A method for repairing a high-order singular shaping pulse waveform

Abstract

The present invention discloses a method for repairing high-order singular shaped pulse waveforms, which is used to repair the singular pulses after the truncated high-order pulse ladder shaping output by a nuclear electronic circuit. First, a waveform space composed of waveform basis vectors is established, and the globally optimal waveform basis vectors are searched. Secondly, the optimal ladder shaping algorithm for the waveform space is obtained; the correlation degree between the measured truncated pulse and the singular trapezoid of the corresponding truncated waveform basis vector is calculated, and the repair decision and the optimal amplitude search are made. Finally, the singular trapezoid of the measured truncated pulse is corrected according to the globally optimal amplitude searched. It overcomes the high-order complexity, volatility of the pulse waveform and the singularity after truncation, and greatly improves the accuracy of energy spectrum measurement.

Description

Technical Field

[0001] The present invention relates to a method for repairing a high-order singular shaped pulse waveform. Background Art

[0002] In nuclear electronics, a front-end analog system composed of a detector, a preamplifier, a C-R / R-C network, an amplifier circuit, and other conditioning circuits, due to the fact that the charge collection time of the detector varies (for example, the charge collection time of a silicon drift detector, a small semiconductor detector, or an ultrafast scintillator detector is relatively short, while the charge collection time of a large-volume germanium detector or a slower scintillator detector is relatively long), and the composition of analog signal processing circuits such as the capacitive-resistive feedback preamplifier cascaded RC network, cascaded RC network, and switch reset preamplifier cascaded CR-RC network connected to the detector is diverse (for example, different numbers of cascaded RC or CR are selected), resulting in the pulse signals output by it (i.e., the front-end analog system) showing various forms and complex waveforms, that is, showing complex high-order characteristics in the S domain, challenging the accuracy, consistency, and reliability of subsequent digital waveform shaping algorithms (such as the trapezoidal shaping algorithm). In addition, in a circuit with a switch reset type preamplifier, there are tail pulses where the signal suddenly jumps to zero, resulting in the appearance of pseudo-peaks (shadow peaks of the full-energy peak) near the full-energy peak of the spectrum line; if the pulses are directly removed, a part of the counting rate will inevitably be lost while eliminating the pseudo-peaks.

[0003] The high-order pulse signals output by the above front-end analog system are difficult to accurately describe with a typical mathematical model; and when these high-order pulse signals have serious tails, the waveform after trapezoidal shaping is a singular trapezoid. The present invention proposes a method for repairing the singular trapezoid after trapezoidal shaping of high-order pulses with tails, and repairs the singular trapezoid through waveform space expansion and related algorithms, effectively restoring the pulse count and eliminating the pseudo-peaks near the full-energy peak of the spectrum line, greatly improving the accuracy of energy spectrum measurement. Summary of the Invention

[0004] The purpose of the present invention is to disclose a method for repairing a high-order singular shaped pulse waveform, which is used to repair the singular pulse after trapezoidal shaping of the tail high-order pulse output by a nuclear electronic circuit. This method can effectively restore the pulse count and eliminate the pseudo-peaks near the full-energy peak of the spectrum line.

[0005] The present invention repairs the singular pulse after trapezoidal shaping of the tail high-order pulse through the following steps ① to ④.

[0006] Step ① is to establish the pulse waveform space, which is realized through the following steps A to C:

[0007] A. Given the rise time t of the trapezoidal pulse a, the sum t of the rise time and the flat-top time of the trapezoidal pulse b , and the width t of the trapezoidal pulse c , and give its z-domain expression.

[0008] B. Select M single-pulse waveform samples, and use them as the fundamental wave to perform K-fold expansion in the pulse waveform space to obtain a waveform space with M*K pulses.

[0009] The single-pulse waveform samples here refer to complete pulses that are separated from each other and have no overlap. The purpose of the expansion is to fully consider the pulse shape fluctuations caused by the test conditions and environment during the measurement process, as well as the high-order complexity of the waveform, and cover the optimal waveform within the spanned space as much as possible, and greatly reduce the ballistic loss.

[0010] C. Unify the dimensions of the expanded waveform space, and after unit normalization, obtain a waveform space composed of waveform basis vectors.

[0011] Step ② Search for the global optimal waveform basis vector in the expanded waveform space after unifying the dimensions and unit normalization, and implement it according to the following A and B steps:

[0012] A. Calculate the comprehensive deviation degree of each waveform basis vector in the waveform space from the remaining M*K - 1 waveform basis vectors.

[0013] B. Select the pulse waveform corresponding to the one with the minimum comprehensive deviation degree as the global optimal waveform basis vector.

[0014] Step ③ Obtain the optimal trapezoidal shaping algorithm for the waveform space; perform trapezoidal shaping on the truncated pulses obtained in actual measurement, and calculate the correlation degree with the trapezoidal-shaped pulses of the optimal waveform basis vectors with the same truncated length (i.e., the same degree of truncation); make a decision on whether to repair and search for the optimal amplitude. It is achieved through the following steps A to C:

[0015] A. Obtain the optimal trapezoidal shaping algorithm for the waveform space X *-

[0016] B. Perform trapezoidal shaping on the truncated pulses obtained in actual measurement, calculate the correlation degree with the trapezoidal-shaped pulses of the optimal waveform basis vectors with the same truncated length (i.e., the same degree of truncation), and make a repair decision, including the following steps (a) to (c):

[0017] (a) Obtain the singular pulse after trapezoidal shaping of the truncated pulse measured actually;

[0018] (b) According to the length of the truncated pulse measured actually, find the trapezoidal-shaped pulse of the optimal waveform basis vector with the same truncated length;

[0019] ​(c) Calculate the relevance and make a judgment on whether it can be repaired; if the pulse can be repaired, proceed to the next step C

[0020] C. Search for the optimal amplitude in the gradient direction of the matching degree.

[0021] Conditions for stopping the search: When the number of iterations n is equal to the set maximum number of iterations or the amplitude remains unchanged for multiple consecutive times, stop the search.

[0022] Step ④ makes a judgment on whether the searched amplitude is globally optimal; in the case of global optimality, correct the singular trapezoidal pulse after the tail-cut high-order pulse is shaped into a trapezoidal pulse in actual measurement:

[0023] Through the above steps ① to ④, the correction of the singular trapezoidal pulse after the tail-cut high-order pulse is shaped in actual measurement is completed.

[0024] The beneficial effects of the present invention are:

[0025] Due to the complexity and volatility of the high-order pulse signals output by the front-end analog system, it is difficult to accurately describe them with typical mathematical models; moreover, when these high-order pulse signals have severe tail-cutting, the waveform after their trapezoidal shaping is a singular trapezoid; the existence of this singular trapezoid greatly reduces the accuracy of energy spectrum measurement and has a great impact on pulse counting at the same time. A method for waveform repair of the singular trapezoid after the tail-cut high-order pulse is shaped proposed by the present invention aims at "global optimality", repairs the singular trapezoid through waveform space expansion and related algorithms, fully considers the pulse shape fluctuations caused by test conditions and environment during the measurement process, as well as the high-order complexity of the waveform, and covers the optimal waveform within the spanned space as much as possible, so that the ballistic loss can be greatly reduced, the pulse counting can be effectively restored and the pseudo-peaks near the full-energy peak of the spectral line can be eliminated, and the accuracy of energy spectrum measurement is greatly improved. Description of the Drawings

[0026] Figure 1 It is a flow chart of the method of the present invention. Detailed Embodiment

[0027] The following will describe the embodiments of the present invention in detail with reference to the drawings. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation manners and processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0028] The repair of the singular pulse after the tail-cut high-order pulse is shaped in the present invention is realized through the following steps ① to ④.

[0029] Step ①, first, establish the pulse waveform space, which is realized through the following steps A to C:

[0030] A. Obtain the z-domain expression from the given trapezoidal pulse waveform parameters

[0031] The rise time \(t\) of the given trapezoidal pulse a , the sum \(t\) of the rise time and the flat-top time of the trapezoidal pulse b , and the width \(t\) of the trapezoidal pulse c , its z-domain expression is as follows:

[0032]

[0033] In formula (1), \(A_0\) is the flat-top amplitude of the trapezoidal pulse, \(Y(z)\) represents the z-transform of the trapezoidal pulse, \(n\) a = \(t\) a / T s , \(n\) b = \(t\) b / T s , \(n\) c = \(t\) c / T s , \(T\) S is the sampling period.

[0034] B. Select \(M\) single-pulse waveform samples and perform \(K\)-fold expansion in the pulse waveform space based on these as the fundamental wave to obtain a waveform space with \(M\times K\) pulses

[0035] Let the set of the selected \(M\) single-pulse waveform samples be \(X\): \(X = \{X_1, X_2, X_3, \cdots, X\) M \(\}\); each waveform sample has \(N\) sampling values, as follows:

[0036] \(X\) i = [x i (0) x i (1) x i (2) \(\cdots\) x i (N - 1)], \(i = 1, \cdots, M\) (2)

[0037] Here, the single-pulse waveform samples refer to complete pulses that are separated from each other and have no overlap. The purpose of the expansion is to fully consider the pulse shape fluctuations caused by test conditions and the environment during the measurement process, cover the optimal waveform within the spanned space as much as possible, and greatly reduce the ballistic loss.

[0038] Let \(\lambda\) be the fluctuation step size, \(1 / \lambda\) be an integer greater than 10, and \(K\), \(\lambda\) satisfy the following relationship:

[0039]

[0040] In formula (3) represents the floor function, \(K\) is an integer greater than 1, \(n\) c see formula (1).

[0041] The extended space composed of M*K waveforms is represented in matrix form as X:

[0042]

[0043] In formula (4), X i (k) (i = 1, …, M; k = 0, 1, …, (K - 1)) has the following two cases (a) and (b):

[0044] (a) When k = 0, 1, …, (1 / λ - 1)

[0045]

[0046] (b) When k = L*1 / λ, L*1 / λ + 1, …, L / λ + 1 / λ - 1)

[0047] X i (k) = {0, x i (L) + λk[x i (L + 1) - x i (L)], x i (L + 1) + λk[x i (L + 2) - x i (L + 1)]

[0048] ,..., x i (N - 2) + λk[x i (N - 1) - x i (N - 2)]}(6) where L ≥ 1 and is an integer.

[0049] C. Unify the dimensions of the extended waveform space X and unitize it to obtain the waveform space composed of waveform basis vectors

[0050] Take the waveform dimension as W, that is, take the first W elements of the waveform to form a new waveform, and W is taken as follows

[0051]

[0052] The waveform space after unifying the dimensions of X is represented by the following X - as follows:

[0053]

[0054] Unitize the M*K waveforms in the waveform space X - as follows:

[0055]

[0056] In formula (9),

[0057]

[0058] represents the sum of all elements of the waveform, represents the element of the waveform with the sequence number w, represents the element of the waveform with the sequence number w, i = 1, …, M; k = 0, 1, … (K - 1).

[0059] each element in the matrix represents a waveform basis vector, and there are M * K waveform basis vectors in total; each waveform basis vector has W elements, that is, W sampling values.

[0060] Step ② Search for the globally optimal waveform basis vector in the extended waveform space after unifying the dimension and normalizing, and implement it according to the following steps A and B:

[0061] A. Calculate the comprehensive deviation degree of each waveform basis vector in

[0062] from the remaining M * K - 1 waveform basis vectors: Taking as an example, the comprehensive deviation degree of this waveform basis vector from other waveform basis vectors

[0063]

[0064] B. Select the pulse waveform corresponding to the one with the minimum comprehensive deviation degree as the optimal waveform basis vector

[0065] Select the minimum value from the following set of comprehensive deviation degrees, denoted as J P,Q , and its corresponding pulse waveform is the optimal waveform basis vector. For the convenience of subsequent algorithm derivation, is denoted as

[0066]

[0067] Step ③ Obtain the optimal trapezoidal shaping algorithm for the waveform space ; perform trapezoidal shaping on the truncated pulse obtained in the actual measurement, and calculate the correlation with the trapezoidally shaped pulse of the optimal waveform basis vector with the same truncated length (i.e., the same degree of truncation); perform the decision on whether it can be repaired and the search for the optimal amplitude, and implement it through the following steps A to C:

[0068] A. Obtain the optimal trapezoidal shaping algorithm for the waveform space ​

[0069] Optimal waveform basis vector The trapezoidal shaping algorithm is as follows:

[0070]

[0071] H(z) is the z-domain expression of the trapezoidal shaping algorithm, and h(0) = 0; For the z-domain expression of, is as follows:

[0072]

[0073] Truncate H(z):

[0074]

[0075] n c See formula (1).

[0076] Optimal waveform basis vector The pulse after trapezoidal shaping is:

[0077]

[0078] B. Perform trapezoidal shaping on the truncated pulse obtained in actual measurement, and calculate the correlation with the pulse after trapezoidal shaping of the optimal waveform basis vector with the same truncation length (i.e., the same truncation degree), and make a repair decision, including the following steps (a) - (c): Perform the following steps (a) - (c):

[0079] (a) Obtain the singular pulse Y after trapezoidal shaping of the truncated pulse x measured actually

[0080]

[0081] Where The number of elements of The truncated pulse here refers to whose length is greater than n a / 2 and less than n c , n a And n c See formula (1).

[0082] (b) According to the length of the truncated pulse measured actually, find the trapezoidal shaping pulse of the optimal waveform basis vector with the same truncation length

[0083]

[0084] (c) Calculate the relevance and make a judgment on whether it can be repaired. If the pulse can be repaired, proceed to the next step C.

[0085] The relevance calculation is as follows

[0086]

[0087] Judgment: When R(n) ≥ ε, judge the pulse can be repaired and proceed to the next step C; otherwise, judge cannot be repaired and discard the pulse; where 0.9 ≤ ε < 1; is the transpose of; n c See formula (1); It should be noted that: and are obtained by shaping the truncated pulse into a trapezoid, so the waveforms of both are singular trapezoidal pulses.

[0088] C. Search for the optimal amplitude in the gradient direction of the matching degree

[0089] In the case where the pulse is judged to be repairable in the above step (c), search for the optimal amplitude according to the following iterative formula:

[0090]

[0091] where A0 is shown in formula (1), A(0) = A0, A(-1) = E(-1) = 0, and γ is a constant greater than zero.

[0092] The matching degree E(n) is calculated as follows:

[0093]

[0094]

[0095]

[0096]

[0097] represents the trapezoidal pulse corresponding after n iterations, n c See formula (1).

[0098] Condition to stop the search: When the number of iterations n is equal to the set maximum number of iterations or the amplitude A(n) remains unchanged continuously for multiple times, stop the search.

[0099] Step ④ determines whether the searched amplitude is globally optimal; in the case of global optimality, the singular trapezoidal pulse after the ladder shaping of the actually measured truncated pulse x is corrected:

[0100] Suppose the number of iterations when the search stops in Step ③ is n opt , when the following relationship holds, the searched amplitude A(n opt ) is judged to be globally optimal.

[0101]

[0102] The actually measured truncated pulse The ladder-shaped pulse of is corrected to:

[0103]

[0104] where, see formula (16), A0 see formula (1), 0 < δ < 0.1, see formula (17).

[0105] In summary, through Steps ① to ④, the correction of the singular trapezoidal pulse after the ladder shaping of the actually measured truncated high-order pulse x is completed.

[0106] As described above, the method for waveform repair of the singular trapezoid after the ladder shaping of the truncated high-order pulse aims at "global optimality", repairs the singular trapezoid through waveform space expansion and related algorithms, fully considers the pulse shape fluctuations caused by test conditions and the environment during the measurement process, as well as the high-order complexity of the waveform, and covers the optimal waveform in the spanned space as much as possible. This can greatly reduce the ballistic loss, effectively restore the pulse count and eliminate the pseudo-peaks near the full-energy peak of the spectrum line, and greatly improve the accuracy of energy spectrum measurement.

[0107] In the above embodiments of the present invention, the method for waveform repair of the singular trapezoid after the ladder shaping of the truncated high-order pulse is described in detail. However, it should be noted that the above is only one embodiment of the present invention. When other types of pulse waveforms are involved in using the repair method proposed in this article, 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 in the protection scope of the present invention.

Claims

1. A method for repairing a high-order singular shaping pulse waveform, characterized in that, The repair of the singular pulse after the formation of the truncated high-order pulse ladder is achieved through the following steps ① to ④: Step ①, establish the pulse waveform space, which is achieved according to the following links A1, B1, and C1: A1. Obtain the z-domain expression from the given trapezoidal pulse waveform parameters Given the rise time \(t\) of the trapezoidal pulse a , the sum \(t\) of the rise time and the flat-top time of the trapezoidal pulse b , and the width \(t\) of the trapezoidal pulse c , their \(z\)-domain expressions are as follows: In formula (1), A0 is the flat-top amplitude of the trapezoidal pulse, Y(z) represents the z-transform of the trapezoidal pulse, and n a = t a / T s , n b = t b / T s , n c = t c / T s , T S is the sampling period; B1. Select M single-pulse waveform samples, and perform K-fold expansion of the pulse waveform space based on these as the fundamental wave to obtain a waveform space with M * K pulses Let the set of M single - pulse waveform samples selected be X: X = {X1, X2, X3,..., X M}; Each waveform sample has N sampling values, as follows: X i = [x i (0)x i (1)x i (2)...x i (N - 1)], i = 1, …, M (2) Here, the single-pulse waveform samples refer to complete pulses that are separated from each other and have no overlap; the purpose of the expansion is to fully consider the pulse shape fluctuations caused by the test conditions and environment during the measurement process, cover the optimal waveform within the spanned space as much as possible, and greatly reduce the ballistic loss; Let λ be the fluctuation step size, 1 / λ be an integer greater than 10, and K and λ satisfy the following relationship: In formula (3) represents the floor function, K is an integer greater than 1, and n c see formula (1); The expanded space composed of M * K waveforms is represented in matrix form X: In formula (4), X i (k) (where i = 1, …, M; k = 0, 1, …, (K - 1)) has the following two cases (a) and (b): (a) When k = 0, 1, …, (1 / λ - 1) (b) When k = L * 1 / λ, L * 1 / λ + 1, …, L / λ + 1 / λ - 1) where L ≥ 1 and is an integer; C1. Unify the dimensions of the expanded waveform space X and unitize it to obtain a waveform space composed of waveform basis vectors Take the waveform dimension as W, that is, take the first W elements of the waveform to form a new waveform, and W is taken as follows The waveform space after X-unifying the dimensions is represented by the following X - as follows: For the waveform space X - normalize the M*K waveforms: In formula (9), Represents The sum of all elements of the waveform, Represents The element of the waveform with sequence number w, Represents The element of the waveform with sequence number w, where i = 1, …, M; k = 0, 1, … (K - 1); X *- Each element in the matrix represents a waveform basis vector, and there are a total of M*K waveform basis vectors; each waveform basis vector has W elements, that is, W sampling values; Step ②, search for the global optimal waveform basis vector in the expanded waveform space with unified dimensions and unitized, which is achieved according to the following links A2 and B2: A2. Calculate X *- The comprehensive deviation degree of each waveform basis vector in Taking as an example, the comprehensive deviation degree of this waveform base vector from other waveform base vectors is calculated according to the following formula: B2. Select the pulse waveform corresponding to the one with the minimum comprehensive deviation as the optimal waveform basis vector Select the minimum value from the following comprehensive deviation sets and denote it as J P,Q , and its corresponding pulse waveform is the optimal waveform basis vector. For the convenience of subsequent algorithm derivation, is denoted as Step ③, obtain the optimal ladder shaping algorithm for the waveform space; perform ladder shaping on the truncated pulse obtained in the actual measurement, and calculate the correlation with the pulse after the ladder shaping of the optimal waveform basis vector with the same truncated length, and make a decision on whether it can be repaired and search for the optimal amplitude; Step ④, judge whether the searched amplitude is globally optimal; in the case of global optimality, correct the singular trapezoidal pulse after the ladder shaping of the actually measured truncated pulse.

2. The high-order singular shaping pulse waveform repair method according to claim 1, characterized in that In the above step ③, obtain the optimal ladder shaping algorithm for the waveform space; Perform ladder shaping on the truncated pulse obtained in the actual measurement, and calculate the correlation with the pulse after the ladder shaping of the optimal waveform basis vector with the same truncated length; make a decision on whether it can be repaired and search for the optimal amplitude, which is achieved according to the following links A3, B3, and C3: A3. Obtain the optimal trapezoidal shaping algorithm for the waveform space X *- ​ Optimal waveform basis vector The trapezoidal shaping algorithm is as follows: $H(z)$ is the $z$-domain expression of the trapezoidal shaping algorithm, and $h(0) = 0$; is the $z$-domain expression of, as follows: Perform truncation processing on H(z): n c See Equation (1); Optimal waveform basis vector Pulse after trapezoidal shaping is as follows: B3. Perform trapezoidal shaping on the truncated pulses obtained in actual measurement, and perform correlation calculation and repair decision on the pulses after trapezoidal shaping with the optimal waveform basis vectors of the same tail length, including the following steps (a) to (c): Perform correlation calculation and make a repair decision, including the following steps (a) to (c): (a) Obtain the truncated pulses actually measured The singular pulses after trapezoidal shaping Among them The number of elements of The trailing pulse here refers to The length of is greater than n a / 2 and less than n c n a and n c See formula (1); (b) According to the actually measured tail-cutting pulse length to obtain the optimal waveform basis vectors with the same tail-cutting length trapezoidal shaping pulse (c) Calculate the correlation and make a decision on whether it can be repaired. If the pulse can be repaired, proceed to the next step C The correlation calculation is performed as follows Decision: When R(n) ≥ ε, the decision pulse is repairable and proceeds to the next step C; otherwise, the decision is not repairable, then discard the pulse; where 0.9 ≤ ε < 1; is the transpose of; n c see formula (1); it should be noted that: and are obtained by trapezoidal shaping of the truncated pulse, so the waveforms of both are singular trapezoidal pulses; C3. Search for the optimal amplitude in the gradient direction of the matching degree In the case where the decision pulse in the above step (c) is repairable, the search for the optimal amplitude is carried out according to the following iterative formula: where A0 is shown in formula (1), A(0) = A0, A(-1) = E(-1) = 0, and γ is a constant greater than zero; The matching degree E(n) is calculated as follows: represents the corresponding trapezoidal pulse after n iterations, where n c see formula (1); Condition for stopping the search: When the iteration number n is equal to the set maximum iteration number or the amplitude A(n) remains unchanged continuously for multiple times, stop the search.

3. The high-order singular shaping pulse waveform repair method according to claim 1, characterized in that In step ④, it is determined whether the searched amplitude is globally optimal; in the case of global optimality, the singular trapezoidal pulse after the actual measured truncated pulse is shaped into a trapezoidal pulse is corrected as follows: Let the number of iterations when the search stops in step ③ be n opt , when the following relationship holds, the searched amplitude A(n opt ) is judged to be globally optimal; Actual measured tail-cut pulse Trapezoidal shaping pulse Is corrected to: Among them, see formula (16), A0 see formula (1), 0 < δ < 0.1, see formula (17); In summary, the truncated high-order pulse obtained from actual measurement is corrected for the singular trapezoidal pulse after trapezoidal shaping through steps ① to ④. ​

Images