CN109165545A - A kind of new signal characteristic extracting methods based on fractal dimension - Google Patents
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Abstract
本发明提出了一种新的基于分形维数的信号特征提取方法，其特征在于，分别提取信号的盒维数、Higuchi分形维数、Katz分形维数及改进盒维数。本发明为了提高特征提取算法对噪声的抗干扰能力，提出了一种新的基于盒维数的调制信号特征提取算法，提出两个新的参量：峰度调和参数和调和平均盒维数，并与传统盒维数、Higuchi分形维数、Katz分形维数，共同构成四维分形维数特征向量，进而实现对信号的多维分形特征提取。本发明计算简单，可以对复杂的调制信号进行识别，这为分形维数在信号识别领域的应用提供了一定的理论依据。The invention proposes a new signal feature extraction method based on fractal dimension, which is characterized in that the box dimension, Higuchi fractal dimension, Katz fractal dimension and improved box dimension of the signal are extracted respectively. In order to improve the anti-interference ability of the feature extraction algorithm to noise, the present invention proposes a new modulated signal feature extraction algorithm based on box dimension, and proposes two new parameters: kurtosis harmonic parameter and harmonic average box dimension, and Together with the traditional box dimension, Higuchi fractal dimension, and Katz fractal dimension, they form a four-dimensional fractal dimension feature vector, and then realize the multi-dimensional fractal feature extraction of the signal. The invention is simple in calculation and can identify complex modulated signals, which provides a certain theoretical basis for the application of fractal dimension in the field of signal identification.
Description
Technical field
The present invention relates to a kind of signal characteristic extracting methods, belong to field of digital information processing.
Background technique
Signal characteristic abstraction is to analyze the correlated characteristic information of signal, and then extraction effectively can distinguish and identify letter
Number process.It is widely used in, and image recognition, noise processed, fault detection and medical diagnosis etc. are nearly all to be related to letter
Cease the field of processing.Signal characteristic abstraction is basis and the key of digital information processing.Signal by feature extraction is special
Whether sign improves and correctly directly affects the recognition effect of whole system.Since the signal of physical presence has very strong complexity
And therefore how erratic behavior efficiently extracts the difficult point that signal characteristic is always the research.
Up to now, feature extraction mode and algorithm emerge one after another, but common signal recognition method still remain it is following
Two o'clock is insufficient: being difficult to non-linear and signal the non-stationary signal feature of accurate description system；It is difficult to solve determining for signal characteristic
Measure evaluation problem.And the representative property of point shape is can be defined with simple method with self-similarity, and generated by iterating,
The wave character of signal can be described effectively.Common fractal dimension mainly has box counting dimension, Higuchi dimension, Katz FRACTAL DIMENSION
Several and Multifractal Dimension etc..These algorithms largely advance the development of digital processing field.With science and technology
Be constantly progressive, environment becomes increasingly complex, and the complexity of signal of communication is increasing, how to efficiently extract the feature of signal
It is the hot spot studied now.
Summary of the invention
The purpose of the present invention is: realize the validity feature extraction under low signal-to-noise ratio environment to signal.
In order to achieve the above object, the technical solution of the present invention is to provide a kind of new signal based on fractal dimension is special
Levy extracting method, which is characterized in that extract box counting dimension, Higuchi fractal dimension, Katz fractal dimension and the improvement of signal respectively
Box counting dimension, in which: improve the extracting method of box counting dimension the following steps are included:
Original signal x (i) is converted to obtain new signal y (i) by Hilbert by step 1；
Step 2, the instantaneous amplitude A (i) that original signal x (i) is found out using the real and imaginary parts of new signal y (i), to instantaneous
Amplitude A (i) is normalized to obtain instant amplitude value a (i)；
Step 3, kurtosis reconciliation parameter Q (i) for calculating original signal x (i):
In formula, N indicates the data length of original signal x (i)；
Step 4 calculates harmonic average box counting dimension K:
In formula, Db(i) box counting dimension for being instant amplitude value a (i).
Preferably, the expression formula of instantaneous amplitude A (i) described in step 2 are as follows:
In formula, Re y (i) indicates the real part of new signal y (i), Im y (i)
Indicate the imaginary part of new signal y (i).
Preferably, the expression formula of instant amplitude value a (i) described in step 2 are as follows:
In formula, MAX (A (i)) indicates the maximum value in instantaneous amplitude A (i).
In existing one dimensional fractal algorithm, each algorithm all respectively has shortcoming, such as Higuchi Cancers Fractional Dimension Feature algorithm
Calculated value is more accurate, but stability is very poor.Katz algorithm stability is slightly good, but and does not have good recognition capability.
Generally, the classifying quality of box counting dimension is preferable, and calculation amount is simple, simulation time is short.But since signal is increasingly complicated, tradition
Box counting dimension face sophisticated signal when still will appear part signal overlapping the case where.Technical solution proposed by the invention exists
It is improved on original box counting dimension, proposes two new parameters, and combine traditional algorithm, form four dimensions feature, reach one
Dimension divides the purpose for carrying out feature extraction to complex modulated signal under shape and identifying.
The present invention proposes a kind of new based on box counting dimension to improve feature extraction algorithm to the anti-interference ability of noise
Modulated signal feature extraction algorithm, propose two new parameters: kurtosis reconciles parameter and harmonic average box counting dimension, and with tradition
Box counting dimension, Higuchi fractal dimension, Katz fractal dimension collectively form four-dimensional Cancers Fractional Dimension Feature vector, and then realize to letter
Number multidimensional fractal characteristic extract.The present invention calculates simply, can identify that this is fractal dimension to complicated modulated signal
Certain theoretical foundation is provided in the application of field of signal identification.
Detailed description of the invention
Fig. 1 is the lower 6 kinds of signals box counting dimension characteristic profile of -10dB~20dB signal-to-noise ratio；
Fig. 2 is the lower 6 kinds of signals Higuchi Dimension Characteristics distribution map of -10dB~20dB signal-to-noise ratio；
Fig. 3 is the lower 6 kinds of signals Katz Dimension Characteristics distribution map of -10dB~20dB signal-to-noise ratio；
Fig. 4 is that the lower 6 kinds of signals of -10dB~20dB signal-to-noise ratio improve back box Dimension Characteristics distribution map.
Specific embodiment
Present invention will be further explained below with reference to specific examples.It should be understood that these embodiments are merely to illustrate the present invention
Rather than it limits the scope of the invention.In addition, it should also be understood that, after reading the content taught by the present invention, those skilled in the art
Member can make various changes or modifications the present invention, and such equivalent forms equally fall within the application the appended claims and limited
Range.
The present invention provides a kind of new signal characteristic extracting methods based on fractal dimension, extract the box dimension of signal respectively
Number, Higuchi fractal dimension, Katz fractal dimension and improvement box counting dimension.
Wherein, extract the box counting dimension of signal the following steps are included:
1. couple original signal x (i) carries out discrete processes, minimum sampling interval is set as ε.
2. calculating the range scale s (k ε) of signal longitudinal coordinate:
In above formula, N0For sampling number, k ε indicates the side length of the box of the different scale of covering signal, S1It indicates to intercept certain
The maximum value of one segment signal sampled point, S2Indicate the minimum value of a certain segment signal sampled point of interception.
All sampling interval collection comprising signal are set as Nkε:
3. selecting matched curve lgk ε~lgNkεThe middle linearity good one section is used as non-scaling section, then: lgNkε=-dBlgkε
+ b, wherein dBIndicate the slope of signal；B indicates the numerical value of matched curve on the y axis；k1≤k≤k2, k1、k2Respectively above-mentioned nothing
The starting point and maximal end point of scaling interval.
4. finally, finding out the slope of this straight line according to the measurement method of least square method, so that it may identification needed for calculating
The box counting dimension D of signal:
Extract signal Higuchi fractal dimension the following steps are included:
1. couple original signal x (i) carries out discrete processes, discrete signal x (n) is obtained.Discrete signal x (n) is recombinated,
Construct k new time seriesesIt is as follows:
In formula, m=1,2,3 ..., k indicate some starting point for the number of winning the confidence, and N indicates the total points of signal.
2. pair curve constituted or time series seek its average length Lm(k):
3. ask overall average length and L (k):
4. total average length L (k) due to discrete-time signal sequence is proportional to scale k, both sides are taken into logarithm simultaneously,
:Wherein, least square method matched curveSlope D be exactly original signal x
(i) Higuchi fractal dimension.
Extract signal Katz fractal dimension the following steps are included:
If original signal x (i) is by series of points (xi, yi) composition, signal length N, then the Katz of original signal x (i) points
Shape dimension D can be obtained by following formula:
In above formula, L is the length of original signal x (i), then L are as follows:
D is initial point (x1, y1) to the maximum distance of other points, then d are as follows:
Improve box counting dimension extracting method the following steps are included:
1. original signal x (i) is converted to obtain new signal y (i) by Hilbert；
2. the instantaneous amplitude A (i) of original signal x (i) is found out using the real and imaginary parts of new signal y (i), to instantaneous amplitude
A (i) is normalized to obtain instant amplitude value a (i).
The expression formula of instantaneous amplitude A (i) are as follows:
In formula, Re y (i) indicates that the real part of new signal y (i), Imy (i) indicate the imaginary part of new signal y (i)
The expression formula of instant amplitude value a (i) are as follows:
In formula, MAX (A (i)) indicates the maximum value in instantaneous amplitude A (i).
3. calculating kurtosis reconciliation parameter Q (i) of original signal x (i):
In formula, N indicates the data length of original signal x (i)；
4. calculating harmonic average box counting dimension K:
In formula, Db(i) box counting dimension for being instant amplitude value a (i).
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Cited By (4)
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| CN110364187A (en) * | 2019-07-03 | 2019-10-22 | 深圳华海尖兵科技有限公司 | A kind of endpoint recognition methods of voice signal and device |
| CN112152731A (en) * | 2020-09-08 | 2020-12-29 | 重庆邮电大学 | Fractal dimension-based unmanned aerial vehicle detection and identification method |
| CN112230270A (en) * | 2020-12-14 | 2021-01-15 | 西南交通大学 | Earthquake early warning method, device, device and readable storage medium |
| CN112269089A (en) * | 2020-10-29 | 2021-01-26 | 广西电网有限责任公司电力科学研究院 | On-site on-line comparison detection device and detection method for power quality monitoring terminal |
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