as claimed in claim 1, wherein a parameter xi in the chaotic oscillator system is 8, α is 3, β is 0.5, and f is 0.2.
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