CN105629290A - Method of forming Mexico hat wavelet by digital nuclear pulse signal - Google Patents

Abstract

The invention discloses a method of forming a Mexico hat wavelet by a digital nuclear pulse signal. The method comprises steps of exponential decay digital nuclear pulse signal Mexico hat wavelet forming real-time data processing, baseline subtraction, ballistic loss quantification, multi-particle pulse shape discrimination and ballistic loss compensation real-time data processing. Defects in data processing aspects of baseline subtraction, ballistic loss quantification and compensation and particle pulse shape discrimination by other nuclear pulse signal digital filtering forming methods are effectively overcome, and a wavelet analysis method is used for enabling the digital nuclear pulse signal to be filtered and formed into a Mexico hat wavelet signal.

Description

A kind of digital core pulse signal Mexico hat wavelet manufacturing process

Technical field

The present invention relates to the Mexico hat wavelet of digital core pulse signal in radiometry to shape, particularly relate to a kind of digital core pulse signal Mexico hat wavelet manufacturing process based on wavelet analysis.

Background technology

Nuclear spectrum measurement technological synthesis multiple subjects such as electronic technology, nuclear detection technology, computer technology. At present, one of its important means having become as elemental analysis, play the part of more and more important role at subjects such as medical science, geology, biology, environmentology, chemistry, archaeology.

In nuclear radiation measurement, the pulse amplitude of the energy of incoming particle and nuclear detector output is directly proportional, and just can analyze emittance by measuring the amplitude of pulse signal. The acquisition of power spectrum, to analyze also be one of most important means in nuclear analytical method, by the acquisition of radiation source power spectrum and analyzing can obtain the important informations such as the structure of radiant matter, the kind of component and content directly or indirectly. The nuclear spectrometer of traditional acquisition power spectrum, is mainly amplified shaping with electronics device, baseline restorer, accumulation are sentenced and abandoned and pulse signal peak value remains the simulation nuclear spectrometer of feature to nuclear signal.

The totally digitilized energy disperse spectroscopy shaped based on digital filtering is increasingly becoming the trend that nuclear instrument develops, digitized energy disperse spectroscopy currently mainly adopts trapezoidal filtering shaping Algorithm, this filtering shaping Algorithm can not solve baseline drift well after baseline deduction problem, ballistic deficit degree quantification problem, multiple particle pulse shape discrimination problem and compensate and cause pulse amplitude decline problem because of ballistic deficit with sensitivity, Mexico's hat wavelet manufacturing process can solve the problems referred to above.

Summary of the invention

It is an object of the invention to open a kind of digital core pulse signal Mexico hat wavelet manufacturing process, the method overcome other digital filtering manufacturing process of core pulse signal deficiency in the data process such as baseline deduction, ballistic deficit quantization and compensation, particle pulse shape discriminating, while filtering noise, with wavelet analysis method, the filtering of digital core pulse signal being configured to Mexico's hat wavelet signal, the digital Mexico hat wavelet solving core pulse shapes demand.

The present invention is achieved by the following technical solutions, specifically includes:

Using the first derivative of Mexico's straw hat morther wavelet as morther wavelet, carry out wavelet transformation with exponential damping core pulse signal, utilize convolution integral character, it is possible to derive the system function that exponential damping core pulse signal Mexico hat wavelet shapes�� in formula₀For Damped exponential signals time constant, s is wavelet transform dimension, h (t) is finite digital signal, in discrete domain, shapes by asking the convolution of exponential damping core pulse signal f (n) and finite digital signal h (n) can realize Mexico's hat wavelet;

Line signals b (t)=kt+c, in formula, k, c are constant, b (t) and system function system functionConvolution be constantly equal to 0, Damped exponential signals superposition b (t) baseline, after Mexico hat wavelet shapes, baseline is constantly equal to 0, without carrying out baseline deduction again after molding;

When there is no ballistic deficit, core pulse signal is after Mexico's hat wavelet shapes, the left and right minimum of waveform is symmetrical, when there is ballistic deficit, ripple row left and right minimum after shaping is no longer symmetrical, the minimizing difference in ripple row left and right after shaping can be used to quantify ballistic deficit degree, and this quantized value is continuous, and utilizes this value measurement ballistic deficit to have higher sensitivity;

After quantifying ballistic deficit degree, it is possible to the ballistic deficit degree according to quantifying carries out multiple particle pulse shape discrimination;

After quantifying ballistic deficit degree, it is possible to adopt according to ballistic deficit degree quantized value the method being multiplied by coefficient to compensate the pulse amplitude caused because of ballistic deficit and decline.

Compared with prior art, one or more embodiments of the invention can have the advantage that

Effectively overcome other digital filtering manufacturing process of core pulse signal deficiency in the data process such as baseline deduction, ballistic deficit quantization and compensation, particle pulse shape discrimination, with wavelet analysis method, the filtering of digital core pulse signal is configured to Mexico's hat wavelet signal, waveform after shaping has following good characteristic: the waveform baseline after shaping is constantly equal to 0, it is not necessary to deduct baseline again; Ballistic deficit can pass through two minimizing differences about Mexico's hat wavelet and quantify, and quantized value is continuous, and utilizes this value measurement ballistic deficit to have higher sensitivity; Particle pulse shape discrimination can be carried out by ballistic deficit quantized value.

Other features and advantages of the present invention will be set forth in the following description, and, partly become apparent from description, or understand by implementing the present invention. The purpose of the present invention and other advantages can be realized by structure specifically noted in description, claims and accompanying drawing and be obtained.

Accompanying drawing explanation

Accompanying drawing is for providing a further understanding of the present invention, and constitutes a part for description, is provided commonly for explaining the present invention with embodiments of the invention, is not intended that limitation of the present invention. In the accompanying drawings:

Tu1Shi Mexico hat wavelet forming process and ballistic deficit quantify schematic diagram;

Wherein Fig. 1 (a) is without the schematic diagram in ballistic deficit situation;

Fig. 1 (b) has the schematic diagram in ballistic deficit situation;

Illustrate: (1) M (t)=f (t) * h (t):

(2) ballistic deficit is quantified as $M=\frac{h}{H}\&CenterDot;k\left(t\right),$ Wherein $k\left(t\right)=\left\{\begin{array}{c}{c}_1,t_1\&le;t<t_2\\ c_2,t_2\&le;t<t_3\\ \mathrm{......}\end{array}\right.$

Tu2Shi Mexico hat wavelet formed data processes Parallel Digital logical block scattergram;

Fig. 3 is ballistic deficit correlative curve relation figure.

Detailed description of the invention

Easy to understand, according to technical scheme, under the connotation not changing the present invention, one of ordinary skill in the art can propose multiple frame modes and the manufacture method of the present invention. Therefore detailed description below and accompanying drawing are only illustrating of technical scheme, and are not to be construed as the whole of the present invention or are considered as defining or limiting of technical solution of the present invention.

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail.

It is as follows that exponential damping digital core pulse signal Mexico hat wavelet shapes real time data processing algorithmic derivation:

Mexico's straw hat mother wavelet function expression formula is:

$g\left(t\right)=(1-t^2)\exp (-\frac{t^2}{2})---(2-1)$

G (t) Convolution-type wavelet basis function is:

$g_s\left(t\right)=\frac{1}{s}g\left(\frac{t}{s}\right)---(2-2)$

The first derivative that �� (t) is g (t), then

$\mathrm{\&psi;}\left(t\right)=\frac{dg\left(t\right)}{dt}=(t^3-3t)\exp (-\frac{t^2}{2})---(2-3)$

Its Fouier is transformed to,

$\widehat{\mathrm{\&psi;}}\left(\mathrm{\&omega;}\right)=\sqrt{2\mathrm{\&pi;}}{\mathrm{j\&omega;}}^3\exp (-\frac{{\mathrm{\&omega;}}^2}{2})---(2-4)$

ObviouslyCan as small echo mother's wave function by the known �� (t) of admissibility condition, its Convolution-type wavelet basis function is,

${\mathrm{\&psi;}}_s\left(t\right)=\frac{1}{s}\mathrm{\&psi;}\left(\frac{t}{s}\right)---(2-5)$

Nuclear radiation detector preamplifier output signal expression is:

$f\left(t\right)=H\&CenterDot;e^{-\frac{t}{{\mathrm{\&tau;}}_0}}u\left(t\right)---(2-6)$

In formula (2-6), H is Damped exponential signals pulse amplitude, ��₀For Damped exponential signals time constant, u (t) as shown in formula (2-7),

$u\left(t\right)=\left\{\begin{array}{c}0,t<0\\ 1,t\&GreaterEqual;0\end{array}\right.---(2-7)$

F (t) derivation obtains,

$\frac{df\left(t\right)}{dt}=-\frac{1}{{\mathrm{\&tau;}}_0}f\left(t\right)+H\&CenterDot;\mathrm{\&delta;}\left(t\right)---(2-8)$

In formula (2-8), �� (t) is unit impulse function, with formula (2-5) for wavelet basis function, f (t) is made wavelet transformation, then

$W_{s}f\left(t\right)=f\left(t\right)*{\mathrm{\&psi;}}_s\left(t\right)=f\left(t\right)*s\frac{{\mathrm{dg}}_s\left(t\right)}{dt}=\frac{df\left(t\right)}{dt}*{\mathrm{sg}}_s\left(t\right)---(2-9)$

Substitution formula (2-2), formula (2-5) and formula (2-8),

$f\left(t\right)*\frac{1}{s}(\frac{t^3}{s^3}-\frac{3t}{s})\exp (-\frac{t^2}{2s^2})=-\frac{s}{{\mathrm{\&tau;}}_0}f\left(t\right)*\frac{1}{s}(1-\frac{t^2}{s^2})\exp (-\frac{t^2}{2s^2})+H\&CenterDot;s\&CenterDot;g_s\left(t\right)---(2-10)$

Arrange,

$H\&CenterDot;s\&CenterDot;g_s\left(t\right)=f\left(t\right)*\&lsqb;\frac{t^3}{s^4}-\frac{3t}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{t^2}{s^2})\&rsqb;\exp (-\frac{t^2}{2s^2})---(2-11)$

Make system function

$h\left(t\right)=\&lsqb;\frac{t^3}{s^4}-\frac{3t}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{t^2}{s^2})\&rsqb;\exp (-\frac{t^2}{2s^2})---(2-12)$

�� in formula (2-12)₀For Damped exponential signals time constant, s is wavelet transform dimension, by formula (2-11) and formula (2-12) it can be seen that the convolution of f (t) and h (t) is:

$M\left(t\right)={\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}f\left(\mathrm{\&tau;}\right)h(t-\mathrm{\&tau;})d\mathrm{\&tau;}=H\&CenterDot;(1-\frac{t^2}{s^2})\exp (-\frac{t^2}{2s^2})---(2-13)$

ObviouslyNamely h (t) is finite digital signal, then h (t) can discrete turn to,

$h\left(n\right)=\left\{\begin{array}{c}{k}_n=\&lsqb;\frac{n^3}{s^4}-\frac{3n}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{n^2}{s^2})\&rsqb;\exp (-\frac{n^2}{2s^2}),\left|n\right|=0,1,2,......,M\\ 0,\left|n\right|>M\end{array}\right.---(2-14)$

In formula (2-14), M is positive integer, it is considered to superposition baseline factors, and formula (2-6) can discrete turn to,

$f\left(n\right)=\left\{\begin{array}{c}kn+c,n=...,-2,-1,\\ F_n=kn+c+H\&CenterDot;e^{-\frac{n}{{\mathrm{\&tau;}}_0}},n=0,1,...,3N-1\\ kn+c,n=3N,3N+1,...\end{array}\right.---(2-15)$

In formula (2-15), N is positive integer, k, and c is constant, it is known that sampled point F_i, timeconstant��₀Can be tried to achieve by following formula,

${\mathrm{\&tau;}}_0=\frac{N}{ln\frac{\underset{i=N}{\overset{2N-1}{\&Sigma;}}{F}_i-\underset{i=0}{\overset{N-1}{\&Sigma;}}{F}_i}{\underset{i=2N}{\overset{3N-1}{\&Sigma;}}{F}_i-\underset{i=N}{\overset{2N-1}{\&Sigma;}}{F}_i}}---(2-16)$

By formula (2-13), formula (2-14) and formula (2-15) it can be seen that in discrete domain,

$M\left(n\right)=\underset{i=-M}{\overset{M}{\&Sigma;}}f(n-i)\&CenterDot;k_i=H\&CenterDot;(1-\frac{i^2}{s^2})\exp (-\frac{i^2}{2s^2})---(2-17)$

Formula (2-17) shapes real time data processing key expression formula for exponential damping digital core pulse signal Mexico hat wavelet. Fig. 2 illustrates Mexico's hat wavelet formed data and processes the distribution of Parallel Digital logical block, worked by many multipliers and many adders concurrent collaborative, formula (2-17) can realize real time data processing, and the filtering namely completing a sampled point within the clock cycle of a sampled point data acquisition calculates.

After system function formula (2-12) filtering shapes, the baseline of waveform is constantly equal to 0, and concrete derivation is as follows:

The following baseline of formula (2-6) superposition might as well be set:

B (t)=k t+c (2-18)

In formula (2-18), k, c are constant, it is clear that

${\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\exp (-\frac{t^2}{2s^2})dt=s\sqrt{2\mathrm{\&pi;}}---(2-19)$

${\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{t}^{2n}\exp (-\frac{t^2}{2s^2})dt=1\&CenterDot;3\&CenterDot;\mathrm{...}\&CenterDot;(2n-1)\&CenterDot;s^{2n+1}\sqrt{2\mathrm{\&pi;}},n=1,2,\mathrm{...}---(2-20)$

${\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{t}^{2n-1}\exp (-\frac{t^2}{2s^2})dt=0,n=1,2,\mathrm{...}---(2-21)$

Then formula (2-18) with the convolution of formula (2-12) is,

$\begin{array}{c}b\left(t\right)*h\left(t\right)=k{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\&lsqb;\frac{(t-\mathrm{\&tau;}){\mathrm{\&tau;}}^3}{s^4}-\frac{3(t-\mathrm{\&tau;})\mathrm{\&tau;}}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(t-\mathrm{\&tau;}-\frac{(t-\mathrm{\&tau;}){\mathrm{\&tau;}}^2}{s^2})\&rsqb;\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ +c{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\&lsqb;\frac{{\mathrm{\&tau;}}^3}{s^4}-\frac{3\mathrm{\&tau;}}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{{\mathrm{\&tau;}}^2}{s^2})\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ =-\frac{k}{s^4}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{\mathrm{\&tau;}}^4\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}+\frac{3k}{s^2}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{\mathrm{\&tau;}}^2\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}+\frac{kt+c}{{\mathrm{\&tau;}}_0}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ -\frac{kt+c}{s^2{\mathrm{\&tau;}}_0}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{\mathrm{\&tau;}}^2\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ =-3\sqrt{2\mathrm{\&pi;}k}\&CenterDot;s+3\sqrt{2\mathrm{\&pi;}k}\&CenterDot;s+\frac{kt+c}{{\mathrm{\&tau;}}_0}\sqrt{2\mathrm{\&pi;}}\&CenterDot;s-\frac{kt+c}{{\mathrm{\&tau;}}_0}\sqrt{2\mathrm{\&pi;}}\&CenterDot;s\\ =0\end{array}---(2-22)$

By formula (2-22) it can be seen that

[f (t)+b (t)] * h (t)=f (t) * h (t) (2-23)

The i.e. baseline of superposing type (2-18) in formula (2-6), after system function formula (2-12) filtering shapes, baseline is constantly equal to 0, and the waveform after shaping is without carrying out baseline deduction again.

As shown in Fig. 1-(b), when there is ballistic deficit, after Mexico's hat wavelet shapes, waveform left and right minimum is no longer symmetrical, and its difference in height is h, and might as well be set as the waveform maximum after shape is H, H namely shape after pulse amplitude values, then ballistic deficit degree can be usedQuantify. It addition, ballistic deficit degree is more big, the time difference t value between the minimum of waveform left and right after shaping is more big.

The core pulse signal that there is ballistic deficit can be simulated by formula (2-24),

$f\left(t\right)=H\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&tau;}}_0-{\mathrm{\&tau;}}_1}\&lsqb;\exp (-\frac{t}{{\mathrm{\&tau;}}_0})-\exp (-\frac{t}{{\mathrm{\&tau;}}_1})\&rsqb;---(2-24)$

Fig. 3-(a) is ballistic deficit degree quantized valueWith time parameter ��₁Relation curve, time parameter ��₁More big, represent that ballistic deficit degree is more big, corresponding ballistic deficit degree quantized valueMore big, ballistic deficit degree quantized valueWith time parameter ��₁Relation curve monotonic increase. Fig. 3-(b) is the time difference t between the waveform left and right minimum after shaping and time parameter ��₁Relation curve. Fig. 3-(c) is ballistic deficit quantized valueWith shape after pulse amplitude H relation curve, according to this relation curve, it is possible to adopt according to ballistic deficit degree quantized value the method being multiplied by certain coefficient to compensate the pulse amplitude caused because of ballistic deficit and decline.

Fig. 3-(a) curve relation figure is monotonically increasing function, therefore can pass through to compare ballistic deficit degree quantized value size, carries out multiple particle pulse shape discrimination.

Although the embodiment that disclosed herein is as above, but described content is only to facilitate the embodiment understanding the present invention and adopt, is not limited to the present invention. Technical staff in any the technical field of the invention; under the premise without departing from the spirit and scope that disclosed herein; any amendment and change can be done in the formal and details implemented; but the scope of patent protection of the present invention, still must be as the criterion with the scope that appending claims defines.

Claims (6)

1. a digital core pulse signal Mexico hat wavelet manufacturing process, it is characterised in that this digital core pulse signal Mexico hat wavelet manufacturing process includes: exponential damping digital core pulse signal Mexico hat wavelet shapes real time data processing algorithm; Baseline deduction method; Ballistic deficit quantization method; Multiple particle pulse shape discrimination method; Ballistic deficit compensates real time data processing algorithm.

2. a kind of digital core according to claim 1 pulse signal Mexico hat wavelet manufacturing process, it is characterised in that it is as follows that exponential damping digital core pulse signal Mexico hat wavelet shapes real time data processing algorithmic derivation:

Nuclear radiation detector preamplifier output signal expression is:

$f\left(t\right)=H\&CenterDot;e^{-\frac{t}{{\mathrm{\&tau;}}_0}}u\left(t\right)---(1-1)$

In formula (1-1), H is Damped exponential signals pulse amplitude, ��₀For Damped exponential signals time constant, u (t) as shown in formula (1-2),

$u\left(t\right)=\left\{\begin{array}{c}0,t<0\\ 1,t\&GreaterEqual;0\end{array}\right.---(1-2)$

Make system function

$h\left(t\right)=\&lsqb;\frac{t^3}{s^4}-\frac{3t}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{t^2}{s^2})\&rsqb;\exp (-\frac{t^2}{2s^2})---(1-3)$

�� in formula (1-3)₀For Damped exponential signals time constant, s is wavelet transform dimension, then the convolution of f (t) and h (t) is:

$M\left(t\right)={\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}f\left(\mathrm{\&tau;}\right)h(t-\mathrm{\&tau;})d\mathrm{\&tau;}=H\&CenterDot;(1-\frac{t^2}{s^2})\exp (-\frac{t^2}{2s^2})---(1-4)$

ObviouslyNamely h (t) is finite digital signal, then h (t) can discrete turn to,

$h\left(n\right)=\left\{\begin{array}{c}{k}_n=\&lsqb;\frac{n^3}{s^4}-\frac{3n}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{n^2}{s^2})\&rsqb;\exp (-\frac{n^2}{2s^2}),\left|n\right|=0,1,2,......,M\\ 0,\left|n\right|>M\end{array}\right.---(1-5)$

In formula (1-5), M is positive integer, it is considered to superposition baseline factors, and formula (1-1) can discrete turn to,

$f\left(n\right)=\left\{\begin{array}{c}kn+c,n=...,-2,-1,\\ F_n=kn+c+H\&CenterDot;e^{-\frac{n}{{\mathrm{\&tau;}}_0}},n=0,1,...,3N-1\\ kn+c,n=3N,3N+1,...\end{array}\right.---(1-6)$

In formula (1-6), N is positive integer, k, and c is constant, it is known that sampled point F_i, timeconstant��₀Can be tried to achieve by following formula,

${\mathrm{\&tau;}}_0=\frac{N}{ln\frac{\underset{i=N}{\overset{2N-1}{\&Sigma;}}{F}_i-\underset{i=0}{\overset{N-1}{\&Sigma;}}{F}_i}{\underset{i=2N}{\overset{3N-1}{\&Sigma;}}{F}_i-\underset{i=N}{\overset{2N-1}{\&Sigma;}}{F}_i}}---(1-7)$

By formula (1-4), formula (1-5) and formula (1-6) it can be seen that in discrete domain,

$M\left(n\right)=\underset{i=-M}{\overset{M}{\&Sigma;}}f(n-i)\&CenterDot;k_i---(1-8)$

Formula (1-8) shapes real time data processing key expression formula for exponential damping digital core pulse signal Mexico hat wavelet.

3. as claimed in claim 2 a kind of digital core pulse signal Mexico hat wavelet manufacturing process, it is characterised in that after system function formula (1-3) filtering shapes, the baseline of waveform is constantly equal to 0, concrete derive as follows:

The following baseline of formula (1-1) superposition might as well be set:

B (t)=k t+c (1-9)

In formula (1-9), k, c are constant, it is clear that

${\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\exp (-\frac{t^2}{2s^2})dt=s\sqrt{2\mathrm{\&pi;}}---(1-10)$

${\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{t}^{2n}\exp (-\frac{t^2}{2s^2})dt=1\&CenterDot;3\&CenterDot;\mathrm{...}\&CenterDot;(2n-1)\&CenterDot;s^{2n+1}\sqrt{2\mathrm{\&pi;}},n=1,2,\mathrm{...}---(1-11)$

${\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{t}^{2n-1}\exp (-\frac{t^2}{2s^2})dt=0,n=1,2,\mathrm{...}---(1-12)$

Then formula (1-9) with the convolution of formula (1-3) is,

$\begin{array}{c}b\left(t\right)*h\left(t\right)=k{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\&lsqb;\frac{(t-\mathrm{\&tau;}){\mathrm{\&tau;}}^3}{s^4}-\frac{3(t-\mathrm{\&tau;})\mathrm{\&tau;}}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(t-\mathrm{\&tau;}-\frac{(t-\mathrm{\&tau;}){\mathrm{\&tau;}}^2}{s^2})\&rsqb;\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ +c{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\&lsqb;\frac{{\mathrm{\&tau;}}^3}{s^4}-\frac{3\mathrm{\&tau;}}{s^2}+\frac{1}{{\mathrm{\&tau;}}_0}(1-\frac{{\mathrm{\&tau;}}^2}{s^2})\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ =-\frac{k}{s^4}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{\mathrm{\&tau;}}^4\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}+\frac{3k}{s^2}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{\mathrm{\&tau;}}^2\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}+\frac{kt+c}{{\mathrm{\&tau;}}_0}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ -\frac{kt+c}{s^2{\mathrm{\&tau;}}_0}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{\mathrm{\&tau;}}^2\exp (-\frac{{\mathrm{\&tau;}}^2}{2s^2})d\mathrm{\&tau;}\\ =-3\sqrt{2\mathrm{\&pi;}}k\&CenterDot;s+3\sqrt{2\mathrm{\&pi;}}k\&CenterDot;s+\frac{kt+c}{{\mathrm{\&tau;}}_0}\sqrt{2\mathrm{\&pi;}}\&CenterDot;s-\frac{kt+c}{{\mathrm{\&tau;}}_0}\sqrt{2\mathrm{\&pi;}}\&CenterDot;s\\ =0\end{array}---(1-12)$

By formula (1-12) it can be seen that

[f (t)+b (t)] * h (t)=f (t) * h (t) (13)

The i.e. baseline of superposing type (1-9) in formula (1-1), after system function formula (3) filtering shapes, baseline is constantly equal to 0, and the waveform after formation is without carrying out baseline deduction again.

4. as claimed in claim 2 a kind of digital core pulse signal Mexico hat wavelet manufacturing process, it is characterized in that, formula (1-1) exists in ballistic deficit situation, after system function formula (1-3) filters molding, in formula (1-4), the minimum on Mexico's hat wavelet function M (t) left side and the minimum on the right occur asymmetric, it is possible to quantify ballistic deficit degree by the minimizing difference in left and right.

5. as claimed in claim 3 a kind of digital core pulse signal Mexico hat wavelet manufacturing process, it is characterised in that after quantifying ballistic deficit degree, it is possible to the ballistic deficit degree according to quantifying carries out multiple particle pulse shape discrimination.

6. as claimed in claim 3 a kind of digital core pulse signal Mexico hat wavelet manufacturing process, it is characterized in that, after quantifying ballistic deficit degree, it is possible to adopt according to ballistic deficit degree quantized value the method being multiplied by coefficient to compensate the pulse amplitude caused because of ballistic deficit and decline.