Pulse shaping method based on curvature transformation

Abstract

The invention discloses a pulse shaping method based on curvature transformation, which belongs to the field of nuclear signal analysis, and aims at constructing a basic signal unit by researching a multi-curvature shaping algorithm, and after bipolar pulse shaping is realized through delay differential operation of the basic unit, integral operation is carried out once, so that the pulse shaping precision is improved. According to the method, a pulse forming algorithm which can complete any curvature output by changing forming parameters on the basis of any-shape trapezoidal signals is obtained, and the technical problems that in the prior art, the pulse curvature feature changing process is tedious, and multi-scene requirements cannot be met are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of nuclear signal analysis, and in particular relates to a pulse shaping method based on curvature transformation. Background Art

[0002] Digital nuclear pulse processing technology is an important means for nuclear instruments to obtain and analyze nuclear pulse characteristic information, which has led to the development of different types of shaping algorithms. Since commonly used shaping algorithms have fixed implementation methods and different applicable conditions, in order to meet different application requirements, when deploying multiple shaping algorithms for digital nuclear instruments, it will not only increase the use of system signal resources, but also reduce the flexibility of the instrument.

[0003] Based on this problem, the present invention is based on arbitrary trapezoidal shaping, and realizes a multi-curvature pulse shaping algorithm that can output different curvature changes only by changing the shaping parameters, and simplifies it into a linear combination of weighted and shifted unit pulses. The influence of shaping parameters on the curvature change of multi-curvature pulse shaping output is studied through simulation, and the law of the influence of curvature characteristics on the frequency characteristics of the pulse shaping algorithm and the ability to separate piled pulses is analyzed. Finally, an X-ray fluorescence measurement experimental platform is built to analyze the energy resolution and counting rate performance of the multi-curvature pulse shaping algorithm. The results show that the shaping parameters na and nc affect the proportion of concave curvature and convex curvature components in the rising edge change of the pulse shaping output, respectively. Under the same peak time, the pulse shaping algorithm with a larger proportion of concave curvature components has a stronger ability to separate piled pulses and a better pulse pass rate performance. By shortening the peak time and appropriately increasing the proportion of convex curvature components in the pulse shaping output, the energy resolution performance of the energy spectrum in high counting rate scenarios can be improved.

[0004] The inventors found in actual use that these prior arts have at least the following technical problems:

[0005] The curvature characteristics cannot be changed quickly and cannot adapt to the needs of multiple environments. Summary of the invention

[0006] In view of the problem in the prior art that multi-curvature pulse forming is that the procedure for changing curvature characteristics is cumbersome and cannot adapt to multiple environmental requirements, the present invention proposes a pulse forming method based on curvature transformation, the purpose of which is to quickly change the curvature characteristics to adapt to multiple environmental requirements.

[0007] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is:

[0008] A pulse shaping method based on curvature transformation is provided. An input signal with exponential decay signal characteristics is discretized and then passed through an impulse shaping system based on z-transform to obtain an impulse signal. After expansion, the impulse signal is subjected to an inverse z-transform to obtain an impulse signal v(n) with an amplitude of A. Then, a synthesis system is established based on the unit impulse signal v(n) to obtain a time domain expression h of a trapezoidal signal of arbitrary shape. AT (n), by h AT (n) Perform two differential operations to decompose it into a linear combination of weighted and shifted unit pulses, and obtain the recursive formula for arbitrary trapezoidal pulse shaping. The symmetric trapezoidal pulse shaping algorithm is realized by this recursive formula. After obtaining the arbitrary trapezoidal pulse shaping algorithm, the trapezoidal shaping of different shapes can be realized by changing the shaping parameters. The bipolar zero area signal is composed of two arbitrary trapezoidal signals. and The multi-curvature pulse shaping algorithm is obtained by integrating the bipolar zero-area signal once. The formula is as follows:

[0009] V1(n)=v i (n)-d·v i (n-1)

[0010]

[0011] Among them, na, nb, and nc jointly determine the peak time, nd is the flat-top width, the delay parameter m = na + nb + nc + nd-1, and V1 (n) is the result of exponential signal impulse shaping;

[0012] It is the intermediate process of forming trapezoids of arbitrary shapes;

[0013] The result of trapezoidal forming of arbitrary shape;

[0014] V o (n) is the multi-curvature pulse shaping result, v i (n) is the input signal, n is the time scale in the discrete domain;

[0015] By expanding and merging the above formulas, the time domain recursive formula of the multi-curvature pulse shaping algorithm is simplified as follows:

[0016] V1(n)=v i (n)-d·v i (n-1)

[0017] V2(n)=nc·(V1(n)+V1(n-nc-nb-m)-V1(n-na)-V1(n-na-nb-nc-m))+

[0018] na·(V1(n-nc-m)+V1(n-na-nb-nc)-V1(nm)-V1(n-na-nb))

[0019] V3(n)=V3(n-1)+V2(n)

[0020] V4(n)=V4(n-1)+V3(n)

[0021] V o (n) = V o (n-1)+V4(n)

[0022] Where d = exp(-T s / τ), T s is the sampling period of ADC, τ is the time decay constant of single exponential signal, exp is the sign replacement of exponential signal; V1(n), V2(n), V3(n), V4(n) are the intermediate processes of multi-curvature pulse shaping.

[0023] The optimal input signal with exponential decay signal characteristics is as follows: i (t) = A·e -t / τ ,

[0024] where v i (t) is the input signal, A is the signal amplitude, e is the natural logarithm, τ is the time decay constant of the single exponential signal, and t is the continuous domain time scale.

[0025] Preferably, after the input signal is discretized, the impulse signal is obtained through the impulse shaping system based on z-transform as follows:

[0026] A=(1-d·z -1 )·V i (z),

[0027] Where d = exp(-T s / τ), T s is the sampling period of the ADC, τ is the time decay constant of the single exponential signal, V i (z) is the z-transform result of the input signal, Z is e Ts .

[0028] Preferably, the impulse signal is inversely z-transformed to obtain an impulse signal v(n) with an amplitude of A as follows:

[0029] v(n)=A·δ(n)=v i (n)-d·v i (n-1)

[0030] Where δ(n) is the unit impulse signal.

[0031] Preferably, a synthesis system is established from the unit impulse signal to obtain the time domain expression h of an arbitrary shape trapezoidal signal AT (n) are as follows:

[0032]

[0033] Better, for h AT (n) Perform two differential operations to simplify the synthesis of the pulse shape defined by the time domain expression and decompose it into a linear combination of weighted and / or shifted unit pulses to obtain the recursive formula for arbitrary trapezoidal pulse shaping as follows:

[0034] V1(n)=v i (n)-d·v i (n-1)

[0035] V2(n)=nc·(V1(n)-V1(n-na))+na·(V1(n-na-nb-nc)-V1(n-na-nb))

[0036] V3(n)=V3(n-1)+V2(n)

[0037] V AT (n) = V AT (n-1)+V3(n).

[0038] Preferably, the forming parameters determine the shape of the trapezoidal forming, and thus determine the change in curvature of the final forming pulse output.

[0039] Preferably, the larger the shaping parameter na is, the wider the width of the rising edge of the trapezoidal shaping pulse with positive polarity is, and the larger the proportion of the concave curvature in the rising edge of the finally obtained shaping pulse is.

[0040] Preferably, the smaller the ratio of the molding parameter na to the peak time, the larger the proportion of the convex curvature component and the smaller the cutoff frequency; the larger the ratio of the molding parameter na to the peak time, the larger the proportion of the concave curvature component and the stronger the accumulation pulse separation ability.

[0041] Preferably, the larger the forming parameter nc is, the wider the width of the falling edge of the trapezoidal forming pulse with positive polarity is, and the larger the proportion of the convex curvature in the rising edge of the final forming pulse is; after the peak time is determined, increasing the size of the forming parameter na will correspondingly reduce the size of the forming parameter nc.

[0042] Compared with the prior art, the technical solution of the present invention has the following advantages / benefits:

[0043] 1. The present invention can obtain shaped pulses with different curvature characteristics only by changing the shaping parameters, which greatly reduces the difficulty of obtaining multi-curvature pulses and improves the efficiency in practical applications and scientific research.

[0044] 2. The obtained multi-curvature pulses can adapt to the experimental test environment with multi-curvature requirements without the need to build the experimental platform again. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0046] Figure 1 This is a waveform diagram of a common target shaped pulse and its differential result.

[0047] Figure 2 It is a graph of any trapezoidal pulse and its differential waveform.

[0048] Figure 3 It is the multi-curvature pulse waveform under different forming parameters.

[0049] Figure 4 It is an amplitude-frequency characteristic curve diagram of the amplitude-frequency characteristic curve of the trapezoidal shaping under different curvature shaping algorithms and different peak reaching times.

[0050] Figure 5 It is the target accumulation nuclear pulse signal and the pulse shaping curves with different curvatures at the same peak time.

[0051] Figure 6 1 is a pulse parameter setting of different curvatures according to an embodiment of the present invention.

[0052] Figure 7 It is the relationship between the peak area and peak time of the characteristic peak of different curvature shaping algorithms in the embodiments of the present invention.

[0053] Figure 8 This is the relationship between the energy resolution and peak time of different curvature shaping algorithms in the embodiments of the present invention.

[0054] Fig. 9 Relationship diagram of the optimal energy resolution range of different curvature shaping algorithms under different pipe flows. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. Therefore, the detailed description of the embodiments of the present invention provided below is not intended to limit the scope of the claimed invention, but merely represents the selected embodiments of the present invention.

[0056] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and thus, once an item is defined in one drawing, it may not be further defined or explained in the subsequent drawings.

[0057] Embodiment 1:

[0058] After the input signal of the nuclear radiation detector system passes through different digital shaping systems, it allows the extraction of nuclear pulse characteristic information, such as amplitude, accumulation, particle identification and arrival time, while optimizing and improving the system signal-to-noise ratio. Nuclear pulse shaping algorithms are mainly divided into three categories according to the curvature characteristics: convex curvature shaping, trapezoidal shaping and concave curvature shaping. Among them, the common convex curvature shaping are sine shaping, cosine shaping and Gaussian shaping, which have the advantages of small ballistic loss and high signal-to-noise ratio; concave curvature shaping is mainly represented by peak shaping, which has the best pulse passing performance under high counting rate conditions; the advantage of trapezoidal shaping is that the synthesis method is simple, and it performs well in many comprehensive performances such as noise suppression, counting rate and ballistic loss.

[0059] At present, the derivation processes of forming algorithms with different curvature characteristics have little correlation. Therefore, the present invention proposes a multi-curvature pulse forming algorithm with different curvature characteristics that can be realized by only changing the forming parameters.

[0060] After any finite width unipolar signal is differentiated, its output is a bipolar zero-area signal. The relationship between the common target shaped pulse and its differential result is as follows: Figure 1 As shown. Figure 1 It can be seen that the differential results of different shaped pulses are composed of simple signal units. For example, the trapezoidal shaped pulses are differentiated into rectangular pulse signals, and the concave and convex shaped pulses are differentiated into positive and negative sawtooth pulse signals.

[0061] Therefore, with the goal of constructing a basic signal unit, after the basic unit is used to realize bipolar pulse shaping through delayed differential operation, an integral operation is performed to obtain pulse shaping outputs with three curvatures. Figure 1As shown, a pulse shaped output OUT1 of a signal IN1, a pulse shaped output OUT2 of a signal IN2, and a pulse shaped output OUT3 of a signal IN3 are shown.

[0062] The present invention expands on this relationship and uses a trapezoidal signal of any shape as a basic signal to obtain a pulse shaping method with an output of any curvature.

[0063] The input signal in the rational case usually has the characteristics of an exponentially decaying signal as shown below.

[0064] v i (t) = A·e -t / τ

[0065] where v i (t) is the input signal, A is the signal amplitude, e is the natural logarithm, τ is the time decay constant of the single exponential signal, and t is the continuous time scale.

[0066] The exponential decay signal is discretized and then the impulse signal is obtained through an impulse shaping system based on z-transform.

[0067] A=(1-d·z -1 )·V i (z)

[0068] Where d = exp(-T s / τ), T s is the sampling period of the ADC, τ is the time decay constant of the single exponential signal, V i (z) is the discretized Z-transform result.

[0069] After expansion, perform an inverse z-transform to obtain an impulse signal v(n) with an amplitude of A:

[0070] v(n)=A·δ(n)=v i (n)-d·v i (n-1)

[0071] Where δ(n) is the unit impulse signal, v i (n) is the input signal, v(n) is the impulse signal;

[0072] Then, a synthesis system is established starting from the unit impulse signal. The time domain expression of an arbitrary shape trapezoidal signal is h AT (n) is shown in the following formula.

[0073]

[0074] like Figure 2 As shown, by h AT(n) Perform two differential operations to simplify the pulse shape defined by the time domain expression and decompose it into a linear combination of weighted and / or shifted unit pulses. The recursive formula for arbitrary trapezoidal pulse shaping can be obtained:

[0075] V1(n)=v i (n)-d·v i (n-1)

[0076] V2(n)=nc·(V1(n)-V1(n-na))+na·(V1(n-na-nb-nc)-V1(n-na-nb))

[0077] V3(n)=V3(n-1)+V2(n)

[0078] V AT (n) = V AT (n-1)+V3(n)

[0079] Where na is the rising edge width, nb is the flat top width, and nc is the falling edge width. The subsequent symmetrical trapezoidal pulse shaping algorithm is implemented by the above formula.

[0080] After obtaining the arbitrary trapezoidal pulse shaping algorithm, the trapezoidal shaping of different shapes can be achieved by changing the shaping parameters. The bipolar zero-area signal is composed of two arbitrary trapezoidal signals. and The multi-curvature pulse shaping algorithm is obtained by integrating the bipolar zero-area signal once:

[0081] V1(n)=v i (n)-d·v i (n-1)

[0082]

[0083] The delay parameter m = na + nb + nc + nd-1, where na, nb, and nc determine the shape of the trapezoidal forming, and thus determine the final output curvature change, and nd is the flat-top width of the multi-curvature pulse forming;

[0084] V1(n) is the result of impulse shaping of the exponential signal;

[0085] It is the intermediate process of forming trapezoids of arbitrary shapes;

[0086] The result of trapezoidal forming of arbitrary shape;

[0087] V o (n) is the multi-curvature pulse shaping result, v i (n) is the input signal, and n is the time scale in the discrete domain.

[0088] By expanding and merging the above formulas, we can get the time domain recursive formula of the multi-curvature pulse shaping algorithm:

[0089] V1(n)=v i (n)-d·v i (n-1)

[0090] V2(n)=nc·(V1(n)+V1(n-nc-nb-m)-V1(n-na)-V1(n-na-nb-nc-m))+

[0091] na·(V1(n-nc-m)+V1(n-na-nb-nc)-V1(nm)-V1(n-na-nb))

[0092] V3(n)=V3(n-1)+V2(n)

[0093] V4(n)=V4(n-1)+V3(n)

[0094] V o (n) = V o (n-1)+V4(n)

[0095] V1(n), V2(n), V3(n), and V4(n) are the intermediate processes of multi-curvature pulse shaping; the shaping parameters na, nb, and nc jointly determine the peak time, the shaping parameter nd is the flat top width, and the delay parameter m = na+nb+nc+nd-1;

[0096] Finally, a pulse forming method was obtained that can obtain a variety of curvature characteristics by only changing the forming parameters.

[0097] Embodiment 2:

[0098] The shaping parameters determine the shape of the trapezoidal forming, which in turn determines the curvature change of the final shaping pulse output.

[0099] Using the formula: v i (t) = A·e -t / τ .

[0100] Simulate the nuclear signal, where A = 1, τ = 18T s , T s =50ns. The output results of multi-curvature pulse shaping under different shaping parameters are as follows Figure 3 As shown, where t p is the peak time, Figure 3As shown, the larger the na is, the wider the rising edge width of the trapezoidal forming pulse with positive polarity is, and the larger the proportion of the concave curvature in the rising edge of the final shaped pulse is; the larger the nc is, the wider the falling edge width of the trapezoidal forming pulse with positive polarity is, and the larger the proportion of the convex curvature in the rising edge of the final shaped pulse is; after the peak time is determined, increasing the size of na will correspondingly reduce the size of nc, and vice versa.

[0101] Example 3: Using v i (t) = A·e -t / τ Conduct simulations,

[0102] Where A=1,τ=18T s , T s =50ns. Multi-curvature pulse shaping is performed on it, and the peak time t p =20T s , the flat top is zero (nd=0), and the forming result is Fourier transformed. Finally, the amplitude-frequency characteristics of different forming algorithms under the same peak time are obtained as follows Figure 4 (a) From Figure 4 It can be seen from (a) that the smaller the ratio of na to peak time, the larger the proportion of convex curvature component and the smaller the cutoff frequency. Among them, the shaping algorithm with output approximate Gaussian shape has the best suppression effect on high-frequency noise.

[0103] Taking the symmetrical trapezoidal formation as an example, the amplitude-frequency characteristics of the trapezoidal formation under different peak times are as follows: Figure 4 (b) It can be seen that increasing the peak time enhances the shaping algorithm’s ability to suppress high-frequency noise and reduces the cut-off frequency, but it also increases the probability of pulse accumulation.

[0104] Example 4: Using v i (t) = A·e -t / τ Perform simulation, where T s =50ns,τ=18T s , A=1, peak-to-peak distance t d 30T s , the simulation results of the pile-up core pulse are as follows Figure 5 (a) Then, multi-curvature pulse forming and trapezoidal forming were performed under the same set of peak time forming parameters. The forming parameters at which trapezoidal forming can separate piled pulses were used as the dividing line to analyze the piled pulse separation capabilities of different forming algorithms. The peak time of forming parameters t p =30T s , the results are as follows Figure 5 (b) As can be seen from the figure, the larger the ratio of na to peak time, the larger the proportion of concave curvature components, and the stronger the pile-up pulse separation ability. pThe half multi-curvature pulse shaping algorithm can obtain two real amplitudes, the trapezoidal shaping algorithm can only obtain one real amplitude, and the shaping pulse with all convex curvatures obtains a distorted amplitude.

[0105] Embodiment 5:

[0106] The experimental platform uses an X-ray fluorescence spectrometer equipped with a Fast SDD detector to measure the characteristic X-rays (125eV@ 55 Fe, 5.9KeV peak), the tube voltage of the X-ray tube is 49kV (rated voltage is 50kV, rated tube current is 1mA), the tube current sizes are set to 7.8μA, 39.2μA and 98.0μA respectively, and the original nuclear pulse signals at different input count rates are obtained, where the data acquisition board uses an ADC with a sampling rate of 20MSPS.

[0107] According to the forming parameter settings, the pulse forming algorithm with different curvature changes is obtained. The parameter settings are as follows: Figure 6 shown.

[0108] The relationship between peak area and peak time of different shaping algorithms is as follows Figure 7 As shown in the figure, it can be seen that under the same peak time, the forming algorithm with a larger proportion of concave curvature has a larger characteristic peak area and a better pulse passing performance. The reason is that the forming algorithm with a larger proportion of concave curvature has a stronger ability to separate piled pulses.

[0109] The relationship between energy resolution and peak time of different curvature shaping algorithms is as follows: Figure 8 As shown in the figure, it can be seen that with the increase of pipe flow, the energy resolution of the energy spectrum of different shaping algorithms gradually decreases, and at the same time, the energy resolution shows a trend of first increasing and then losing with the increase of peak time. The main reason for the loss is the aggravation of the accumulation, which leads to the amplitude extraction of the shaped pulse with amplitude distortion, which makes the energy spectrum broadened and the energy resolution reduced.

[0110] The multi-curvature pulse shaping algorithm proposed in the present invention uses an arbitrary shape trapezoidal shaping pulse as the basic signal, which can achieve pulse shaping output with different curvature changes after signal transformation processing. The arbitrary shape trapezoidal shaping output result is simplified into a weighted and shifted linear combination of unit impulse signals through differentiation. The recursive algorithm obtained in this way is convenient for deployment and application on digital nuclear instruments.

[0111] Time domain characteristics: The forming parameters na and nc affect the proportion of concave curvature and convex curvature components in the rising edge change of the forming output, respectively, and are positively correlated;

[0112] Frequency domain characteristics: Under the same peak time, the shaping algorithm with a larger proportion of convex curvature has a smaller cutoff frequency and better filtering performance. Among them, the shaping algorithm with an output shape close to Gaussian has the best suppression effect on high-frequency noise;

[0113] Pile-up pulse separation capability and counting rate performance: Under the same peak time, the greater the proportion of concave curvature, the stronger the pile-up pulse separation capability and the better the pulse passing rate performance;

[0114] Energy resolution performance: Adding a convex curvature component to the shaped pulse can improve the optimal energy resolution performance of the pulse shaping algorithm at the same peak time;

[0115] Under different pipe flows, the optimal energy resolution of different shaping algorithms corresponds to the peak time zone and the results are as follows: Fig. 9 As shown. Figure 8 and Fig. 9 It can be seen that when the tube current is 7.8μA, the probability of pulse accumulation is small, and the optimal energy resolution performance level between the shaping algorithms is equivalent; after increasing the tube current, the probability of pulse accumulation increases, reducing the peak time of the shaping pulse and increasing the convex curvature component in the shaping pulse, which can slow down the rate of loss of the optimal energy spectrum energy resolution.

[0116] The above are only preferred embodiments of the present invention. It should be noted that the above preferred embodiments should not be regarded as limiting the present invention, and the protection scope of the present invention should be based on the scope defined by the claims. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the spirit and scope of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A pulse shaping method based on curvature transformation, characterized in that: The input signal is converted into an impulse signal through an impulse shaping system. A synthesis system is established based on the unit impulse signal to obtain a time domain expression of an arbitrary trapezoidal signal. The time domain expression is decomposed to simplify the synthesis of the pulse shape defined by the time domain expression, and a recursive formula for arbitrary trapezoidal pulse shaping is obtained. The symmetric trapezoidal pulse shaping algorithm is realized by this recursive formula. After obtaining the arbitrary trapezoidal pulse shaping algorithm, the bipolar zero area signal is composed of two arbitrary trapezoidal signals, and a differential operation is performed on the bipolar zero area signal to obtain a multi-curvature pulse shaping algorithm.

2. The pulse shaping method based on curvature transformation according to claim 1, characterized in that: The input signal has an exponential decay signal characteristic: i (t) = A·e -t / τ , where v i (t) is the input signal, A is the signal amplitude, e is the natural logarithm, τ is the time decay constant of the single exponential signal, and t is the continuous time scale.

3. The pulse shaping method based on curvature transformation according to claim 2, characterized in that: After the input signal is discretized, the amplitude A of the impulse signal is obtained through the impulse shaping system based on z-transform as follows: A=(1-d·z -1 )·V i (of), Where d = exp(-T s / τ), T s is the sampling period of the ADC, τ is the time decay constant of the single exponential signal, V i (z) is the discretized Z-transform result.

4. The pulse shaping method based on curvature transformation according to claim 3, characterized in that: Perform an inverse z-transform on the impulse shaping result of the input signal to obtain an impulse signal with an amplitude of A as follows: v(n)=A·δ(n)=v i (n)-d·v i (n-1) Where δ(n) is the unit impulse signal, v i (n) is the input signal, v(n) is the impulse signal.

5. The pulse shaping method based on curvature transformation according to claim 4, characterized in that: The time domain expression of the arbitrary shape trapezoidal signal obtained by establishing a synthesis system based on the unit impulse signal is as follows: h AT (n) is the time domain expression.

6. The pulse shaping method based on curvature transformation according to claim 5, characterized in that: The time-domain expression is differentiated twice to simplify the synthesis of the pulse shape defined by the time-domain expression and decompose it into a linear combination of weighted and / or shifted unit pulses. The recursive formula for arbitrary trapezoidal pulse shaping is obtained as follows: V1(n)=v i (n)-d·v i (n-1) V2(n)=nc·(V1(n)-V1(n-na))+na·(V1(n-na-nb-nc)-V1(n-na-nb)) V3(n)=V3(n-1)+V2(n) V AT (n)=V AT (n-1)+V3(n); The multi-curvature pulse shaping algorithm is obtained by integrating the bipolar zero-area signal once, and the formula is as follows V1(n)=v i (n)-d·v i (n-1) V1(n) is the result of impulse shaping of the exponential signal; It is the intermediate process of forming any trapezoidal shape; The result of trapezoidal forming of arbitrary shape; V o (n) is the multi-curvature pulse shaping result, v i (n) is the input signal, n is the time scale in the discrete domain; The above time domain recursion formula is simplified as follows: V1(n)=v i (n)-d·v i (n-1) V2(n)=nc·(V1(n)+V1(n-nc-nb-m)-V1(n-na)-V1(n-na-nb-nc-m))+ na·(V1(n-nc-m)+V1(n-na-nb-nc)-V1(nm)-V1(n-na-nb)) V3(n)=V3(n-1)+V2(n) V4(n)=V4(n-1)+V3(n) In o (n)=V o (n-1)+V4(n) Where d = exp(-T s / τ), T s is the sampling period of ADC, τ is the time decay constant of single exponential signal, exp is the sign replacement of exponential signal; V1(n), V2(n), V3(n), V4(n) are the intermediate processes of multi-curvature pulse shaping; The forming parameters na, nb, and nc jointly determine the peak time, the forming parameter nd is the flat top width, and the delay parameter m=na+nb+nc+nd-1.

7. The pulse shaping method based on curvature transformation according to claim 6, characterized in that: The shaping parameters determine the shape of the trapezoidal shaping, and further determine the curvature change of the final shaping pulse output.

8. The pulse shaping method based on curvature transformation according to claim 7, characterized in that: The larger the shaping parameter na is, the wider the width of the rising edge of the trapezoidal shaping pulse with positive polarity is, and the larger the proportion of the concave curvature in the rising edge of the finally obtained shaped pulse is.

9. The pulse shaping method based on curvature transformation according to claim 6, characterized in that: The smaller the ratio of the forming parameter na to the peak time, the larger the proportion of the convex curvature component and the smaller the cutoff frequency; the larger the ratio of the forming parameter na to the peak time, the larger the proportion of the concave curvature component and the stronger the accumulation pulse separation ability.

10. The pulse shaping method based on curvature transformation according to claim 7, characterized in that: The larger the forming parameter nc is, the wider the falling edge width of the trapezoidal forming pulse with positive polarity is, and the larger the proportion of the convex curvature in the rising edge of the final forming pulse is; after the peak time is determined, increasing the size of the forming parameter na will correspondingly reduce the size of the forming parameter nc.

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