CN109257156A - The method of extraction TWACS signal of communication feature based on time frequency analysis - Google Patents

The method of extraction TWACS signal of communication feature based on time frequency analysis Download PDF

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Publication number
CN109257156A
CN109257156A CN201811025171.4A CN201811025171A CN109257156A CN 109257156 A CN109257156 A CN 109257156A CN 201811025171 A CN201811025171 A CN 201811025171A CN 109257156 A CN109257156 A CN 109257156A
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China
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signal
time
leakage inductance
wigner
impedance
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CN201811025171.4A
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Chinese (zh)
Inventor
毕晓伟
张勇
刘晗
张鹍
金志强
毕晓涛
王辉
王鹏
苏静华
王玉家
王艳梅
聂其兵
周洁
刘磊
刘小芸
赵晓红
郑大伟
苑超
徐霞
夏立磊
王蒙
王一蒙
张立杨
李迅
吴奎华
梁荣
冯亮
杨波
杨慎全
刘淑莉
李昭
李凯
刘钊
庞怡君
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State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
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State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
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Priority to CN201811025171.4A priority Critical patent/CN109257156A/en
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00Arrangements affording multiple use of the transmission path
    • H04L5/14Two-way operation using the same type of signal, i.e. duplex
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B17/00Monitoring; Testing
    • H04B17/30Monitoring; Testing of propagation channels
    • H04B17/391Modelling the propagation channel
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • H04L25/03012Arrangements for removing intersymbol interference operating in the time domain
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • H04L25/03159Arrangements for removing intersymbol interference operating in the frequency domain

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  • Engineering & Computer Science (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Measurement Of Resistance Or Impedance (AREA)

Abstract

The embodiment of the invention discloses the method for the extraction TWACS signal of communication feature based on time frequency analysis, the mode including establishing frequency communication analyzes the transmission characteristic of modulated signal;By analyzing Instant Fourier Transform, wigner-ville distribution, propose the wigner-ville distribution method for inhibiting cross jamming, the wigner-ville distribution method of cross jamming is inhibited to have good time-frequency focusing and distracter rejection characteristic, and there is good computational efficiency, it can overcome the defect that the influence of the sending and receiving end voltage zero-cross time difference, the anti-interference ability of power frequency communication system is greatly strengthened, there is extraordinary application value.

Description

The method of extraction TWACS signal of communication feature based on time frequency analysis
Technical field
The present invention relates to frequency communication technology fields, specifically the extraction TWACS signal of communication based on time frequency analysis The method of feature.
Background technique
TWACS (Two Way Automatic Communication System, bi-directional Glenn shunt technology) is a kind of It is real using the voltage and current distorted signal at system voltage zero crossing suitable for the bi-directional digital communication technology of distribution network Existing information transmission, has many advantages, such as that realization is simple, low in cost, good in anti-interference performance, can pass through transformer telecommunication, Compare the power grid environment for being suitble to complexity.
The time domain specification for accurately detecting modulated signal is the key that TWACS technology, and existing modulated signal time domain is special There are interference free performance difference and the nonadjustable defects of time frequency resolution for the detection method of sign.
Summary of the invention
The method of the extraction TWACS signal of communication feature based on time frequency analysis is provided in the embodiment of the present invention, to solve Interference free performance difference and the problem of time frequency resolution nonadjustable defect in the prior art.
In order to solve the above-mentioned technical problem, the embodiment of the invention discloses following technical solutions:
The present invention provides the methods of the extraction TWACS signal of communication feature based on time frequency analysis, comprising the following steps:
The mode for establishing frequency communication analyzes the transmission characteristic of modulated signal;
Using Time-Frequency Analysis Method, the time domain of modulated signal is determined.
Further, the mode includes frequency communication main website A, user terminal B and transformer substation end main transformer one One end of one end connection impedance R1 of secondary side E, transformer substation end main transformer primary side E, transformer substation end main transformer primary side E's One end of other end connection switch S, the other end of switch S pass through one end of impedance R connection leakage inductance L, the other end difference of leakage inductance L One end, one end of impedance R2 and one end of leakage inductance L5 of leakage inductance L1 are connected, the other end of leakage inductance L5 passes through impedance R5 connection switch S One end, the other end of impedance R2 passes through one end of leakage inductance L2 connection capacitor C and one end of impedance R3, the other end company of capacitor C One end of switch S is connect, the other end of impedance R3 is separately connected one end of leakage inductance L4 and one end of leakage inductance L ', leakage inductance by leakage inductance L3 The other end of L4 passes through one end of impedance R4 connection switch S, and the other end of leakage inductance L ' passes sequentially through impedance R ' and switch S ' connection One end of switch S.
Further, the Time-Frequency Analysis Method includes Short Time Fourier Transform method, wigner-ville distribution method and inhibits to intersect The wigner-ville distribution method of interference.
Further, the process of the Short Time Fourier Transform method are as follows:
To signal subsection, intercept as several segments local stationary signal;
Fourier transformation is taken to several segments local stationary signal respectively, obtains the local spectrum of every segment signal;
According to the difference of different local spectrums, the time varying characteristic of signal is obtained.
Further, the window Fourier transform of time signal f (t) are as follows:
S (t) is window function, and window is rectangular window or Hamming window.
Further, the wigner-ville distribution of multi signal are as follows:
F (t), g (t) respectively indicate two signals,For signal f (t), the mutual Wigner distribution of g (t), f*(τ/2 t-) are the conjugate complex number form of f (τ/2 t-), g*(τ/2 t-) are g (τ/2 t-) Conjugate complex number form;Wf(t, ω), Wg(t, ω) is from spectral term, 2Re [Wf+g(t, ω)] it is distracter.
Further, inhibit the wigner-ville distribution of cross jamming are as follows:
W(t,ω)=Wf(t,ω)Q(t,ω)
In formula,For the spectrum window letter certainly based on short time discrete Fourier transform Number, s (t) are the rectangular window function of short time discrete Fourier transform, and f (τ) is signal;Wf(t, ω) is the wigner-ville distribution of signal.
The effect provided in summary of the invention is only the effect of embodiment, rather than invents all whole effects, above-mentioned A technical solution in technical solution have the following advantages that or the utility model has the advantages that
1, by analysis Instant Fourier Transform, wigner-ville distribution, the wigner-ville distribution for inhibiting cross jamming is proposed Method inhibits the wigner-ville distribution method of cross jamming to have good time-frequency focusing and distracter rejection characteristic, and has very Good computational efficiency, can overcome the defect that the influence of the sending and receiving end voltage zero-cross time difference, greatly strengthen the anti-dry of power frequency communication system Ability is disturbed, there is extraordinary application value.
2, mode of the bi-directional Glenn shunt in power distribution network is built, the transient state of signal is analyzed using circuit analysis method Characteristic simplifies the description and analytic process of time frequency analysis, improves efficiency.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below There is attached drawing needed in technical description to be briefly described, it should be apparent that, for those of ordinary skill in the art Speech, without creative efforts, is also possible to obtain other drawings based on these drawings.
Fig. 1 is the flow diagram of the method for the invention embodiment;
Fig. 2 is frequency communication mode schematic diagram of the present invention;
Fig. 3 is the schematic diagram of TWACS downlink signal transmission characteristic of the present invention;
Fig. 4 is receiving end of the present invention mostly distortion cumulative signal amplitude schematic diagram;
Fig. 5 is the emulation signal schematic representation of frequency communication mode of the present invention;
Fig. 6 A is the time-domain diagram for the power frequency modulated signal that the present invention is obtained using Short Time Fourier Transform method;
Fig. 6 B is the time-domain diagram for the power frequency modulated signal that the present invention is obtained using wigner-ville distribution method;
Fig. 6 C is time-domain diagram of the present invention using the power frequency modulated signal for inhibiting the wigner-ville distribution method of cross jamming to obtain;
Fig. 7 is single distorted signal schematic diagram of the invention;
Fig. 8 A is the time-domain diagram for single distorted signal that the present invention is obtained using Short Time Fourier Transform method;
Fig. 8 B is the time-domain diagram for single distorted signal that the present invention is obtained using wigner-ville distribution method;
Fig. 8 C is time-domain diagram of the present invention using the single distorted signal for inhibiting the wigner-ville distribution method of cross jamming to obtain;
Fig. 9 is 7 times of distortion cumulative signal schematic diagrames of the invention;
Figure 10 A is the time-domain diagram for more distorted signals that the present invention is obtained using Short Time Fourier Transform method;
Figure 10 B is the time-domain diagram for more distorted signals that the present invention is obtained using wigner-ville distribution method;
Figure 10 C is time-domain diagram of the present invention using the more distorted signals for inhibiting the wigner-ville distribution method of cross jamming to obtain.
Specific embodiment
In order to clarify the technical characteristics of the invention, below by specific embodiment, and its attached drawing is combined, to this hair It is bright to be described in detail.Following disclosure provides many different embodiments or example is used to realize different knots of the invention Structure.In order to simplify disclosure of the invention, hereinafter the component of specific examples and setting are described.In addition, the present invention can be with Repeat reference numerals and/or letter in different examples.This repetition is that for purposes of simplicity and clarity, itself is not indicated Relationship between various embodiments and/or setting is discussed.It should be noted that illustrated component is not necessarily to scale in the accompanying drawings It draws.Present invention omits the descriptions to known assemblies and treatment technology and process to avoid the present invention is unnecessarily limiting.
As shown in Figure 1, the present invention is based on time frequency analysis extraction TWACS signal of communication feature method comprising steps of
S1 establishes the mode of frequency communication, analyzes the transmission characteristic of modulated signal;
S2 determines the time domain of modulated signal using Time-Frequency Analysis Method.
In step S1, the essence of bi-directional Glenn shunt signal is from silicon rectification device to power grid modulation distortion signal.Core Thought is that information is carried using the small distortion of voltage and current waveform, and modulated process can be equivalent to power grid one is small Instantaneous short-circuit failure.The fault current very little, time are very short.Within the time to failure removal of breaking down, the electricity of fault point Pressure and electric current will undergo country's process from transient state to stable state.The present embodiment is using analytic approach in shop come the temporary of molecular signal Step response.
As shown in Fig. 2, for a distribution transformer by a branch line and thereon, it is logical to establish power frequency for convenient for expressing Believe mode.Mode includes frequency communication main website A, user terminal B and transformer substation end main transformer primary side E, R, L point Not Biao Shi downlink signal modulation impedance and leakage inductance, R ', L ' respectively indicate the modulation impedance and leakage inductance of uplink signal, and R1, L1 are The equivalent impedance and leakage inductance of main transformer, R2, L2 are the equivalent impedance and leakage inductance of branch route, and R3, L3 are user transformers Equivalent impedance and leakage inductance, R4, L4 are the equivalent load impedance and leakage inductance of user terminal, and R5, L5 are that the equivalent load of tributary user hinders Anti- and leakage inductance, C are the reactive compensation capacitor of branch where user, and switch S and switch S ' simulate the silicon for generating downlink signal respectively The silicon rectification device of rectifying device and uplink signal.
One end of one end connection impedance R1 of transformer substation end main transformer primary side E, transformer substation end main transformer primary side E Other end connection switch S one end, the other end of switch S passes through one end of impedance R connection leakage inductance L, and the other end of leakage inductance L divides Not Lian Jie one end of leakage inductance L1, one end of impedance R2 and leakage inductance L5 one end, the other end of leakage inductance L5 opened by impedance R5 connection One end of S is closed, the other end of impedance R2 passes through one end of leakage inductance L2 connection capacitor C and one end of impedance R3, the other end of capacitor C One end of connection switch S, the other end of impedance R3 are separately connected one end of leakage inductance L4 and one end of leakage inductance L ' by leakage inductance L3, leakage The other end for feeling L4 passes through one end of impedance R4 connection switch S, and the other end of leakage inductance L ' passes sequentially through impedance R ' and switch S ' even Connect one end of switch S.
T=t before v (t)=00Moment closure switch S generates short trouble, and fault current is i (t), first The t=t of a i (t)=01Moment disconnects S and cuts off failure, there is Δ t=t1-t0.According to the state of closure switch S, it is divided into-∞ < t < t0, t0< t < t1With t > t1Three periods analyze the voltage and current of power grid.V (t) indicates distortion current.
In TWACS, modulated signal is divided into downlink signal and two kinds of uplink signal.Wherein, downlink signal uses voltage modulated, Transmission direction is to represent command information from main website A to terminal B;Uplink signal use current-modulation, transmission direction from terminal B to Main website A, transmission is user data.The change frequency of modulated signal and the parameter current of power distribution network are related.
The modulation of TWACS downlink signal is an instantaneous short-circuit process, due to the presence of capacitive and inductive load, modulated signal It will appear oscillation disturbances.In Δ t, modulated signal has been superimposed a transient signal on electric current, has crossed Δ t and has shaken later It swings, and frequency of oscillation is very high, about in 200Hz between 600Hz.Because fault current is smaller, excision is rapid, so will not Voltage and current is produced a very large impact.
As shown in figure 3, UAAnd UBIt is the voltage for respectively indicating main website and user terminal, uAAnd uBRespectively indicate main website and use The voltage distortion signal of family terminal, distorted signal time delay is very small as seen from the figure, and decay also very little;And UAAnd UBBetween exist Phase difference, the numerical value of phase difference and the load state of power distribution network it is related.Each power frequency period samples 100 points, and 50 points are hair Voltage over zero is held, distorted signal center is just in originator voltage over zero.
As shown in figure 4, adding up to the live more distorted signals of distribution transformer low-pressure side, discovery distorted signal center is not In receiving end voltage over zero, the presence of account for voltage phase difference can have an impact to signal time domain deviation is received.
In step S2, Time-Frequency Analysis method (Joint Time-Frequency Domain Analysis, JTFA) is again Referred to as time-frequency domain method of localization, it can provide the localised information of signal time-frequency domain simultaneously, be suitble to believe bi-directional Glenn shunt Number carry out analysis and feature extraction.The Time-Frequency Analysis Method of the embodiment of the present invention includes Short Time Fourier Transform method, Wigner point Cloth method and the wigner-ville distribution method for inhibiting cross jamming.
Short Time Fourier Transform method (Short Time Fourier Transform, STFT) if be to signal subsection interception Dry section local stationary signal, takes Fourier transformation to several segments local stationary signal respectively, obtains the local spectrum of every segment signal; According to the difference of different local spectrums, the time varying characteristic of signal is obtained.For time signal f (t), window Fourier transform is fixed Justice are as follows:
S (t) is window function, if window function meets normalization condition, inversion formula are as follows:
Wherein normalization condition is the space s (t) ∈ L2 (R), and the window Fourier transform of ts (t) ∈ L2 (R) is in short-term Fourier transformation, window can according to need selection rectangular window, Hamming window etc..
Two-dimensional function F (ω, τ) (- ∞ < ω <+ω ,-∞ < τ <+ω) reflects part of the signal near the τ moment Spectrum signature features signal f (t) in the information in two domain of time-frequency with the passage of τ.
And the spectrogram of Short Time Fourier Transform is defined as the energy density frequency spectrum in moment t signal, i.e.,
In general, window function s (t) is shorter, and temporal resolution is higher;Window function s (t) is longer, frequency resolution It is higher.Once time frequency resolution determines that, and not with signal frequency and time change this means that window function is selected And change.
Wigner-ville distribution method is distributed as a kind of energy type time-frequency combination, Wigner-Willie time-frequency distributions (Wigner- Ville Distribution, WVD) it establishes on the approximate basic to signal frequency, there is high-resolution, energy centrality With the tracking characteristics such as instantaneous frequency.Signal f's (t) is distributed from Wigner is defined as:
f*(t) be signal f (t) conjugate complex number form.
In signal analysis, the signal of finite length can only be chosen, therefore to do windowing process to signal, obtained in this way Distribution is known as Pseudo-T-norm L-Fuzzy semigroups (Pseudo Wigner-Ville Distribution, PWVD), Pseudo-T-norm L-Fuzzy semigroups are as follows:
H (t) is a window function, Hamming window, Gaussian window etc. can be selected, institute's windowed function is shorter in the time domain, in frequency domain Smooth effect be more obvious.When there are multiple signals, by taking dual signal f (t), g (t) as an example, wigner-ville distribution are as follows:
It is distributed for the mutual Wigner of signal f (t), g (t).Formula (6) in, from spectral term Wf(t, ω), Wg(t, ω) can regard the Energy distribution of signal, but distracter 2Re [W asf+g(t, ω)] deposit So that the readable of time frequency distribution map is deteriorated, when signal especially to be analyzed is multicomponent data processing.
According to the analysis to Short Time Fourier Transform method and wigner-ville distribution method, on the one hand, Short Time Fourier Transform Time-frequency characteristics can be effectively extracted, distracter is not present, but its time frequency resolution is low, cannot effectively track signal frequency variation; On the other hand, wigner-ville distribution has high-resolution, energy centrality and tracking instantaneous frequency, but when handling multicomponent data processing Cross jamming can be generated.
When handling the power network signal of noise circumstance complexity, a kind of algorithm for more preferably combining two methods advantage is needed.It is logical Crossing, from window function is composed in conjunction with wigner-ville distribution, will propose a kind of Wigner for inhibiting interference point based on short time discrete Fourier transform Cloth algorithm greatly reduces the influence of distracter.According to improvement unified algorithm of the time frequency analysis algorithm-based on STFT and WVD (STFT-WVD), certainly spectrum window function of the selection based on short time discrete Fourier transform are as follows:
Wherein, s (t) is the rectangular window function of short time discrete Fourier transform, is able to suppress the wigner-ville distribution of cross influence just It can indicate are as follows:
W(t,ω)=Wf(t,ω)Q(t,ω) (8)
In formula (8), Wf(t, ω) is the wigner-ville distribution of signal f (t).
Below according to model shown in FIG. 1, using MATLAB, (matrix laboratory, matrix labotstory are the U.S. The business mathematics software that MathWorks company produces is calculated for algorithm development, data visualization, data analysis and numerical value Advanced techniques computational language and interactive environment) generate power frequency as shown in Figure 5 and modulate downlink signal.
The time domain of Fig. 6 A, Fig. 6 B and Fig. 6 C are respectively obtained using three kinds of Time Domain Analysis for the downlink signal of Fig. 5 Figure, the energy peak that time domain determines is substantially at the originator voltage zero-cross moment.Because original signal is state no interference signal, frequency division at three kinds Analysis method effect is all good, most concentrates especially with the resulting energy peak of wigner-ville distribution, overcomes frequency communication sending and receiving end The impact effect of the voltage zero-cross time difference is best.
The front and back period of distribution transformer low-pressure side measured signal is subjected to calculus of differences, it is abnormal to obtain list as shown in Figure 7 Varying signal, since electric network noise is serious, distorted signal can not be differentiated.
For single distorted signal of Fig. 7, using three kinds of Time Domain Analysis, respectively obtain Fig. 8 A, Fig. 8 B and Fig. 8 C when Domain figure, it is seen that live distorted signal is submerged in noise, and video analysis curve does not have apparent area of energy concentration domain, can not be determined Modulated signal time domain.
When transmitting terminal continuously transmits the modulating-coding of same information, distorted signal can also obtain the increasing of cumulative multiple By force, Fig. 9 is 7 times of distortion cumulative signals.
Figure 10 A, Figure 10 B and figure are respectively obtained using three kinds of video analysis methods for 7 times of distortion cumulative signals of Fig. 9 The time-domain diagram of 10C, it is seen that the signal-to-noise ratio after the cumulative synthesis of distorted signal greatly improves, and three kinds of time frequency analysis curves all occur bright Aobvious area of energy concentration domain, but the wigner-ville distribution energy peak of cross jamming is inhibited most to concentrate.The voltage zero-cross moment adopts 100 Near sampling point, energy peak and distribution transformer low-pressure side zero passage differ less than 30 sampling intervals.
The energy peak of downlink signal is substantially near the voltage zero-cross of substation's modulation transformer, it is believed that here it is The voltage zero-cross time difference of frequency communication Transmitting and Receiving End, this makes it possible to the time domains for determining the modulated signal.
The above is the preferred embodiment of the present invention, for those skilled in the art, Without departing from the principles of the invention, several improvements and modifications can also be made, these improvements and modifications are also regarded as this hair Bright protection scope.

Claims (7)

1. the method for the extraction TWACS signal of communication feature based on time frequency analysis, characterized in that the following steps are included:
The mode for establishing frequency communication analyzes the transmission characteristic of modulated signal;
Using Time-Frequency Analysis Method, the time domain of modulated signal is determined.
2. the method for the extraction TWACS signal of communication feature according to claim 1 based on time frequency analysis, characterized in that The mode includes frequency communication main website A, user terminal B and transformer substation end main transformer primary side E, transformer substation end main transformer One end of one end connection impedance R1 of depressor primary side E, the other end connection switch S's of transformer substation end main transformer primary side E One end, the other end of switch S pass through one end of impedance R connection leakage inductance L, the other end of leakage inductance L be separately connected leakage inductance L1 one end, One end of impedance R2 and one end of leakage inductance L5, the other end of leakage inductance L5 pass through one end of impedance R5 connection switch S, and impedance R2's is another One end passes through one end of leakage inductance L2 connection capacitor C and one end of impedance R3, one end of the other end connection switch S of capacitor C, impedance The other end of R3 is separately connected one end of leakage inductance L4 and one end of leakage inductance L ' by leakage inductance L3, and the other end of leakage inductance L4 passes through impedance One end of R4 connection switch S, the other end of leakage inductance L ' pass sequentially through one end of impedance R ' and switch S ' connection switch S.
3. the method for the extraction TWACS signal of communication feature according to claim based on time frequency analysis, characterized in that institute Stating Time-Frequency Analysis Method includes Short Time Fourier Transform method, wigner-ville distribution method and the wigner-ville distribution method for inhibiting cross jamming.
4. the method for the extraction TWACS signal of communication feature according to claim 3 based on time frequency analysis, characterized in that The process of the Short Time Fourier Transform method are as follows:
To signal subsection, intercept as several segments local stationary signal;
Fourier transformation is taken to several segments local stationary signal respectively, obtains the local spectrum of every segment signal;
According to the difference of different local spectrums, the time varying characteristic of signal is obtained.
5. the method for the extraction TWACS signal of communication feature according to claim 4 based on time frequency analysis, characterized in that The window Fourier transform of time signal f (t) are as follows:
S (t) is window function, and window is rectangular window or Hamming window.
6. the method for the extraction TWACS signal of communication feature according to claim 3 based on time frequency analysis, characterized in that The wigner-ville distribution of multi signal are as follows:
F (t), g (t) respectively indicate two signals,For signal f (t), g (t) mutual Wigner distribution, f*(τ/2 t-) are the conjugate complex number form of f (τ/2 t-), g*(τ/2 t-) are the conjugation of g (τ/2 t-) Plural form;Wf(t, ω), Wg(t, ω) is from spectral term, 2Re [Wf+g(t, ω)] it is distracter.
7. the method for the extraction TWACS signal of communication feature according to claim 3 based on time frequency analysis, characterized in that Inhibit the wigner-ville distribution of cross jamming are as follows:
In formula,For the spectrum window function certainly based on short time discrete Fourier transform, s (t) For the rectangular window function of short time discrete Fourier transform, f (τ) is signal;Wf(t, ω) is the wigner-ville distribution of signal.
CN201811025171.4A 2018-09-04 2018-09-04 The method of extraction TWACS signal of communication feature based on time frequency analysis Pending CN109257156A (en)

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CN110287948A (en) * 2019-07-24 2019-09-27 成都理工大学 A kind of Wigner-Wei Li time-frequency Decomposition based on energy separation
CN110287948B (en) * 2019-07-24 2021-04-27 成都理工大学 Wegener-Weili time-frequency decomposition method based on energy separation

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Application publication date: 20190122