A method for forming a secondary edge-shaped flat-top pulse

Abstract

The present invention discloses a method for forming a secondary edge-shaped flat-top pulse, which is used to perform secondary edge-shaped flat-top pulse shaping on the high-order pulse signal output by the front-end analog system of a nuclear radiation detector. Starting from the decomposition of the system function and combining the progressive construction process of the pulse signal in the time domain and the z domain, this method overcomes the limitations of previous pulse shaping based on low-order typical pulse signals, which ignores the "high-order" and "complex" nature of the physical system. The rich characteristics of the formed secondary edge-shaped flat-top pulse are beneficial to the adoption of high-performance analysis algorithms (such as deep learning, etc.) in pulse recognition and overlapping pulse decomposition, and are conducive to greatly improving the accuracy of energy spectrum measurement.

Description

Technical Field

[0001] The present invention relates to a method for forming a secondary edge-shaped flat-top pulse. Background Art

[0002] The front-end analog system of a nuclear radiation detector is jointly composed of a detector, a preamplifier, a C-R / R-C network, an amplifier circuit, and other conditioning circuits. The system function exhibits high-order characteristics, so the nuclear pulse waveform output by it also exhibits high-order complexity. In addition, due to the "high-order", "slimming", and "flat-top" characteristics of the secondary edge-shaped flat-top pulse, it plays an important role in improving the accuracy of pulse recognition and overlapping pulse decomposition; naturally, it can greatly improve the accuracy of energy spectrum measurement.

[0003] In view of the high-order complexity of the nuclear pulse signal output by the above nuclear radiation detection system and the high-order complexity and advantages of the secondary edge-shaped flat-top pulse, the present invention specifically studies a method for shaping the high-order complex nuclear pulse signal into a high-order complex secondary edge-shaped flat-top pulse. For this purpose, considering the complexity of pulse signal shaping, the present invention adopts a progressive shaping method.

[0004] This method starts from the decomposition of the system function and combines the progressive construction processes in the time domain and z domain of the secondary edge-shaped flat-top pulse, overcoming the limitations of previous pulse shaping that completely relies on low-order typical pulse signals (such as exponential decay signals, step signals, impulse signals, etc.) and ignores the "high-order" and "complex" characteristics of the actual physical system, providing a new means for the "complex" shaping of "complex" signals. In addition, the "high-order", "slimming", and "flat-top" characteristics of the shaped secondary edge-shaped flat-top pulse provide more distinct signal features for high-performance analysis algorithms (such as deep learning, etc.) used in subsequent pulse recognition and overlapping pulse decomposition, making pulse recognition more accurate (for example, the trained deep learning network has more accurate recognition ability), and can greatly improve the accuracy of energy spectrum measurement. Summary of the Invention

[0005] The object of the present invention is to disclose a method for forming a secondary-edge flat-top pulse, which is used for waveform shaping of the pulse signal output by the front-end analog system of a nuclear radiation detector, so as to realize the secondary-edge flat-top pulse shaping of the nuclear pulse signal, that is, to shape the complex nuclear pulse signal output by the front-end high-order system into a secondary-edge flat-top pulse. Starting from the decomposition of the system function and combining the progressive construction process of the secondary-edge flat-top pulse in the time domain and the z domain, this method overcomes the limitation of pulse shaping based entirely on low-order typical pulse signals (such as exponential decay signals, step signals, impulse signals, etc.) in the past, which ignores the "high-order" and "complex" nature of the actual physical system, and provides a new means for the "complex" shaping of "complex" signals. In addition, the "high-order", "slimming", and "flat-top" characteristics of the shaped secondary-edge flat-top pulse provide more distinct signal characteristics for the high-performance analysis algorithms (such as deep learning, etc.) used in subsequent pulse recognition and overlapping pulse decomposition, making pulse recognition more accurate (for example, the trained deep learning network has more accurate recognition ability), and can greatly improve the accuracy of energy spectrum measurement.

[0006] Since the expressions of the pulse signal output by the high-order system and the secondary-edge flat-top pulse signal are both relatively complex, the process of shaping the complex high-order pulse signal into a secondary-edge flat-top pulse becomes particularly difficult. The present invention adopts a progressive shaping method.

[0007] The secondary-edge flat-top pulse shaping of the high-order pulse signal output by the front-end analog system of the nuclear radiation detector in the present invention is realized through the following steps ① to ⑧.

[0008] Step ① First, design a digital secondary-edge flat-top pulse, the parameter values of which are obtained by converting according to the nuclear pulse counting rate. This pulse has the characteristics of "high-order", "slimming", and "flat-top".

[0009] Step ② Design a notch-type rectangular pulse according to the parameters n a 、n b 、n c of the secondary-edge flat-top pulse, including the time-domain and z-domain expressions.

[0010] Step ③ Design a ramp-type step pulse according to the parameters of the secondary-edge flat-top pulse, including the time-domain and z-domain expressions.

[0011] Step ④ Design a bipolar sawtooth pulse according to the parameters of the secondary-edge flat-top pulse, including the time-domain and z-domain expressions.

[0012] Step ⑤ Deduce the z-domain expression of the secondary-edge flat-top pulse according to the bipolar sawtooth pulse.

[0013] Step ⑥: Decomposition of the system function and calculation of the inverse system function before the second-order edge-shaped flat-top pulse shaping are implemented according to the following steps A to C:

[0014] A. Decomposition when the expression of the system function is a rational fraction in the z-domain;

[0015] B. Decomposition when the expression of the system function is a rational fraction in the s-domain;

[0016] C. Calculation of the system function of the inverse system.

[0017] Step ⑦: Calculate the output response of the inverse system when the nuclear pulse signal is input, and adopt the method of cascading responses to advance step by step.

[0018] Step ⑧: The algorithm for shaping the nuclear pulse signal into a second-order edge-shaped flat-top pulse is carried out according to the following steps:

[0019] According to the expression of the second-order edge-shaped flat-top pulse Y(z) in Step ⑤, obtain its corresponding time-domain expression y(n); then, according to y(n) and the system output response, perform second-order edge-shaped flat-top pulse shaping on the measured nuclear pulse x(n).

[0020] Through Steps ① to ⑧, the shaping of the high-order nuclear pulse signal output by the detection system into a second-order edge-shaped flat-top pulse is completed.

[0021] The beneficial effects of the present invention are as follows:

[0022] Since the front-end analog system of the nuclear radiation detector usually involves many circuit links and the system function shows high-order characteristics, the pulse waveform output by it also shows high-order complexity. In addition, due to the "high-order", "slimming", and "flat-top" characteristics of the second-order edge-shaped flat-top pulse, this plays an important role in improving the accuracy of pulse recognition and overlapping pulse decomposition; naturally, it can greatly improve the accuracy of energy spectrum measurement.

[0023] In view of the high-order complexity of the nuclear pulse signal output by the above nuclear radiation detection system and the high-order complexity of the second-order edge-shaped flat-top pulse, the present invention specifically studies a method for shaping the high-order complex nuclear pulse signal into a high-order complex second-order edge-shaped flat-top pulse. For this reason, considering the complexity of pulse signal shaping, the present invention adopts a progressive shaping method.

[0024] This method starts from the decomposition of system functions and combines the progressive construction processes in the time domain and z-domain of the quadratic edge-shaped flat-top pulse, overcoming the limitations of previous pulse shaping that was completely based on low-order typical pulse signals (such as exponential decay signals, step signals, impulse signals, etc.) and ignored the "high-order" and "complex" nature of the actual physical system. It provides a new means for the "complex" shaping of "complex" signals. In addition, the "high-order", "slimming", and "flat-top" characteristics of the shaped quadratic edge-shaped flat-top pulse provide more distinct signal features for high-performance analysis algorithms (such as deep learning, etc.) used in subsequent pulse recognition and overlapping pulse decomposition, making pulse recognition more accurate (for example, the trained deep learning network has more accurate recognition ability), and can greatly improve the accuracy of energy spectrum measurement. Description of the Drawings

[0025] Figure 1 is a quadratic edge-shaped flat-top pulse signal, Figure 2 is a flowchart of the method of the present invention. Detailed Embodiment

[0026] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation methods and processes are given. However, the protection scope of the present invention is not limited to the following embodiments.

[0027] The present invention relates to a method for shaping a quadratic edge-shaped flat-top pulse. Since the expressions of the pulse signals output by high-order systems and quadratic edge-shaped flat-top pulse signals are both relatively complex, the process of shaping complex high-order pulse signals into quadratic edge-shaped flat-top pulses becomes particularly difficult. Therefore, the present invention adopts the following steps ① to ⑧ to implement the quadratic edge-shaped flat-top pulse shaping algorithm for high-order pulses.

[0028] Step ① Design the following digital quadratic edge-shaped flat-top pulse

[0029]

[0030] where n b +n a =n c ; the parameters n a , n b , n c are all integers, obtained by converting the nuclear pulse counting rate; n is also an integer; the quadratic edge-shaped flat-top pulse is as Figure 1 shown, with the characteristics of edge "high-order" (here it is the second power, that is, second order), "slimming", and "flat-top".

[0031] Express formula (1) as the following expression:

[0032]

[0033] In formula (2), u(·) represents the unit step sequence.

[0034] Step ② designs the notch-type rectangular pulse d(n) according to the parameters n a , n b , n c of the quadratic-edge flat-top pulse.

[0035] Notch-type rectangular pulse (time domain):

[0036] d(n) = u(n) - u(n - n a ) + u(n - n b ) - u(n - n c ) (3)

[0037] Notch-type rectangular pulse (z domain):

[0038]

[0039] Step ③ designs the ramp-type step pulse p(n) according to the parameters n a , n b , n c of the quadratic-edge flat-top pulse.

[0040] Ramp-type step pulse p(n) (time domain):

[0041] p(n) = u(n)n - u(n - n a )(n - n a ) + u(n - n b )(n - n b ) - u(n - n c )(n - n c )

[0042] = d(n)n + u(n - n a )n a - u(n - n b )n b + u(n - n c )n c (5) where d(n) is shown in formula (3) and u(·) represents the unit step sequence.

[0043] Ramp-type step pulse p(n) (z domain):

[0044]

[0045] Where is:

[0046]

[0047] Step ④ designs a bipolar sawtooth pulse according to the parameters n a , n b , n c of the second-order edge-shaped flat-top pulse

[0048] Bipolar sawtooth pulse (time domain):

[0049]

[0050] Bipolar sawtooth pulse (z domain):

[0051]

[0052] Step ⑤ derives the z-domain expression Y(z) of y(n) of the second-order edge-shaped flat-top pulse from the bipolar sawtooth pulse

[0053] Since there is the following relationship between the bipolar sawtooth pulse r(n) and the second-order edge-shaped flat-top pulse y(n):

[0054]

[0055] The relationship between the z-domain bipolar sawtooth pulse R(z) and the z-domain second-order edge-shaped flat-top pulse Y(z) can be obtained as follows:

[0056] Y(z) = Y(z)z -1 + R(z) (11)

[0057] The z-domain second-order edge-shaped flat-top pulse Y(z) is further obtained as:

[0058]

[0059] Step ⑥ The decomposition of the system function before the second-order edge-shaped flat-top pulse shaping and the obtaining of the system inverse function are realized according to the following links A to C:

[0060] A. When the expression of the system function is a rational fraction in the z domain, its decomposition is as follows:

[0061]

[0062] where a N = 1, a N ≥ b M .

[0063] B. When the expression of the system function is a rational fraction in the s domain, its decomposition is as follows:

[0064]

[0065] where a N = 1, aN ≥b M 。

[0066] The z-domain expression of its corresponding discrete system function is as follows:

[0067]

[0068] Let where T is the sampling period, then:

[0069]

[0070] It is consistent with case A, so the subsequent steps will be uniformly analyzed using the z-domain system function.

[0071] It should be noted that: Formulas (13) and (16) represent system functions without repeated poles and repeated zeros, which is consistent with the actual physical circuit system because there are no electronic components with exactly the same parameters.

[0072] C. The system function of the inverse system is as follows:

[0073]

[0074] Step ⑦ Obtain the output response of the nuclear pulse signal input to the inverse system, which is carried out according to the following A and B links:

[0075] A. When N = M

[0076] Assume that the discrete signal obtained after sampling the nuclear pulse signal output by the front-end analog system is x(n); the output response obtained by inputting x(n) into the inverse system is w(n):

[0077]

[0078] where "*" represents the convolution operation, and u(n) is the unit step sequence.

[0079] B. When N > M

[0080] Assume that the discrete signal obtained after sampling the nuclear pulse signal output by the front-end analog system is x(n); the output response obtained by inputting it into the inverse system is w(n).

[0081] The inverse system function is cascaded by two parts: The first part Assume its output response is w J (n); the second part Assume its output response is w(n).

[0082] The output response w of the first part J (n) is obtained by the following recurrence in the way of cascading responses and advancing step by step:

[0083]

[0084] wherein represents the response output by the (z + α j ), and j = M + 1, M + 2, …, N - 1, N.

[0085] The output response w(n) of the second part is as follows:

[0086]

[0087] The algorithm for shaping the nuclear pulse signal x(n) into a second-order edge-shaped flat-top pulse in step ⑧ is carried out according to the following steps:

[0088] According to the expression of the second-order edge-shaped flat-top pulse Y(z) in step ⑤, the corresponding time-domain expression y(n) is obtained as follows.

[0089]

[0090] Perform second-order edge-shaped flat-top pulse shaping on the measured nuclear pulse x(n), and the shaped pulse X(n) is:

[0091]

[0092] X(n) is the time-domain expression of the pulse after second-order edge-shaped flat-top pulse shaping.

[0093] In summary, through steps ① to ⑧, second-order edge-shaped flat-top pulse shaping is performed on the high-order complex nuclear pulse signal output by the detection system.

[0094] For the second-order edge-shaped flat-top pulse shaping of nuclear pulse signals with high-order complexity, the present invention adopts a progressive shaping method. Starting from the decomposition of the system function and combining the progressive construction process of the second-order edge-shaped flat-top pulse in the time domain and the z domain, it overcomes the limitation of pulse shaping that was previously completely based on low-order typical pulse signals (such as exponential decay signals, step signals, impulse signals, etc.) and ignored the "high-order" and "complex" nature of the actual physical system, providing a new means for the "complex" shaping of "complex" signals. In addition, the rich characteristics of the shaped second-order edge-shaped flat-top pulse are conducive to the use of high-performance analysis algorithms (such as deep learning, etc.) in pulse recognition and overlapping pulse decomposition, which is conducive to greatly improving the accuracy of energy spectrum measurement.

[0095] In the above embodiments of the present invention, the method for forming a quadratic edge-shaped flat-top pulse of the nuclear pulse signal output by the detection system has been described in detail. However, it should be noted that the above is only one embodiment of the present invention. When other types of shaping methods involve using the methods described herein, the present invention is still valid. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for forming a quadratic edge-shaped flat-top pulse, characterized in that, The second - order edge - shaped flat - top pulse shaping of the high - order pulse signal output by the front - end analog system of the nuclear radiation detector is achieved through the following steps ① to ⑧: Step ① Design the following digital second - order edge - shaped flat - top pulse Among them, n b + n a = n c ; The parameter n a , n b , n c are all integers, obtained by converting according to the nuclear pulse counting rate; n also takes an integer; Express formula (1) as the following expression: In formula (2), u(·) represents the unit step sequence; Step ② designs a notch-type rectangular pulse d(n) (in the time domain) according to the parameters n a , n b , n c of the second-order edge-shaped flat-top pulse: d(n) = u(n) - u(n - n a ) + u(n - n b ) - u(n - n c ) (3) Notch - type rectangular pulse (Z - domain): Step ③ designs the ramp-type step pulse p(n) according to the parameters n a , n b , n c of the quadratic edge-shaped flat-top pulse: ramp-type step pulse p(n) (time domain): Where, d(n) is shown in formula (3), and u(·) represents the unit step sequence; Ramp - type step pulse p(n) (z - domain): Among them is as follows: Step ④ designs a bipolar sawtooth pulse according to the parameters n a , n b , n c of the quadratic edge-shaped flat-top pulse Bipolar saw - tooth pulse (time - domain): Bipolar saw - tooth pulse (z - domain): Step ⑤ Derive the z - domain expression Y(z) of y(n) of the second - order edge - shaped flat - top pulse according to the bipolar saw - tooth pulse. Since there is the following relationship between the bipolar saw - tooth pulse r(n) and the second - order edge - shaped flat - top pulse y(n): From this, the relationship formula between the z - domain bipolar saw - tooth pulse R(z) and the z - domain second - order edge - shaped flat - top pulse Y(z) can be obtained: Y(z) = Y(z)z -1 + R(z) (11) Further obtain the z - domain second - order edge - shaped flat - top pulse Y(z) as: Step ⑥ Decompose the system function before the second - order edge - shaped flat - top pulse shaping and obtain the inverse system function, which is realized according to the following links A to C: A. When the expression of the system function is a rational fraction in the z - domain, its decomposition is as follows: where a N = 1, a N ≥ b M ; B. When the expression of the system function is a rational fraction in the s - domain, its decomposition is as follows: where a N = 1, a N ≥ b M ; The z - domain expression of its corresponding discrete system function is as follows: Let where T is the sampling period, then: It is the same as the situation in A, so the subsequent steps are uniformly analyzed using the z - domain system function; It should be noted that: formulas (13) and (16) represent the system functions without repeated poles and repeated zeros; C. The system function of the inverse system is as follows: Step ⑦ Obtain the output response of the nuclear pulse signal input to the inverse system, which is carried out according to the following links A and B: A. When N = M Let the discrete signal obtained by sampling the nuclear pulse signal output by the front - end analog system be x(n); the output response obtained by inputting x(n) into the inverse system is w(n): Where "*" represents the convolution operation, and u(n) is the unit step sequence; B. When N > M Let the discrete signal obtained by sampling the nuclear pulse signal output by the front - end analog system be x(n), and the output response obtained by inputting it into the inverse system is w(n); The inverse system function is cascaded by two parts: the first part Let its output response be w J (n); the second part Let its output response be w(n); Output response w of the first part J (n), which is obtained by successive recursion in the way of cascading responses as follows: Among them represents the response output by the (z + α j ) link, where j = M + 1, M + 2, …, N - 1, N; The output response w(n) of the second part is as follows: Step ⑧ The algorithm for shaping the nuclear pulse signal x(n) into a second - order edge - shaped flat - top pulse is carried out according to the following link: According to the expression of the second - order edge - shaped flat - top pulse Y(z) in step ⑤, obtain its corresponding time - domain expression y(n) as follows: Perform second - order edge - shaped flat - top pulse shaping on the measured nuclear pulse x(n), and the shaped pulse X(n) is: X(n) is the time - domain expression of the pulse after the second - order edge - shaped flat - top pulse shaping; In summary, through steps ① to ⑧, the high - order pulse signal output by the detection system is shaped into a second - order edge - shaped flat - top pulse.

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