CN110207689A - A kind of pulsar signal denoising and discrimination method based on Wavelet Entropy - Google Patents

A kind of pulsar signal denoising and discrimination method based on Wavelet Entropy Download PDF

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CN110207689A
CN110207689A CN201910464593.XA CN201910464593A CN110207689A CN 110207689 A CN110207689 A CN 110207689A CN 201910464593 A CN201910464593 A CN 201910464593A CN 110207689 A CN110207689 A CN 110207689A
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pulsar
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CN110207689B (en
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孙景荣
赵聪聪
张华�
许录平
魏晨依
谢林昌
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Xidian University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/24Querying
    • G06F16/245Query processing
    • G06F16/2455Query execution
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/21Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/211Selection of the most significant subset of features

Abstract

The invention belongs to pulsar signal processing technology field, a kind of pulsar signal denoising based on Wavelet Entropy and discrimination method are disclosed.Pulsar signal is decomposed first with wavelet transformation, calculates the Wavelet Entropy in each subinterval after wavelet decomposition.Wavelet Entropy and wavelet threshold are combined so that it is determined that each layer high-frequency wavelet coefficient threshold value thresholding.Pulsar signal using threshold value threshold processing with noise.Further according to different pulsar signals each section energy value present differentiation the characteristics of, calculate sample in all pulsar signals the Wavelet Entropy in each section numerical value.Being loaded into database as a result, carrying out construction feature parameter in conjunction with corresponding title for the Wavelet Entropy numerical value of each pulsar signal is recorded, then is compared with unknown pulsar signal feature, and completes the identification to pulsar signal.The present invention only uses Wavelet Entropy algorithm, while signal denoising, can extract the small echo entropy amount of being characterized of signal to complete the task of identification.

Description

A kind of pulsar signal denoising and discrimination method based on Wavelet Entropy
Technical field
The invention belongs to pulse signal processing technology field more particularly to a kind of pulsar signal denoisings based on Wavelet Entropy And discrimination method.
Background technique
Currently, the immediate prior art: the ultrastability in pulsar signal period, it is provided for spacecraft navigation New research direction, but the performance of the high interference and receiving device of long propagation distance and interstellar space material, are received It include very noisy in pulsar signal.Under normal circumstances, signals with noise, which will become workable useful signal, to be gone It makes an uproar processing.During pulsar identification, and need first to carry out denoising.Existing algorithm is mostly by pulsar signal Denoising, identification is divided into two parts to study, and proposes different algorithms for the two parts.These algorithms are all used for Single-issue is solved, and solves the denoising of pulsar navigation system using two kinds of algorithms and recognizes the two compatible signal processings Problem reduces the efficiency of system.
In conclusion problem of the existing technology is: existing pulse signal Processing Algorithm is all used to solve single ask Topic solves the denoising of pulsar navigation system using two kinds of algorithms and recognizes the two compatible signal processing problems, reduces The efficiency of system.
Solve the difficulty of above-mentioned technical problem:
It solves to denoise and recognize both of these problems simultaneously using a kind of method, should meet and filter out noise and reach extraction again The purpose of noise.Existing technology is intended to inhibit and eliminate noise signal, and other way is recycled to extract signal characteristic.It is existing Technology does not provide a possibility that extracting both features, and Wavelet Entropy method is effectively extracted noise signal after signal decomposition Feature and pulsar signal feature.
Solve the meaning of above-mentioned technical problem:
X-ray pulsar signal processing is a key component of airmanship, while restrict navigation accuracy.Therefore it grinds The denoising and identification for studying carefully X-ray pulsar signal have the precision and efficiency that improve X-ray pulsar navigation system important Meaning.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of, and the pulsar signal based on Wavelet Entropy is denoised and is distinguished Knowledge method.
The invention is realized in this way a kind of pulsar signal denoising and discrimination method based on Wavelet Entropy, described to be based on The pulsar signal of Wavelet Entropy denoises and discrimination method includes:
The first step decomposes pulsar signal using wavelet transformation, calculates the Wavelet Entropy in each subinterval after wavelet decomposition; Wavelet Entropy and wavelet threshold are combined and determine each layer high-frequency wavelet coefficient threshold value thresholding;Using threshold value threshold processing with noise Pulsar signal;
The characteristics of second step, differentiation is presented in the energy value according to different pulsar signals in each section;Calculate sample In all pulsar signals the Wavelet Entropy in each section numerical value;
Third step, by the Wavelet Entropy numerical value of each pulsar as a result, in conjunction with corresponding title, construction feature parameter is loaded into It is compared into database, then with unknown pulsar signal, and completes the identification to pulsar signal.
Further, the first step specifically includes:
(1) wavelet transformation for carrying out m scale to the pulsar signal x (n) that band is made an uproar first, obtains the discrete of each scale Wavelet coefficient, the coefficient of the high fdrequency component at k moment is expressed as d under jth decomposition scaleJ, k, the coefficient of low frequency component is expressed as aJ, k, The sample frequency of signal is expressed as fs, wherein j=1,2 ..., 5;K=1,2 ..., 10;Preferably, using db6 as wavelet basis Function carries out the wavelet transform of 5 scales to pulsar sequence;
(2) according to each layer scattering wavelet coefficient, the wavelet energy E of the high frequency coefficient in each section is calculated separatelyJ, k;Letter Number jth layer coefficients dJ, kIt is divided into n section, then the energy in this layer of each section are as follows:
Wherein m is sampling number;
(3) wavelet energy distribution probability is k-th of subinterval wavelet coefficient ENERGY EJ, kWith this layer of wavelet coefficient gross energy Ej Ratio;
PJ, k=EJ, k/Ej
The Wavelet Entropy W in the section KkFor;
Wk=-∑jPJ, kln(PJ, k);
The maximum section of small echo entropy is found, and calculates the noise estimate variance σ in this section:
WhereinReach the wavelet coefficient intermediate value in maximum section for small echo entropy in wavelet coefficient section.System The number specific calculation method of intermediate value is as follows:
Wherein, γ1For the adjustment factor of threshold value thresholding, regulatory factorβ;According to the feature of signal, regulation coefficient and because The value of son, adaptively determines threshold value thresholding.λjFor the threshold value of high frequency coefficient, then the threshold value of high frequency coefficient is;
Wherein, γ2For the adjustment factor of threshold value thresholding, the threshold value of each layer coefficients is adjusted according to the actual situation, and N is sample letter Number length;
Threshold process is carried out to high frequency coefficient, the pulsar signal after being denoised is reconstructed;By calculating mean square error Difference obtains the performance indicator of denoising effect;
Wherein, x ' (n) is denoised signal.
Further, the second step specifically includes:
(1) pulsar signal database is established, the Wavelet Entropy in each section is successively calculated, as characteristic parameter, with pulsar Signal name is stored together in the database;
(2) the small echo entropy for calculating unknown pulse star signal, is compared with the data in database;Utilize two groups of signals Variance between characteristic parameter is compared, and determines whether feature has uniqueness;The formula of variance of characteristic parameter is;
Wherein, s1j(n), s2j(n) the small echo entropy of two kinds of signal jth layers;
(3) it draws a conclusion, pulsar PSR 0531+21 signal whether there is in existing database.If it does, side Difference is 0;Otherwise the pulsar is considered as not in given data storehouse.
Another object of the present invention is to provide the pulsar signal denoisings and identification described in a kind of application based on Wavelet Entropy The spacecraft of method.
Another object of the present invention is to provide the pulsar signal denoisings and identification described in a kind of application based on Wavelet Entropy The pulsar signal processing system of method.
In conclusion advantages of the present invention and good effect are as follows: the present invention provides one in view of the deficiency of existing algorithm Pulsar signal denoising and discrimination method of the kind based on Wavelet Entropy;Wavelet Entropy algorithm is only used, it, can be with while signal denoising The small echo entropy amount of being characterized of signal is extracted to complete the task of identification.
Detailed description of the invention
Fig. 1 is the pulsar signal denoising provided in an embodiment of the present invention based on Wavelet Entropy and discrimination method flow chart.
Fig. 2 is the original signal waveform figure of not Noise provided in an embodiment of the present invention.
Fig. 3 is the signals and associated noises waveform diagram that signal-to-noise ratio provided in an embodiment of the present invention is 20db.
Fig. 4 is each scale discrete wavelet coefficient waveform diagram provided in an embodiment of the present invention.
Fig. 5 is each layer coefficients small echo entropy provided in an embodiment of the present invention.
Fig. 6 is the waveform diagram of signal after denoising provided in an embodiment of the present invention.
Fig. 7 is original signal provided in an embodiment of the present invention, signals and associated noises, denoised signal comparison diagram.
Fig. 8 is each layer Wavelet Entropy line chart of different pulsar signals provided in an embodiment of the present invention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.
The high frequency coefficient of present invention combination wavelet transformation, determines suitable threshold value, achievees the purpose that denoising.Gained will be calculated Characteristic parameter of the Wavelet Entropy as identification signal, achieve the purpose that identify pulsar signal.
Application principle of the invention is explained in detail with reference to the accompanying drawing.
As shown in Figure 1, the pulsar signal denoising and discrimination method provided in an embodiment of the present invention based on Wavelet Entropy includes Following steps:
S101: pulsar signal is decomposed using wavelet transformation, calculates the Wavelet Entropy in each subinterval after wavelet decomposition;It will Wavelet Entropy and wavelet threshold, which combine, determines each layer high-frequency wavelet coefficient threshold value thresholding;Arteries and veins using threshold value threshold processing with noise Rush star signal;
S102: the characteristics of differentiation is presented in the energy value according to different pulsar signals in each section;It calculates in sample Numerical value of all pulsar signals in the Wavelet Entropy in each section;
S103: by the Wavelet Entropy numerical value of each pulsar as a result, in conjunction with corresponding title, construction feature parameter is loaded into It in database, then is compared with unknown pulsar signal, and completes the identification to pulsar signal.
Pulsar signal denoising and discrimination method provided in an embodiment of the present invention based on Wavelet Entropy specifically includes following step It is rapid:
Step 1, denoising;
(1) wavelet transformation for carrying out m scale to the pulsar signal x (n) that band is made an uproar first, obtains the discrete of each scale Wavelet coefficient, the coefficient of the high fdrequency component at k moment is expressed as d under jth decomposition scaleJ, k, the coefficient of low frequency component is expressed as aJ, k, The sample frequency of signal is expressed as fs, wherein j=1,2 ..., 5;K=1,2 ..., 10;Preferably, using db6 as wavelet basis Function carries out the wavelet transform of 5 scales to pulsar sequence;
(2) according to each layer scattering wavelet coefficient, the wavelet energy E of the high frequency coefficient in each section is calculated separatelyJ, k.Letter Number jth layer coefficients dJ, kIt is divided into n section, then the energy in this layer of each section are as follows:
Wherein m is sampling number.
(3) wavelet energy distribution probability is k-th of subinterval wavelet coefficient ENERGY EJ, kWith this layer of wavelet coefficient gross energy Ej Ratio;
PJ, k=EJ, k/Ej (3)
The Wavelet Entropy W in the section KkFor;
Wk=-∑jPJ, kln(PJ, k) (4)
The maximum section of small echo entropy is found, and calculates the noise estimate variance σ in this section:
WhereinReach the wavelet coefficient intermediate value in maximum section for small echo entropy in wavelet coefficient section.System The number specific calculation method of intermediate value is as follows:
Wherein, γ1For the adjustment factor of threshold value thresholding, regulatory factorβ.According to the feature of signal, regulation coefficient and because The value of son, to adaptively determine threshold value thresholding.λjFor the threshold value of high frequency coefficient, then the threshold value of high frequency coefficient is;
Wherein, γ2For the adjustment factor of threshold value thresholding, the threshold value of each layer coefficients is adjusted according to the actual situation, and N is sample letter Number length.
Threshold process is carried out to high frequency coefficient by above formula (6), the pulsar signal after being denoised is reconstructed.Formula (8) it is the expression formula of mean square error, by calculating mean square error, obtains the performance indicator of denoising effect.
Wherein, x ' (n) is denoised signal.
Step 2: classification
(1) pulsar signal database is established, the Wavelet Entropy in each section is successively calculated according to (7) formula, as characteristic parameter, It is stored together in the database with pulsar signal title.
(2) the small echo entropy for calculating unknown pulse star signal, is compared with the data in database.Utilize two groups of signals Variance between characteristic parameter is compared, and determines whether feature has uniqueness.The formula of variance of characteristic parameter is;
VARj=[∑n(s1j(n)-s2j(n))2]1/2 (9)
Wherein, s1j(n), s2j(n) the small echo entropy of two kinds of signal jth layers.
(3) it draws a conclusion, pulsar PSR 0531+21 signal whether there is in existing database.If it does, side Difference is 0;Otherwise the pulsar is considered as not in given data storehouse.
Application principle of the invention is further described combined with specific embodiments below.
For carrying out denoising using PSR 0531+21 signal below and establish database identification, said in conjunction with attached drawing Bright a specific embodiment of the invention.
In order to which more efficiently the denoising of processing pulsar signal and identification problem, the present invention are handled simultaneously using Wavelet Entropy Both of these problems.For signal after wavelet transformation, the size of entropy reflects the position of noise power and the feature of Energy distribution.In conjunction with The above two o'clock, the present invention is by threshold denoising and aspect ratio to solving both of these problems.At the same time, the present invention is real in emulation 29 group pulse star signal characteristic databases are established as an example, compared the residual values between 21 group pulse star signals in example, Comparison process can be rapidly completed.For not unknown pulse star signal in the database, can be included in after determining pulsar title Database.The characteristic information constantly updated in property data base can also be used as the reference frame of other research contents.Specifically Implementation process includes the following steps:
Step S1: from European pulsar database (European Pulsar Network Data Archive, EPNDA) The observation data for obtaining pulsar, obtain pulsar PSR 0531+21 signal sequence by processing.Small echo is write in MATLAB Threshold denoising program.Pulsar signal sequence is read from file, as shown in Fig. 2, drawing the contour curve of pulsar.With noise Carrying out wavelet threshold denoising than the signals and associated noises for 20db is example.
The step of this example uses PSR 0531+21 signal, carries out wavelet threshold denoising is as follows:
S1-1: as shown in figure 3, drawing the PSR 0531+21 signal profile for having white Gaussian noise.Respectively to noisy pulse Star signal carries out wavelet transformation, obtains the discrete wavelet coefficient of each scale.Different values is set, preferably, find suitable Decomposition order.The wavelet transform of 5 scales is finally carried out to pulsar sequence as wavelet basis function using db6.Arteries and veins It is as shown in Figure 4 to rush star signal transformation results.
S1-2: every layer coefficients are divided into 10 sections.As shown in table 1, the high frequency in each section is calculated separately according to formula (2) The wavelet energy value of coefficient.As shown in figure 5, calculating the small echo entropy in each section according to formula (4).
The wavelet energy value of the high frequency coefficient in 1 10 sections of table
The maximum section of small echo entropy is the 6th section, and according to formula (5) calculate the noise estimate variance σ in this section= 0.0142.According to the feature of signal, the value of regulation coefficient and the factor, to adaptively determine threshold value thresholding.Threshold value thresholding Adjustment factor γ1=1.5, γ2=0.8, regulatory factorβ=1.As shown in table 2, high frequency coefficient is obtained according to formula (7) Threshold value.
The threshold value of 2 each layers of high frequency coefficient of table
Decomposition order 1 2 3 4 5
Threshold value 0.0796 0.0632 0.0300 0.0070 0.0066
Threshold process is carried out to high frequency coefficient by above formula (6), the pulsar signal after being denoised is reconstructed.Such as figure Pulsar signal waveform diagram shown in 4, after being denoised.Mean square error is calculated using formula (8), the performance for obtaining denoising effect refers to Mark.As shown in table 3, as signal-to-noise ratio becomes larger, denoising effect is become better and better.The processor of computer used in emulation experiment is Intel (R) Core (TM) i5-3470CPU@3.20Ghz, system type are 64 bit manipulation systems, the processor based on X64.Program operation On matlabR2017 platform, simulation time 0.349s.The calculation method of this example is relatively simple, is not related to complicated fortune It calculates, the speed of service is very fast.
3 PSR 0531+21 Signal-to-Noise of table and mean variance
SNR/db 5 10 20 25 30 35
RMSE 0.5098 0.2961 0.1048 0.0585 0.0348 0.0231
Step S2: using the signal sequence of 25 pulsars as sample, whether verifying Wavelet Entropy can become characteristic parameter The problem of.
S2-1: whether according to the matching degree of characteristic signal, determining Wavelet Entropy can be used as characteristic parameter steps are as follows:
S2-1-1: from European pulsar database (European Pulsar Network Data Archive, EPNDA) The observation data for obtaining pulsar, obtain the signal sequence of 25 pulsars.
S2-1-2: Wavelet Entropy identification program is write in MATLAB.Pulsar signal sequence is read from file, establishes number According to library Pulsar.mat.The Wavelet Entropy that each section is successively calculated according to (7) formula, as characteristic parameter, with pulsar signal title It is stored in the database pul_feature.mat of characteristic variable together.
S2-1-3: according to the information of database, different each layer Wavelet Entropy broken lines of pulsar signal are drawn in the same coordinate system Figure.As shown in fig. 7, wherein preceding 25 pulsar signals are the small echo entropy without the original pulse star of noise.From figure, we Available, each layer small echo entropy for being stored in the different pulsar signals of database is not completely overlapped.For different observation frequencies Same pulsar under rate, part level will appear overlapping phenomenon, this just illustrates that same pulsar has similar profile. Under different observing frequencies, profile has different performance characteristics.Same pulsar signal adds different white Gaussian noises, The difference of the Wavelet Entropy of different levels is less, and figure middle conductor tends towards stability.The small echo entropy of different levels is in certain region It floats.The case where straight line occur is less.The experimental result of amplitude from the sample of broken line fluctuation is available, different pulsar letters Number there is different small echo entropy, Wavelet Entropy can be used as the parameter of pulsar signal feature identification.
S2-2: by 25 group pulse sing datas in database, by one group of PSR 0531+21 signal and other 24 groups of signals Wavelet Entropy data do variance, the variance of the Wavelet Entropy of available different levels.
The step of S2-2-1: this example uses PSR 0531+21 signal, carries out Wavelet Entropy identification is as follows:
S2-2-1: the small echo entropy for calculating PSR 0531+21 signal obtains comparison result using formula of variance (9).Such as Shown in table 4.
The variance of pulsar signal in each layer small echo entropy and database of 4 PSR 0531+21 signal of table
S2-3: drawing a conclusion, PSR 0531+21 signal and identical PSR 0531+21 signal present in database Residual error be 0, the residual error of remaining signal is all larger than 0.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.

Claims (5)

1. a kind of pulsar signal denoising and discrimination method based on Wavelet Entropy, which is characterized in that the arteries and veins based on Wavelet Entropy It rushes star signal denoising and discrimination method includes:
The first step decomposes pulsar signal using wavelet transformation, calculates the Wavelet Entropy in each subinterval after wavelet decomposition;It will be small Wave entropy and wavelet threshold, which combine, determines each layer high-frequency wavelet coefficient threshold value thresholding;Pulse using threshold value threshold processing with noise Star signal;
The characteristics of second step, differentiation is presented in the energy value according to different pulsar signals in each section;Calculate institute in sample There is pulsar signal in the numerical value of the Wavelet Entropy in each section;
Third step, by the Wavelet Entropy numerical value of each pulsar as a result, in conjunction with corresponding title, construction feature parameter is loaded into number It is compared according in library, then with unknown pulsar signal, and completes the identification to pulsar signal.
2. the pulsar signal denoising based on Wavelet Entropy and discrimination method as described in claim 1, which is characterized in that described the One step specifically includes:
(1) wavelet transformation for carrying out m scale to the pulsar signal x (n) that band is made an uproar first, obtains the discrete wavelet of each scale Coefficient, the coefficient of the high fdrequency component at k moment is expressed as d under jth decomposition scaleJ, k, the coefficient of low frequency component is expressed as aJ, k, signal Sample frequency be expressed as fs, wherein j=1,2 ..., 5;K=1,2 ..., 10;Preferably, using db6 as wavelet basis function, The wavelet transform of 5 scales is carried out to pulsar sequence;
(2) according to each layer scattering wavelet coefficient, the wavelet energy E of the high frequency coefficient in each section is calculated separatelyJ, k;Signal jth Layer coefficients dJ, kIt is divided into n section, then the energy in this layer of each section are as follows:
Wherein m is sampling number;
(3) wavelet energy distribution probability is k-th of subinterval wavelet coefficient ENERGY EJ, kWith this layer of wavelet coefficient gross energy EjRatio Value;
PJ, k=EJ, k/Ej
The Wavelet Entropy W in the section KkAre as follows:
Wk=-∑jPJ, kln(PJ, k);
The maximum section of small echo entropy is found, and calculates the noise estimate variance σ in this section:
WhereinReach the wavelet coefficient intermediate value in maximum section for small echo entropy in wavelet coefficient section.Median coefficient Specific calculation method is as follows:
Wherein, γ1For the adjustment factor of threshold value thresholding, regulatory factorβ;According to the feature of signal, regulation coefficient and the factor Value, adaptively determines threshold value thresholding;λjFor the threshold value of high frequency coefficient, then the threshold value of high frequency coefficient are as follows:
Wherein, γ2For the adjustment factor of threshold value thresholding, the threshold value of each layer coefficients is adjusted according to the actual situation, and N is sample signal Length.
Threshold process is carried out to high frequency coefficient, the pulsar signal after being denoised is reconstructed;By calculating mean square error, obtain To the performance indicator of denoising effect;
Wherein, x ' (n) is denoised signal.
3. the pulsar signal denoising based on Wavelet Entropy and discrimination method as described in claim 1, which is characterized in that described the Two steps specifically include:
(1) pulsar signal database is established, the Wavelet Entropy in each section is successively calculated, as characteristic parameter, with pulsar signal Title is stored together in the database;
(2) the small echo entropy for calculating unknown pulse star signal, is compared with the data in database;Utilize two groups of signal characteristics Variance between parameter is compared, and determines whether feature has uniqueness;The formula of variance of characteristic parameter is;
Wherein, s1j(n), s2j(n) the small echo entropy of two kinds of signal jth layers;
(3) it draws a conclusion, pulsar PSR 0531+21 signal whether there is in existing database.If it does, variance is 0;Otherwise the pulsar is considered as not in given data storehouse.
4. a kind of pulsar signal denoising and discrimination method using described in claims 1 to 3 any one based on Wavelet Entropy Spacecraft.
5. a kind of pulsar signal denoising and discrimination method using described in claims 1 to 3 any one based on Wavelet Entropy Pulsar signal processing system.
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