CN111404542A - Double-exponential nuclear signal counting method and device - Google Patents

Double-exponential nuclear signal counting method and device Download PDF

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CN111404542A
CN111404542A CN202010249031.6A CN202010249031A CN111404542A CN 111404542 A CN111404542 A CN 111404542A CN 202010249031 A CN202010249031 A CN 202010249031A CN 111404542 A CN111404542 A CN 111404542A
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CN111404542B (en
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周建斌
王明
喻杰
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Sichuan Xstar Measurement Control Technology Co ltd
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    • H—ELECTRICITY
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Abstract

The application provides a double-exponential nuclear signal counting method and a device, which relate to the technical field of nuclear signal processing, and the method comprises the following steps: acquiring a dual-index nuclear signal to be counted; inputting the dual-exponential nuclear signal to be counted to a pre-established transfer function, and acquiring an impulse signal output by the transfer function; and counting the to-be-counted double-exponential nuclear signals according to the impulse signals. In the implementation process, the dual-exponential nuclear signal to be counted is input to a pre-established transfer function, the output signal is an impulse signal with short dead time, a sampling period is occupied, and the dual-exponential nuclear signal is accurately counted by identifying accumulated nuclear signals.

Description

Double-exponential nuclear signal counting method and device
Technical Field
The application relates to the technical field of nuclear signal processing, in particular to a double-exponential nuclear signal counting method and device.
Background
To obtain accurate nuclear information in nuclear science technology, it is often necessary to electronically detect nuclear signals and extract nuclear information from the nuclear signals. With the development of high-speed digital processing chips and high-speed ADCs, the digitization of core signals and the digital processing technology thereof are gradually mature. However, at high counting rates, the pile-up between nuclear signals is severe, which greatly reduces the counting accuracy of the nuclear signals. In order to obtain more accurate counting rate information, the main solutions at present are: a method for reducing the width of the kernel signal, a maximum likelihood estimation method and a single exponential impulse forming method. However, the kernel signals output by these methods are still relatively wide, and the accumulation dead time of the kernel signals is still relatively large, so that the dual-index kernel signals cannot be accurately counted under the condition of high counting rate.
Disclosure of Invention
An embodiment of the present invention provides a method and an apparatus for counting dual-exponential nuclear signals, so as to solve the problem that the prior art cannot accurately count the dual-exponential nuclear signals.
In a first aspect, an embodiment of the present application provides a double-exponential nuclear signal counting method, where the method includes: acquiring a dual-index nuclear signal to be counted; inputting the dual-exponential nuclear signal to be counted to a pre-established transfer function, and acquiring an impulse signal output by the transfer function; and counting the to-be-counted double-exponential nuclear signals according to the impulse signals.
In the implementation process, the dual-exponential nuclear signal to be counted is input to the pre-established transfer function, and the system can convert the dual-exponential nuclear signal into a narrow-beam output impulse signal, so that the dual-exponential nuclear signal can be accurately counted.
Optionally, before the bi-exponential nuclear signal to be counted is input to the pre-established transfer function, the method includes: acquiring an ideal bi-exponential nuclear signal and an ideal impulse signal corresponding to the ideal bi-exponential nuclear signal; and establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal.
In the implementation process, in order to enable the established transfer function to accurately output the impulse signal according to the input dual-exponential nuclear signal to be counted, an ideal dual-exponential nuclear signal and an ideal impulse signal corresponding to the ideal dual-exponential nuclear signal can be selected when the transfer function is established, so that the transfer function can accurately output the output signal according to the input signal, and then the dual-exponential nuclear signal is accurately counted.
Optionally, the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) The ideal impulse signal is vo(t) ═ a (t), where a represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant of the slow component in the ideal bi-exponential nuclear signal, and M represents the decay time constant of the fast component in the ideal bi-exponential nuclear signal; the establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal includes: processing the ideal dual-exponential kernel signal and the ideal impulse signal in a Z transformation mode, and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure BDA0002433750250000021
wherein H (z) represents the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period; and sorting the transfer function to be sorted according to the sampling period to obtain a sorting transfer function, wherein the sorting transfer function is as follows: (d)1-d2)z-1vo[z]＝(1-d1z-1)(1-d2z-1)vi[z](ii) a And performing inverse transformation on the sorting transfer function to obtain the transfer function, wherein the transfer function is as follows:
Figure BDA0002433750250000022
wherein v isiRepresenting the input bi-exponential nuclear signal, voRepresenting the output impulse signal.
In the implementation process, a transfer function is directly established according to the ideal double-exponential nuclear signal and the ideal impulse signal, the transfer function can effectively convert the input double-exponential signal into an impulse response output signal, and the pulse accumulation of the double-exponential nuclear signal to be counted is effectively identified, so that the double-exponential nuclear signal can be accurately counted.
Optionally, the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) The ideal impulse signal is vo(t) ═ a (t), where a represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant of the slow component in the ideal bi-exponential nuclear signal, and M represents the decay time constant of the fast component in the ideal bi-exponential nuclear signal; the establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal includes: processing the ideal dual-exponential kernel signal and the ideal impulse signal in a Z transformation mode, and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure BDA0002433750250000031
wherein H (z) represents the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period; arranging the transfer functions to be arranged into a cascade function according to a cascade decomposition principle, wherein the cascade function comprises a first sub-function, a second sub-function, a third sub-function and a fourth sub-function, and the cascade function is as follows: h (z) ═ H1(z)·H2(z)·H3(z)·H4(z) wherein H1(z)＝(1-d1z-1)，H1(z) represents the first sub-function for converting the slow component of the input bi-exponential kernel signal into a unit impulse output signal, H2(z)＝(1-d1z-1)，H2(z) represents the second sub-function for converting fast components in the input bi-exponential kernel signal into a unit impulse output signal, H3(z)＝z，H3(z) represents the third sub-function for aligning the input dual fingersThe time when the nuclear signal is generated;
Figure BDA0002433750250000032
H4(z) representing the fourth sub-function, which is an amplifier for amplifying the output signal amplitude; performing inverse transformation on the first sub-function, the second sub-function, the third sub-function, and the fourth sub-function, respectively, to establish the transfer function, where the transfer function is:
Figure BDA0002433750250000041
wherein v is1(n) first intermediate variable representing input bi-exponential kernel signal, v2(n) a second intermediate variable representing the input bi-exponential nuclear signal, v3(n) a third intermediate variable representing the input bi-exponential nuclear signal, v0And (n) represents an output impulse signal.
In the implementation process, transfer functions comprising different sub-functions are established according to the ideal bi-exponential nuclear signals and the ideal impulse signals, the different sub-functions have different functions, and parameter values in the transfer functions can be changed according to actual requirements, so that output signals can effectively identify pulses accumulated by the bi-exponential nuclear signals to be counted, and therefore the bi-exponential nuclear signals can be accurately counted.
Alternatively, when d1＝e-1/τSaid output impulse signal v0(n) the slow component tail is eliminated; where τ represents the decay time constant.
Alternatively, when d2＝e-1/τSaid output impulse signal v0(n) the fast component tail in (n) is eliminated; where τ represents the decay time constant.
In a second aspect, an embodiment of the present application provides a double-exponential nuclear signal counting apparatus, where the apparatus includes: the device comprises a to-be-counted dual-index nuclear signal acquisition module, a counting module and a counting module, wherein the to-be-counted dual-index nuclear signal acquisition module is used for acquiring a to-be-counted dual-index nuclear signal; the impulse signal acquisition module is used for inputting the dual-exponential kernel signal to be counted to a pre-established transfer function and acquiring an impulse signal output by the transfer function; and the counting module is used for counting the dual-exponential nuclear signals to be counted according to the impulse signals.
Optionally, the apparatus comprises: an ideal signal obtaining module, configured to obtain an ideal bi-exponential nuclear signal and an ideal impulse signal corresponding to the ideal bi-exponential nuclear signal; and the transfer function establishing module is used for establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal.
Optionally, the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) The ideal impulse signal is vo(t) ═ a (t), where a represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant of the slow component in the ideal bi-exponential nuclear signal, and M represents the decay time constant of the fast component in the ideal bi-exponential nuclear signal; the transfer function establishing module comprises: a first transfer function establishing unit, configured to perform Z transform processing on the ideal bi-exponential kernel signal and the ideal impulse signal, and establish a transfer function to be sorted, where the transfer function to be sorted is:
Figure BDA0002433750250000051
wherein H (z) represents the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period; a sorting transfer function obtaining unit, configured to sort the transfer function to be sorted according to the sampling period to obtain a sorting transfer function, where the sorting transfer function is: (d)1-d2)z-1vo[z]＝(1-d1z-1)(1-d2z-1)vi[z](ii) a A transfer function obtaining unit, configured to perform inverse transformation on the sorted transfer function to obtain the transfer function, where the transfer function is:
Figure BDA0002433750250000052
wherein v isiRepresenting input dual-exponential kernelsSignal, voRepresenting the output impulse signal.
Optionally, the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) The ideal impulse signal is vo(t) ═ a (t), where a represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant of the slow component in the ideal bi-exponential nuclear signal, and M represents the decay time constant of the fast component in the ideal bi-exponential nuclear signal; the transfer function establishing module comprises: a second transfer function establishing unit, configured to process the ideal bi-exponential kernel signal and the ideal impulse signal in a Z transform manner, and establish a transfer function to be sorted, where the transfer function to be sorted is:
Figure BDA0002433750250000053
wherein H (z) represents the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period; a cascade function obtaining unit, configured to sort the transfer function to be sorted into a cascade function according to a cascade decomposition principle, where the cascade function includes a first sub-function, a second sub-function, a third sub-function, and a fourth sub-function, and the cascade function is: h (z) ═ H1(z)·H2(z)·H3(z)·H4(z) wherein H1(z)＝(1-d1z-1)，H1(z) represents the first sub-function for converting the slow component of the input bi-exponential kernel signal into a unit impulse output signal, H2(z)＝(1-d1z-1)，H2(z) represents the second sub-function for converting fast components in the input bi-exponential kernel signal into a unit impulse output signal, H3(z)＝z，H3(z) representing the third sub-function for aligning the instants of generation of the input bi-exponential kernel signal,
Figure BDA0002433750250000061
H4(z) representing the fourth sub-function, which is an amplifier, for adjusting the output impulse signal amplitude; performing inverse transformation on the first sub-function, the second sub-function, and the third sub-function, respectively, to establish the transfer function, where the transfer function is:
Figure BDA0002433750250000062
wherein v is1(n) first intermediate variable representing input bi-exponential kernel signal, v2(n) a second intermediate variable representing the input bi-exponential nuclear signal, v3(n) a third intermediate variable representing the input bi-exponential nuclear signal, v0And (n) represents an output impulse signal.
Alternatively, when d1＝e-1/τSaid output impulse signal v0(n) the slow component tail is eliminated; where τ represents the decay time constant.
Alternatively, when d2＝e-1/τSaid output impulse signal v0(n) wherein the trailing of the fast component is eliminated; where τ represents the decay time constant.
In a third aspect, an embodiment of the present application provides an electronic device, including a processor and a memory, where the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the processor, the electronic device executes the method provided in the first aspect.
In a fourth aspect, embodiments of the present application provide a readable storage medium, on which a computer program is stored, where the computer program runs the method provided in the first aspect as described above when being executed by a processor.
Additional features and advantages of the present application will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the embodiments of the present application. The objectives and other advantages of the application may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
Fig. 1 is a flowchart of a method for counting a dual-exponential core signal according to an embodiment of the present application;
fig. 2 is a schematic diagram of a nuclear signal screening system according to an embodiment of the present disclosure;
fig. 3 is a flowchart of a transfer function establishing method according to an embodiment of the present application;
fig. 4 is a schematic diagram of a dual-exponential core signal and an impulse signal according to an embodiment of the present application;
fig. 5 is a flowchart of another transfer function establishing method provided in the embodiment of the present application;
FIG. 6 is a schematic diagram of input signals and output signals of a transfer function according to an embodiment of the present application;
FIG. 7 is a schematic diagram of input signals and output signals of another transfer function provided by an embodiment of the present application;
fig. 8 is a block diagram of a dual-exponent core signal counting apparatus according to an embodiment of the present disclosure;
fig. 9 is a block diagram of an electronic device according to an embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present application, the terms "first", "second", and the like are used only for distinguishing the description, and are not to be construed as indicating or implying relative importance.
To obtain accurate nuclear information in nuclear science technology, it is often necessary to electronically detect nuclear signals and extract nuclear information from the nuclear signals. With the development of high-speed digital processing chips and high-speed ADCs, the digitization of core signals and the digital processing technology thereof are gradually mature. However, at high counting rates, the pile-up between nuclear signals is severe, which greatly reduces the counting accuracy of the nuclear signals. In order to obtain more accurate counting rate information, the main solutions at present are: a method for reducing the width of the kernel signal, a maximum likelihood estimation method and a single exponential impulse forming method. However, the kernel signals output by these methods are still relatively wide, and the accumulation dead time of the kernel signals is still relatively large, so that the dual-index kernel signals cannot be accurately counted under the condition of high counting rate.
In order to obtain a high-counting-rate and high-precision energy spectrum, a fast-slow channel energy spectrum obtaining model is provided at present, the slow channel forming time is longer, so that higher energy resolution can be obtained, the fast channel accumulation dead time is short, and more accurate counting rate can be obtained. The existing slow channel forming method mainly adopts trapezoidal forming, and on the aspect of fast channel forming, a stacking discrimination impulse system for single-index nuclear signal research, a deconvolution unit impulse forming system and the like are provided, and the problem of stacking dead time of single-index nuclear signals can be mainly solved. However, the method ignores that the core signal is a quasi-dual-exponential signal with a certain rising edge, so that the accumulation dead time in the fast forming system is still longer, and the problem that the dual-exponential core signal cannot be accurately counted is caused.
In order to accurately count the dual-exponential nuclear signals, an embodiment of the present application provides a dual-exponential nuclear signal counting method, please refer to fig. 1, which includes the following steps:
step S110: and acquiring a double-index nuclear signal to be counted.
The dual-index nuclear signal to be counted can be obtained through the SDD detector, the SDD detector needs a certain time to collect electric charges generated by radiation, the nuclear signal has a certain rising time, the nuclear signal becomes a negative index signal after passing through the C-R network, the time constant is tau RC, and when the nuclear signal is transmitted through the front-end circuit, due to the influences of distributed capacitance and resistance, the output nuclear signal is converted into a quasi-dual-index nuclear signal.
Step S120: and inputting the dual-exponential kernel signal to be counted to a pre-established transfer function, and acquiring an impulse signal output by the transfer function.
Step S130: and counting the double-exponential nuclear signals to be counted according to the impulse signals.
In the digital nuclear signal processing, the nuclear signal discriminating system can be used to discriminate the time of generating the nuclear signal and record the number of the nuclear signals, as shown in fig. 2, which is a schematic diagram of the nuclear signal discriminating system, wherein v (t) input by the system is a dual-exponential nuclear signal to be counted, and s (t) output is an ideal impulse signal, and the time of generating the impulse signal can be used to position the time of generating the nuclear signal in the dual-exponential nuclear signal, and can also be used to count the nuclear signal in the dual-exponential nuclear signal.
In the implementation process, the dual-exponential nuclear signal to be counted is input to the pre-established transfer function, and the pre-established transfer function can solve the problem of long accumulation dead zone time, so that the impulse signal can be accurately output, and the dual-exponential nuclear signal can be accurately counted.
Before the bi-exponential nuclear signal to be counted is input to the pre-established transfer function, the transfer function needs to be established, and in order to ensure the accuracy of the transfer function, an ideal bi-exponential nuclear signal and an ideal impulse signal corresponding to the ideal bi-exponential nuclear signal can be obtained first, and then the transfer function is established according to the ideal bi-exponential nuclear signal and the ideal impulse signal.
In order to enable the established transfer function to accurately output impulse signals according to the input dual-exponential nuclear signals to be counted, the ideal dual-exponential nuclear signals and the ideal impulse signals corresponding to the ideal dual-exponential nuclear signals can be selected when the transfer function is established, so that the transfer function can accurately output signals according to the input signals, and then the dual-exponential nuclear signals are accurately counted.
In order to meet different core signal processing requirements, the embodiments of the present application provide the following two different ways to establish the transfer function.
As a first embodiment, the transfer function may be established directly. Taking an ideal bi-exponential nuclear signal as vi(t)＝A(e-t/M-e-t/m) Ideal impulse signal is vo(t) ═ A (t), where A represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant for the slow component of the ideal bi-exponential nuclear signal, and M represents the decay time constant for the fast component of the ideal bi-exponential nuclear signal. Referring to fig. 3, fig. 3 is a flowchart of a transfer function establishing method according to an embodiment of the present application, where a process of establishing a transfer function according to an ideal bi-exponential kernel signal and an ideal impulse signal includes the following steps:
step S310: processing the ideal double-exponential kernel signal and the ideal impulse signal in a Z transformation mode, and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure BDA0002433750250000101
where H (z) denotes the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period;
step S320: and arranging the transfer function to be arranged according to the sampling period to obtain an arrangement transfer function, wherein the arrangement transfer function is as follows:
(d1-d2)z-1vo[z]＝(1-d1z-1)(1-d2z-1)vi[z]；
step S330: and performing inverse transformation on the principle transfer function to obtain a transfer function, wherein the transfer function is as follows:
Figure BDA0002433750250000102
wherein v isiRepresenting the input bi-exponential nuclear signal, voRepresenting the output impulse signal.
According to the formula v representing an ideal bi-exponential nuclear signali(t)＝A(e-t/M-e-t/m) Taking the slow component decay time constant M in the ideal bi-exponential nuclear signal as 50, the fast component decay time constant M in the ideal bi-exponential nuclear signal as 2.5, the number of stacked pulses as 5, and the stacking time width as 4Ts, 10Ts, 20Ts, and 50Ts in sequence, simulating in MAT L AB, please refer to fig. 4, where fig. 4 is a schematic diagram of a bi-exponential nuclear signal and an impulse signal provided in the embodiment of the present application, it can be seen that the ideal bi-exponential nuclear signal is a continuous signal, and then inputting the ideal bi-exponential nuclear signal to a transfer function, an impulse signal can be obtained, and the impulse signal is simulated, that is, the discrete signal in fig. 4, and the impulse signal has 5 impulse responses, that is, the pulse stacking of the bi-exponential nuclear signal to be counted can be effectively identified according to the transfer function established by the method.
In the implementation process, a transfer function is directly established according to the ideal double-exponential nuclear signal and the ideal impulse signal, the transfer function can effectively identify the impulse response in the input nuclear signal, and effectively identify the stacked double-exponential nuclear signal to be counted, so that the double-exponential nuclear signal can be accurately counted.
As a second embodiment, a transfer function may be established that includes a plurality of sub-functions. Taking an ideal bi-exponential nuclear signal as vi(t)＝A(e-t/M-e-t/m) Ideal impulse signal is vo(t) ═ a (t), where a represents ideally bisThe amplitude of the exponential nuclear signal, t represents time, t is more than or equal to 0, M represents a slow component decay time constant in the ideal bi-exponential nuclear signal, and M represents a fast component decay time constant in the ideal bi-exponential nuclear signal.
Referring to fig. 5, fig. 5 is a flowchart of another transfer function establishing method according to an embodiment of the present application, where a process of establishing a transfer function according to an ideal bi-exponential kernel signal and an ideal impulse signal includes the following steps:
step S410: processing the ideal double-exponential kernel signal and the ideal impulse signal in a Z transformation mode, and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure BDA0002433750250000111
where H (z) denotes the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period;
step S420: the transfer function to be sorted is sorted into a cascade function according to a cascade decomposition principle, the cascade function comprises a first sub-function, a second sub-function, a third sub-function and a fourth sub-function, and the cascade function is as follows:
H(z)＝H1(z)·H2(z)·H3(z)·H4(z) wherein H1(z)＝(1-d1z-1)，H1(z) denotes a first sub-function for converting the slow component of the input bi-exponential kernel signal into a unit impulse output signal, H2(z)＝(1-d1z-1)，H2(z) denotes a second sub-function for converting fast components in the input bi-exponential kernel signal into a unit impulse output signal, H3(z)＝z，H3(z) representing a third sub-function for aligning the time instants at which the input bi-exponential kernel signals are generated;
Figure BDA0002433750250000121
H4(z) represents a fourth sub-functionAnd the fourth sub-function is an amplifier used for adjusting the amplitude of the output impulse signal.
Step S430: respectively carrying out inverse transformation on the first sub-function, the second sub-function, the third sub-function and the fourth sub-function to establish a transfer function, wherein the transfer function is as follows:
Figure BDA0002433750250000122
wherein v is1(n) first intermediate variable representing input bi-exponential kernel signal, v2(n) a second intermediate variable representing the input bi-exponential nuclear signal, v3(n) a third intermediate variable representing the input bi-exponential nuclear signal, v0And (n) represents an output impulse signal.
First subfunction H1(z) for eliminating slow component long tail in the bi-exponential nuclear signal, for example, the original bi-exponential nuclear signal as shown in the upper left diagram in fig. 6 may be obtained by using a method of acquiring the output signal of the SDD detector by using a high-speed ADC clocked at 20MHz, and in order to study the influence of the key parameters of different sub-functions in the transfer function on the output signal, the original bi-exponential nuclear signal may be preliminarily calculated by fitting, where the slow component decay time constant M of the original bi-exponential nuclear signal is 50, the fast component decay time constant M of the original bi-exponential nuclear signal is 5/3, and then d is d1、d2Respectively is d1 *＝e-1/50、d2 *＝e-3/5While separately applying d in the transfer function1Get e-1/10、e-1/50And e-1/200Three values, then according to the first intermediate variable v of the transfer function1(n) calculate the output signal as shown in the upper right, lower left and lower right plots of FIG. 6, respectively. The upper right-hand diagram in FIG. 6 shows the equation d1<d1 *The output signal of the time transfer function, where v can be seen1(n) has a long tail with positive term attenuation, and the upper right graph in FIG. 6 shows that when d is1>d1 *The output signal of the time transfer function, where v can be seen1(n) long tail signal with negative term output signal, the upper right graph in FIG. 6 representingWhen d is1＝d1 *The output signal of the time transfer function, where v can be seen1The output signal of (n) has no long tail, i.e. the transfer function can eliminate tail due to slow components in the output signal.
Third subfunction H3(z) for the second subfunction H2(z) time-advanced by one bit, the fourth sub-function H4(z) is amplifier only, the second sub-function H2(z) for eliminating stacking due to fast component tailing in the bi-exponential nuclear signal, for example, the original bi-exponential nuclear signal as shown in the upper left diagram in fig. 7 can be obtained by using the method of acquiring the output signal of the SDD detector through the high-speed ADC with the clock of 20MHz, in order to ensure accurate study of d2The influence on the output signal of the transfer function can be taken as d1＝d1 *＝e-1/50. First, d in the transfer function2Get e-5/5Then output impulse signal v according to the transfer functiono(n) calculating the output signal, which is shown in the upper right-hand diagram of FIG. 7, and then calculating d in the transfer function2Get e-3/5Then output impulse signal v according to the transfer functiono(n) calculating the output signal, which is shown in the lower left corner of FIG. 7, and finally d in the transfer function2Get e-6/5Then output impulse signal v according to the transfer functiono(n) calculating the output signal, which is shown in the lower right hand diagram of FIG. 7, it can be seen that when d is2>d2 *When the output signal of the transfer function presents a reverse impulse sequence, approximately 5 continuous impulse sequences with larger share are output, when d2<d2 *When the output signal of the transfer function presents the same direction impulse sequence, about 5 continuous impulse sequences with larger share are output, and when d2＝d2 *The output signal of the time transfer function outputs a homodromous impulse sequence, and outputs a continuous impulse sequence with 2 shares larger than that of an ideal output signal, but not an impulse point of the ideal output signal, because the real core signal is not an ideal double-exponential but has a double-exponential-like core signal. That is to say that the position of the first electrode,due to the second sub-function H2(z) is used for eliminating fast component tailing in the double-exponential nuclear signal, and the transfer function in the application can obtain more accurate output signals, so that the double-exponential nuclear signal is accurately counted.
In the implementation process, transfer functions comprising different sub-functions are established according to the ideal double-exponential nuclear signals and the ideal impulse signals, the different sub-functions have different functions, and parameter values in the transfer functions can be changed according to actual requirements, so that pulse accumulation of the double-exponential nuclear signals to be counted can be effectively identified by the output signals, and the double-exponential nuclear signals can be accurately counted.
According to the implementation process, when d is1＝e-1/τTime-lapse, output impulse signal v0The slow-to-tail in (n) is eliminated; where τ represents the decay time constant.
From the above implementation, it can also be seen that when d2＝e-1/τTime-lapse, output impulse signal v0(n) wherein the trailing of the fast component is eliminated; where τ represents the decay time constant.
Based on the same inventive concept, an embodiment of the present application further provides a dual-exponent nuclear signal counting apparatus 100, please refer to fig. 8, and fig. 8 is a block diagram of the dual-exponent nuclear signal counting apparatus 100 according to the embodiment of the present application. The apparatus may be a module, a program segment, or code on an electronic device. It should be understood that the double-exponential nuclear signal counting device 100 corresponds to the above-mentioned embodiment of the method of fig. 1, and can perform the steps related to the embodiment of the method of fig. 1, and the specific functions of the double-exponential nuclear signal counting device 100 can be referred to the above description, and the detailed description is appropriately omitted here to avoid redundancy.
Optionally, the double-exponential nuclear signal counting apparatus 100 includes:
a to-be-counted dual-index nuclear signal obtaining module 110, configured to obtain a to-be-counted dual-index nuclear signal;
the impulse signal obtaining module 120 is configured to input the dual-exponential kernel signal to be counted to a pre-established transfer function, and obtain an impulse signal output by the transfer function;
and the counting module 130 is configured to count the dual-exponential core signal to be counted according to the impulse signal.
Optionally, the apparatus comprises:
the ideal signal acquisition module is used for acquiring an ideal bi-exponential nuclear signal and an ideal impulse signal corresponding to the ideal bi-exponential nuclear signal;
and the transfer function establishing module is used for establishing a transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal.
Optionally, the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) Ideal impulse signal is vo(t) ═ a (t), where a represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant of the slow component in the ideal bi-exponential nuclear signal, and M represents the decay time constant of the fast component in the ideal bi-exponential nuclear signal;
the transfer function establishing module comprises:
the first transfer function establishing unit to be sorted is used for processing the ideal double-exponential kernel signal and the ideal impulse signal in a Z transformation mode and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure BDA0002433750250000151
where H (z) denotes the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period;
the arrangement transfer function obtaining unit is used for arranging the transfer function to be arranged according to the sampling period to obtain an arrangement transfer function, and the arrangement transfer function is as follows:
(d1-d2)z-1vo[z]＝(1-d1z-1)(1-d2z-1)vi[z]；
a transfer function obtaining unit, configured to perform inverse transformation on the rational transfer function to obtain a transfer function, where the transfer function is:
Figure BDA0002433750250000152
wherein v isiRepresenting the input bi-exponential nuclear signal, voRepresenting the output impulse signal.
Optionally, the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) Ideal impulse signal is vo(t) ═ a (t), where a represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M represents the decay time constant of the slow component in the ideal bi-exponential nuclear signal, and M represents the decay time constant of the fast component in the ideal bi-exponential nuclear signal;
the transfer function establishing module comprises:
a second transfer function establishing unit to be sorted, configured to process the ideal bi-exponential kernel signal and the ideal impulse signal in a Z transform manner, and establish a transfer function to be sorted, where the transfer function to be sorted is:
Figure BDA0002433750250000153
where H (z) denotes the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period;
a cascade function obtaining unit, configured to sort the transfer function to be sorted into a cascade function according to a cascade decomposition principle, where the cascade function includes a first subfunction, a second subfunction, a third subfunction, and a fourth subfunction, and the cascade function is:
H(z)＝H1(z)·H2(z)·H3(z)·H4(z) wherein H1(z)＝(1-d1z-1)，H1(z) denotes a first sub-function for converting slow components in the input bi-exponential kernel signal into a unit impulse output signal, H2(z)＝(1-d1z-1)，H2(z) represents a second sub-function for doubling the inputConversion of fast components in the exponential kernel signal into a unit impulse output signal, H3(z)＝z，H3(z) representing a third sub-function for aligning the time instants at which the input bi-exponential kernel signals are generated;
Figure BDA0002433750250000161
H4(z) representing a fourth sub-function, the fourth sub-function being an amplifier for adjusting the amplitude of the output impulse signal;
a second transfer function establishing unit, configured to perform inverse transformation on the first sub-function, the second sub-function, the third sub-function, and the fourth sub-function, respectively, to establish a transfer function, where the transfer function is:
Figure BDA0002433750250000162
wherein v is1(n) first intermediate variable representing input bi-exponential kernel signal, v2(n) a second intermediate variable representing the input bi-exponential nuclear signal, v3(n) a third intermediate variable representing the input bi-exponential nuclear signal, v0And (n) represents an output impulse signal.
Alternatively, when d1＝e-1/τTime-lapse, output impulse signal v0(n) the slow component tail is eliminated; where τ represents the decay time constant.
Alternatively, when d2＝e-1/τTime-lapse, output impulse signal v0(n) the fast component tail in (n) is eliminated; where τ represents the decay time constant.
Referring to fig. 9, fig. 9 is a block diagram of an electronic device according to an embodiment of the present disclosure, where the electronic device includes: at least one processor 901, at least one communication interface 902, at least one memory 903, and at least one communication bus 904. Wherein the communication bus 904 is used for implementing direct connection communication of these components, the communication interface 902 is used for communicating signaling or data with other node devices, and the memory 903 stores machine readable instructions executable by the processor 901. When the electronic device is in operation, the processor 901 communicates with the memory 903 via the communication bus 904, and the machine-readable instructions when called by the processor 901 perform the methods described above.
The processor 901 may be an integrated circuit chip having signal processing capabilities. The processor 901 may be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. Which may implement or perform the various methods, steps, and logic blocks disclosed in the embodiments of the present application. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The Memory 903 may include, but is not limited to, a Random Access Memory (RAM), a Read Only Memory (ROM), a Programmable Read Only Memory (PROM), an Erasable Read Only Memory (EPROM), an electrically Erasable Read Only Memory (EEPROM), and the like.
It will be appreciated that the configuration shown in fig. 9 is merely illustrative and that the electronic device may include more or fewer components than shown in fig. 9 or have a different configuration than shown in fig. 9. The components shown in fig. 9 may be implemented in hardware, software, or a combination thereof. In this embodiment of the application, the electronic device may be, but is not limited to, a dedicated detection device, a desktop, a notebook computer, a smart phone, an intelligent wearable device, a vehicle-mounted device, or other physical devices, and may also be a virtual device such as a virtual machine. In addition, the electronic device is not necessarily a single device, but may also be a combination of multiple devices, such as a server cluster, and the like.
The embodiment of the present application provides a readable storage medium, and when being executed by a processor, the computer program performs the method processes performed by the electronic device in the method embodiment shown in fig. 1.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working process of the apparatus described above may refer to the corresponding process in the foregoing method, and will not be described in too much detail herein.
In summary, the present application provides a method and an apparatus for counting a dual-exponential nuclear signal, the method comprising: acquiring a dual-index nuclear signal to be counted; inputting the dual-exponential nuclear signal to be counted to a pre-established transfer function, and acquiring an impulse signal output by the transfer function; and counting the to-be-counted double-exponential nuclear signals according to the impulse signals. In the implementation process, the dual-exponential nuclear signal to be counted is input to a pre-established transfer function, the output signal is an impulse signal with short dead time, a sampling period is occupied, and the dual-exponential nuclear signal is accurately counted by identifying accumulated nuclear signals.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Furthermore, the functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (10)

1. A method of double-exponential nuclear signal counting, the method comprising:
acquiring a dual-index nuclear signal to be counted;
inputting the dual-exponential nuclear signal to be counted to a pre-established transfer function, and acquiring an impulse signal output by the transfer function;
and counting the to-be-counted double-exponential nuclear signals according to the impulse signals.
2. The method of claim 1, wherein prior to inputting the bi-exponential kernel signal to be counted to the pre-established transfer function, the method comprises:
acquiring an ideal bi-exponential nuclear signal and an ideal impulse signal corresponding to the ideal bi-exponential nuclear signal;
and establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal.
3. The method of claim 2, wherein the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) The ideal impulse signal is vo(t) ═ a (t), where a represents the ideal bisThe amplitude of the exponential nuclear signal, t represents time, t is more than or equal to 0, M represents a slow component decay time constant in the ideal bi-exponential nuclear signal, and M represents a fast component decay time constant in the ideal bi-exponential nuclear signal;
the establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal includes:
processing the ideal dual-exponential kernel signal and the ideal impulse signal in a Z transformation mode, and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure FDA0002433750240000011
wherein H (z) represents the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period;
and sorting the transfer function to be sorted according to the sampling period to obtain a sorting transfer function, wherein the sorting transfer function is as follows:
(d1-d2)z-1vo[z]＝(1-d1z-1)(1-d2z-1)vi[z]；
and performing inverse transformation on the sorting transfer function to obtain the transfer function, wherein the transfer function is as follows:
Figure FDA0002433750240000021
wherein v isiRepresenting the input bi-exponential nuclear signal, voRepresenting the output impulse signal.
4. The method of claim 3, wherein the ideal bi-exponential nuclear signal is vi(t)＝A(e-t/M-e-t/m) The ideal impulse signal is vo(t) ═ A (t), where A represents the amplitude of the ideal bi-exponential nuclear signal, t represents time, t ≧ 0, M tableShowing a decay time constant of a slow component in the ideal bi-exponential nuclear signal, and m showing a decay time constant of a fast component in the ideal bi-exponential nuclear signal;
the establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal includes:
processing the ideal dual-exponential kernel signal and the ideal impulse signal in a Z transformation mode, and establishing a transfer function to be sorted, wherein the transfer function to be sorted is as follows:
Figure FDA0002433750240000022
wherein H (z) represents the transfer function to be collated, vo[z]Denotes vo(t) Z transformation, vi[z]Denotes vi(t) Z transformation, d1＝e-Ts/M，d2＝e-Ts/MTs denotes the sampling period;
arranging the transfer functions to be arranged into a cascade function according to a cascade decomposition principle, wherein the cascade function comprises a first sub-function, a second sub-function, a third sub-function and a fourth sub-function, and the cascade function is as follows:
H(z)＝H1(z)·H2(z)·H3(z)·H4(z) wherein H1(z)＝(1-d1z-1)，H1(z) represents the first sub-function for converting slow components in the input bi-exponential kernel signal into a unit impulse output signal, H2(z)＝(1-d1z-1)，H2(z) represents the second sub-function for converting fast components in the input bi-exponential kernel signal into a unit impulse output signal, H3(z)＝z，H3(z) representing the third sub-function for aligning the instants of generation of the input bi-exponential kernel signal,
Figure FDA0002433750240000031
H4(z) represents the fourth sub-function, which is an amplifierFor adjusting the amplitude of the output impulse signal;
performing inverse transformation on the first sub-function, the second sub-function, the third sub-function, and the fourth sub-function, respectively, to establish the transfer function, where the transfer function is:
Figure FDA0002433750240000032
wherein v is1(n) first intermediate variable representing input bi-exponential kernel signal, v2(n) a second intermediate variable representing the input bi-exponential nuclear signal, v3(n) a third intermediate variable representing the input bi-exponential nuclear signal, v0And (n) represents an output impulse signal.
5. The method of claim 4, wherein d is measured1＝e-1/τSaid output impulse signal v0(n) the slow component tail is eliminated;
where τ represents the decay time constant.
6. The method of claim 4, wherein d is measured2＝e-1/τSaid output impulse signal v0(n) the fast component tail in (n) is eliminated;
where τ represents the decay time constant.
7. A double-exponential nuclear signal counting device, characterized in that said device comprises:
the device comprises a to-be-counted dual-index nuclear signal acquisition module, a counting module and a counting module, wherein the to-be-counted dual-index nuclear signal acquisition module is used for acquiring a to-be-counted dual-index nuclear signal;
the impulse signal acquisition module is used for inputting the dual-exponential kernel signal to be counted to a pre-established transfer function and acquiring an impulse signal output by the transfer function;
and the counting module is used for counting the dual-exponential nuclear signals to be counted according to the impulse signals.
8. The apparatus of claim 7, wherein the apparatus comprises:
an ideal signal obtaining module, configured to obtain an ideal bi-exponential nuclear signal and an ideal impulse signal corresponding to the ideal bi-exponential nuclear signal;
and the transfer function establishing module is used for establishing the transfer function according to the ideal bi-exponential kernel signal and the ideal impulse signal.
9. An electronic device comprising a processor and a memory, the memory storing computer readable instructions that, when executed by the processor, perform the method of any of claims 1 to 6.
10. A readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the method according to any one of claims 1 to 6.
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