CN107589441B - Pulse pile-up modification method based on Kalman filter channel - Google Patents

Pulse pile-up modification method based on Kalman filter channel Download PDF

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CN107589441B
CN107589441B CN201710798404.3A CN201710798404A CN107589441B CN 107589441 B CN107589441 B CN 107589441B CN 201710798404 A CN201710798404 A CN 201710798404A CN 107589441 B CN107589441 B CN 107589441B
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pulse signal
core pulse
kalman filter
core
signal
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CN201710798404.3A
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CN107589441A (en
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刘明哲
杨凤
何明富
刘艳华
蒋鑫
柳炳琦
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成都理工大学
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Abstract

The invention discloses a kind of pulse pile-up modification method based on Kalman filter channel, mainly solve calculating existing in the prior art it is complicated, can spectrum distortion the problems such as.This method is the following steps are included: generate core pulse signal S using pulse shapern, obtain core pulse signal SnAfterwards, by core pulse signal SnParameter carries out Initialize installation, that is, chooses the core pulse signal S of outputnAmplitude X0For 0 initial point;To the core pulse signal SnWeak signal removing processing is carried out, the core pulse signal S of accumulation is obtained1n;Differentiate and extract the core pulse signal S of accumulation1n;Kalman filter state and measurement equation are constructed, and by the core pulse signal S of extraction1nCore pulse signal S is obtained through Kalman filter2n;To the core pulse signal S2nAttenuation processing is carried out, and determines whether to meet removing standard.Through the above scheme, invention achieves the purposes of separating piled pulse event, have very high practical value and promotional value in nuclear radiation detection, nuclear electronics technology, digital processing field.

Description

Pulse pile-up modification method based on Kalman filter channel

Technical field

The present invention relates to the fields such as nuclear radiation detection, nuclear electronics technology, Digital Signal Processing, are based especially on Kalman The pulse pile-up modification method of filter channel.

Background technique

Pile-up events are that X (γ) is counted and the critical issue of spectroscopic system, especially there are parameter X-ray and positive electrons Under the high density source of emission computed tomography (PET).As one of two uncertain sources, accumulation is by particle micro- Caused by the internal factor reached in second rank time interval, so that detector cannot be eliminated accurately from previous radiation event The successor of response, to generate a signal in single pulse overlapping part.Pulse pile-up causes handling capacity reduction, extremely Area's time extends, and energy resolution reduces, and leads to radiation detection system reduced performance.

As digital processing unit (ADC) and DSP (FPGA) continue to develop, using the number of the nuclear radiation detection data of processor Word processing executes complicated algorithm to solve pileup pulse, generally comprises: data fitting method, accumulation exclusive method, filtering, transformation approach With it is miscellaneous.But custom design is needed using the electronic module that processor carries out accumulation processing, by use environment factor and electricity Gas characteristic limitation, moreover, electronic module processing pile-up events processing cost is higher.

Data fitting method is the fitting based on digit pulse reshaper to detector signal, even if in the composition close phase of signal Also it can restore pile-up events when adjacent with high precision, meanwhile, it needs largely to be calculated, wirelessly be approached using nonlinear equation The mode of waveform obtains, and amount of calculation is big.It accumulates exclusive method identification and abandons the data of damage, to reduce to the maximum extent The influence to the calculating stress on energy spectrum and processor is accumulated, still, the method is disadvantageous in that, extends dead detector zones The case where time causes energy spectrum distortion, is not suitable for high radioactivity.Currently, filter method is that most common processing is accumulated in real time Mode, such as the homogeneous Poisson process with known strength still need to eliminate Noise Algorithm before feeding filtering.Conversion Method is signal to be converted to the domain that other original bulk events do not show overlapping from time domain, but converting system needs are appropriate online It calculates and optimal separate design.These methods all realize high-precision to sacrifice calculating source.

Therefore, it is necessary to provide the accumulation modification method that a kind of calculating is easy, power spectrum distortion rate is low.

Summary of the invention

The purpose of the present invention is to provide a kind of pulse pile-up modification methods based on Kalman filter channel, main to solve Certainly calculating existing in the prior art it is complicated, can spectrum distortion the problems such as.

To achieve the goals above, The technical solution adopted by the invention is as follows:

Pulse pile-up modification method based on Kalman filter channel, comprising the following steps:

The first step generates core pulse signal S using pulse shapern, obtain core pulse signal SnAfterwards, by core pulse signal SnParameter carries out Initialize installation, that is, chooses the core pulse signal S of outputnAmplitude X0For 0 initial point.

Second step, to the core pulse signal SnIt is purged weak signal processing, obtains the core pulse signal S of accumulation1n, tool Body is as follows:

(1) Kalman filter number of channels is set as n, and in Fixed Time Interval, the maximum quantity of pile-up events is N, core pulse signal SnObtain at least one transmission channel, wherein n is the integer greater than 0.

(2) determine core pulse signal SnWeak signal,For in tkIn moment, i-ththThe amplitude of a core pulse signal. The definition of availability isWhen state.IfWhen,Then it is determined as weak signal, wherein eps is tolerance,And the weak signal is inhibited to pass through transmission channel.

Step 3: building core pulse signal S1nThe state equation of pile-up events, and differentiate and extract the core arteries and veins of the accumulation Rush signal S1n

The amplitude features of (1) first core pulse signal and extraction, i.e., and if only if the amplitude z of the first core pulse signalk1Greatly In 3 times of measurement noise δωWhen, the amplitude of the core pulse signal of extractionAnd the 4th step is allowed access into, otherwise will It is eliminated.

(2) amplitude features of other core pulse signals and extraction, and if only if survey of the deviation greater than 3 times of prediction measured value Measure noise δωWhen, i.e. current measurement value zk2Subtract residual errorGreater than 3 δωWhen, the amplitude of the core pulse signal of extractionAnd the 4th step is allowed access into, otherwise it will be eliminated.The core pulse signal S of extraction is obtained as a result,1n

Step 4: building Kalman filter, and by the core pulse signal S of extraction1nCore arteries and veins is obtained through Kalman filter Rush signal S2n

(1) core pulse signal S is established1nThe state equation of pile-up events, in time tkIt is interior, i-ththThe table of the amplitude of a pulse Show formula are as follows:

Wherein,For in t0Moment i-ththThe amplitude of a pulse, τ are attenuation constant;

In time tk+1It is interior, i-ththThe amplitude expression of a pulse are as follows:

Wherein,For in t0Moment i-ththThe amplitude of a pulse, τ are attenuation constant;

Expression (1-2) is acquired divided by expression formula (1-1) in tk+1In moment, i-ththThe amplitude of a pulse, expression formula Are as follows:

Wherein,For in t0Moment i-ththThe amplitude of a pulse, Δ τ indicate tk+1With tkTime difference, τ is that decaying is normal Number;

Metrical information t is established using expression formula (1-3)kThe state matrix X at momentk, and obtain the core arteries and veins that accumulation quantity is n Rush signal tk+1The state matrix equation X at momentk+1, expression formula are as follows:

Xk+1=FXk+Qk (1-4)

Wherein, F is state-transition matrix, QkFor with measurement noise δωThe state-noise δ unrelated with state-transition matrix Fy's Variance, XkFor tkThe state matrix at moment;

(2) core pulse signal S is established1nThe measurement equation of pile-up events, at the signal terminal of detector, metrical information tk+1The state matrix X at momentk+1And be Zk+1, expression formula are as follows:

Zk+1=HXk+1+Rk+1 (1-5)

Wherein, H is observing matrix, Xk+1For tk+1The state matrix at moment, Rk+1To measure noise δωVariance;

(3) state matrix equation (1-4) is utilized, establishes predicted state equation, expression formula are as follows:

Wherein, F is state-transition matrix,For in tk+1The state estimation at moment,For in tkThe state at moment is estimated Meter;

White noise K in pile-up events is acquired by expression formula (1-6)F, it is indicated with its covariance, establishes predictive estimation association Variance matrix, expression formula are as follows:

Pk+1|k=FPk|kFT+Qk (1-7)

Wherein, F is state-transition matrix, QkFor with measurement noise δωThe state-noise δ unrelated with state-transition matrix Fy's Variance, Pk+1|kFor priori covariance, Pk|kFor Posterior estimator error co-variance matrix, FTFor the transposition of state-transition matrix;

Using expression formula (1-7) predictive estimation covariance matrix, residual error, expression formula are calculated are as follows:

Wherein, H is observing matrix,For the deviation of current measurement value and prediction measured value, zk+1For current measurement value,For true value xk+1|kAnd predicted valueDeviation;

Expression formula (1-5) (1-6) is brought into (1-8), calculating acquires residual covariance Sk+1, expression formula are as follows:

Sk+1=HPk+1|kHT+Rk+1 (1-9)

Wherein, H is observing matrix, Pk+1|kFor priori covariance, HTFor the transposition of observing matrix, Rk+1To measure noise δω Variance;

Optimal kalman gain processing, Kalman's COEFFICIENT K are carried out to residual covariance expression formula (1-9)k+1Expression formula are as follows:

Wherein, HTFor the transposition of observing matrix, Pk+1|kFor priori covariance, Sk+1For residual covariance;

State estimation, pre-evaluation value are updated to expression formula (1-6)Its expression formula are as follows:

Wherein,For status assessmentOptimal estimation, Kk+1For kalman gain,For current measurement value and in advance Survey the deviation of measured value;

Estimate covariance is updated to expression formula (1-7), and obtains required Kalman filter, expression formula are as follows:

Wherein, Pk+1|k+1For Posterior estimator error co-variance matrix;Pk+1|kFor priori covariance, Kk+1For kalman gain, Sk+1For residual covariance,For the transposition of kalman gain;

Step 5: to the core pulse signal S2nAttenuation processing is carried out, and determines whether to meet removing standard, if so, Into second step, otherwise enters the 4th step and continue to filter.

Compared with prior art, the invention has the following advantages:

(1) core pulse signal is carried out initializing set by the present invention, in order to post-processing, determines the mode of initial value It is relatively simple.Also, introduce weak signal gives up differentiation, and data run amount is reduced by way of filtering out weak signal, is removed from The calculating time of weak signal improves operation efficiency to reduce amount of calculation.Moreover, by Kalman filter The setting in channel guarantees at least one transmission channel of core pulse signal, in this way, which the inhibition energy of weak signal can be improved Power.

(2) in addition, the present invention is when carrying out core pulse signal differentiation and extracting, ingenious setting measurement noise and signal amplitude Differentiate, be effectively prevented from interference of the noise-measuring noise to core pulse signal, in turn, realizes good under different noise conditions Anti-noise ability.

(3) moreover, the present invention measures equation and state matrix by establishing core pulse signal, carries out status assessment, And kalman gain is combined to handle, the recursion filter of Time-varying Linear Systems when acquisition, and then realize the pulse generated to X-ray detector The power spectrum distortion rate of separating piled event, pile-up events separation is low, is effectively guaranteed filter effect.

(4) present invention detects output signal at the signal terminal of detector, introduces state matrix equation, and optimize and obtain Kalman filter is obtained, filtering is realized by the correction of state, filter capacity is obviously improved.

Detailed description of the invention

Fig. 1 is that flow chart is corrected in the pulse pile-up based on Kalman filter channel.

Fig. 2 is 15 timing charts containing pile-up events.

Fig. 3 is core pulse signal through 1 pileup pulse discrete state figure of Kalman filter channel.

Fig. 4 is core pulse signal through 2 pileup pulse discrete state figure of Kalman filter channel.

Fig. 5 is core pulse signal through 3 pileup pulse discrete state figure of Kalman filter channel.

Fig. 6 is core pulse signal through 4 pileup pulse discrete state figure of Kalman filter channel.

Fig. 7 is variance δω=0.005 pile-up events discrete state figure.

Fig. 8 is variance δω=0.001 pile-up events discrete state figure.

Fig. 9 is variance δω=0.05 pile-up events discrete state figure.

Figure 10 is variance δω=0.01 pile-up events discrete state figure.

Figure 11 is the waveform diagram that X-ray tube issues.

Figure 12 is that X-ray tube issues waveform through 1 pileup pulse discrete state figure of Kalman filter channel.

Figure 13 is that X-ray tube issues waveform through 2 pileup pulse discrete state figure of Kalman filter channel.

Figure 14 is that X-ray tube issues waveform through 3 pileup pulse discrete state figure of Kalman filter channel.

Figure 15 is that X-ray tube issues waveform through 4 pileup pulse discrete state figure of Kalman filter channel.

Specific embodiment

Present invention will be further explained below with reference to the attached drawings and examples, and embodiments of the present invention include but is not limited to The following example.

The present invention provides arithmetic speed height, anti-noise abilities by force, the energy accumulation that spectrum distortion is low, pulse separation accuracy is high amendment Method has implementation as follows:

The accumulation time is that X (γ) is counted and critical issue, especially computed tomography present in spectroscopic system (PET) there are when parameter X-ray and positron emission for high density source.As one of two uncertain sources, pulse is generated The reason of accumulation is that particle reaches in very short time interval, prevents detector from eliminating response from previous radiation event Successor, to generate a signal in single pulse lap.

As shown in Figure 1, pulse pile-up modification method the following steps are included:

The first step generates core pulse signal S using pulse shapern, obtain core pulse signal SnAfterwards, by core pulse signal SnParameter carries out Initialize installation, that is, chooses the core pulse signal S of outputnAmplitude X0For 0 initial point.

Second step, to the core pulse signal SnIt is purged weak signal processing, obtains the core pulse signal S of accumulation1n, tool Body is as follows:

(1) Kalman filter number of channels is set as n, and in Fixed Time Interval, the maximum quantity of pile-up events is N, core pulse signal SnObtain at least one transmission channel, wherein n is the integer greater than 0.

(2) determine core pulse signal SnWeak signal, and the weak signal is inhibited to pass through transmission channel.

Step 3: differentiating and extracting the core pulse signal S of accumulation1n, specifically comprise the following steps:

The amplitude features of (1) first core pulse signal are greater than 3 times of survey and if only if the amplitude of the first core pulse signal When measuring noise, the first signal enters the 4th step, is otherwise eliminated.

(2) the amplitude features of other signals are greater than 3 times of measurement noise and if only if the difference of measured value and estimated value When, then enter the 4th step, is otherwise eliminated.

Step 4: building kalman filter state and measurement equation, and by the core pulse signal S of extraction1nThrough Kalman Filter obtains core pulse signal S2n, specifically comprise the following steps:

(1) state matrix equation is established.

(2) state matrix equation is utilized, establishes predicted state, and obtain predictive estimation covariance matrix;

(3) predictive estimation covariance matrix is utilized, calculates residual covariance, and carry out optimal kalman gain processing, more New estimation covariance, Kalman filter needed for obtaining.

Step 5: to the core pulse signal S2nAttenuation processing is carried out, and determines whether to meet removing standard, if so, Into second step, otherwise enters the 4th step and continue to filter.

Embodiment 1

As shown in Fig. 2, the present embodiment only produces 15 core pulse waveform S with pulse shaper1As basic data into Row explanation, the implementation of other situations is identical, repeats no more below.Due to core pulse signal be it is random, it is initial in core pulse signal When change, the amplitude of initial point need to be only set as 0.

Inhibit core pulse waveform S1Weak signal, core pulse waveform S1Differentiated and extracted, Fig. 3 to Fig. 6 is to filter through Kalman Wave device obtains waveform S after being filtered2Result.By comparison it is found that the feelings of 4 core pulses accumulation can be applicable in well Condition.

Since noise also has a great impact in the separation process of pileup pulse, by the way that not homoscedastic Gauss white noise is added The pile-up events of sound, and use variance δωEmulate the excellent effect to illustrate of the invention, true value and estimated value it is square Error amount is as shown in table 1:

δω True value Estimated value 0.005 0.00500 0.05370 0.01 0.01016 0.01087 0.05 0.04962 0.05124 0.1 0.10007 0.10589

Noise is studied to pileup pulse separating property by the way that double pile-up events of not homoscedastic white Gaussian noise are added Influence.And proposed method is quantified to the robustness of noise level using mean square error (MSE).The discrete state of acquisition As shown in Figure 7 to 10, it can thus be seen that the present invention can be effectively prevented from noise-measuring noise does to core pulse signal It disturbs, there is good anti-noise ability under different noise conditions.

Embodiment 2

The X-ray from spherical X-ray tube is detected by X-ray detector, the detected waveform of detection card is as schemed Shown in 11, the waveform is after pulse pile-up amendment of the invention, and the discrete state of acquisition is as shown in Figure 12 to Figure 15, by right Than it is found that there is the present invention X-ray pulse to accumulate separating capacity.

To sum up, the present invention dexterously uses Kalman filter, the method for proposing to solve pulse pile-up event, can not only Pulse pile-up separation is effectively performed, and is also equipped with good anti-noise ability, reduces X-ray energy spectrum distortion rate.Through applicant Validation trial, the present invention have many advantages, such as that arithmetic speed is high, anti-noise ability is strong, energy spectrum distortion is low, pulse separation accuracy is high, It can be said that compared with prior art, there is substantive distinguishing features outstanding and significant progress, in nuclear radiation detection, nuclear electronics Technology, digital processing field have wide advance and promotional value.

Above-described embodiment is merely a preferred embodiment of the present invention, and it is not intended to limit the protection scope of the present invention, as long as using Design principle of the invention, and the non-creative variation worked and made is carried out on this basis, it should belong to of the invention Within protection scope.

Claims (2)

1. the pulse pile-up modification method based on Kalman filter channel, which comprises the following steps:
P1 generates core pulse signal S using pulse shapern, obtain core pulse signal SnAfterwards, by core pulse signal SnParameter into Row Initialize installation chooses the core pulse signal S of outputnAmplitude X0For 0 initial point;
P2, to the core pulse signal SnWeak signal removing processing is carried out, the core pulse signal S of accumulation is obtained1n, and it is described clear Except weak signal processing specifically includes:
P21 sets Kalman filter number of channels as n, and in Fixed Time Interval, the maximum quantity of pile-up events is n, core Pulse signal SnObtain at least one transmission channel, wherein n is the integer greater than 0;
P22 determines core pulse signal SnWeak signal, and the weak signal is inhibited to pass through the transmission channel;
P3 differentiates and extracts the core pulse signal S of accumulation1n
P31, the amplitude features of the first core pulse signal are greater than 3 times of measurement and if only if the amplitude of the first core pulse signal When noise, the first signal enters step P4, is otherwise eliminated;
P32, the amplitude features of other signals, i.e., when the difference of measured value and estimated value is greater than 3 times of measurement noise, then P4 is entered step, is otherwise eliminated;
P4, building kalman filter state and measurement equation, and by the core pulse signal S of extraction1nIt is obtained through Kalman filter Obtain core pulse signal S2n
P5, to the core pulse signal S2nAttenuation processing is carried out, and determines whether to meet removing standard, if so, entering step Otherwise P2 enters step P4 and continues to filter.
2. the pulse pile-up modification method according to claim 1 based on Kalman filter channel, which is characterized in that institute It states in step P4, constructs Kalman filter, specifically comprise the following steps:
P41 establishes state matrix equation and measurement equation;
P42 establishes predicted state using state matrix equation, and obtains predictive estimation covariance matrix;
P43 calculates residual covariance, and carry out optimal kalman gain using predictive estimation covariance matrix and measurement equation Processing updates estimate covariance, Kalman filter needed for obtaining.
CN201710798404.3A 2017-09-07 2017-09-07 Pulse pile-up modification method based on Kalman filter channel CN107589441B (en)

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CN104848862A (en) * 2015-06-05 2015-08-19 武汉大学 Precise and synchronous positioning and time-keeping method and system of Mars orbiting detector
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CN103454671A (en) * 2013-08-21 2013-12-18 中国人民解放军第二炮兵工程大学 Nuclear radiation pulse accumulation judging and correcting method based on high-speed digital sampling
CN103940447A (en) * 2014-04-11 2014-07-23 哈尔滨工程大学 Mooring state initial aligning method based on self-adaptive digital filter
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