CN113189634B - Gaussian-like forming method - Google Patents
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Abstract
The invention discloses a Gaussian-like forming method, which performs Gaussian-like forming filtering convolution processing on an input signal, comprises two convolution processing steps and comprises the following steps: s1, performing first convolution processing on an input signal to realize bipolar forming; and S2, performing second convolution processing on the signal obtained in the S1 to realize Gaussian-like forming. The method has the advantages of Gaussian forming and bipolar forming, achieves high-resolution energy spectrum, has good noise resistance, and has baseline drift resistance compared with a common digital forming method. Because the digital Gaussian filter is fully digital, the parameters of the digital Gaussian filter for comparing analog Gaussian shaping are easy to adjust, the pulse of the digital S-K filter for comparing removes the tailing symmetry, the pulse width is narrower, the digital Gaussian filter is suitable for energy spectrum measurement at high counting rate, the digital Gaussian filter for improving the filtering effect can be reused for two times, and the better effect is achieved.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a Gaussian-like forming method.
Background
Nuclear spectroscopy is one of the important methods for performing radioactivity measurement and analysis of material components. In a nuclear spectrum measurement system, a nuclear pulse signal output by a nuclear radiation detector rises quickly, but the falling time is long, so that not only the energy resolution but also the peak position of an energy spectrum curve are influenced. A common approach to solving this problem is to shape the nuclear pulse signal. Gaussian shaping has better comprehensive performance in the aspects of high energy resolution, ballistic deficit and the like, so the Gaussian shaping is a main research direction of nuclear pulse shaping. The analog gaussian shaping system is usually realized by using an analog S-K filter, but on one hand, the analog system has many defects in the aspects of stability, flexibility, spectral peak drift and the like, and on the other hand, with the development of digital electronic technology, digitization becomes the main direction of the development of nuclear analysis instruments, and the key of digitization is digital pulse shaping, so digital gaussian shaping becomes a hotspot of digital nuclear pulse signal processing research.
Due to the symmetry and completeness of Gaussian signals, gaussian filtering methods are used in a large amount in nuclear signal processing and nuclear data processing, a Gaussian filtering algorithm is complex, a real-time digital Gaussian filter is difficult to construct, the nuclear signal analog processing is generally realized by adopting an S-K filter, the nuclear signal digital processing is mainly used for researching a digital ladder filter as a mainstream at home and abroad at present, a CUSP filter and a sawtooth filter are used for PSD research, and impulse filters and other supplement methods for high counting rate research are adopted.
The inventor finds that the prior arts have at least the following technical problems in the practical use process:
the comparison of various forming methods is shown in fig. 2, the digital S-K filter constructed based on the analog system mainly has the defects that the calculation is complex, floating point operation is required, the trailing of the formed pulse is serious, the symmetry of the left side and the right side of the pulse is still to be improved, a single-stage digital S-K may also have a recoil signal, and the like.
Disclosure of Invention
In order to overcome the defects, the inventor of the invention continuously reforms and innovates through long-term exploration and trial and multiple experiments and efforts, and provides a Gaussian-like forming method which is stable and feasible and has excellent performance, a convolution-based Gaussian-like forming filter researched by the inventor comes from digital trapezoid forming and bipolar forming, and has the advantages of Gaussian forming and bipolar forming, and the Gaussian-like forming filter has better anti-noise capability while realizing high-resolution energy spectrum and also has baseline drift resistance capability compared with a common digital forming method. Because the system is fully digital, parameters of digital Gaussian shaping compared with analog Gaussian shaping are easy to adjust, trailing symmetry of pulses of a comparative digital S-K filter is better after being removed, the pulse width is narrower and suitable for energy spectrum measurement at high counting rate, the algorithm is much simpler when a real-time digital system is realized, the algorithm can be parallel to an AD sampling system at high speed, and the algorithm is simpler compared with the Gaussian shaping algorithm realized based on concave-convex shaping combination. In order to improve the filtering effect, the digital Gaussian-like forming filter can be used in series in two stages, so that a better effect is achieved.
In order to achieve the purpose, the invention adopts the technical scheme that: providing a Gaussian-like shaping method, performing Gaussian-like shaping filtering convolution processing on an input signal, wherein the method comprises two convolution processing steps, and comprises the following steps:
s1, performing first convolution processing on an input signal to realize bipolar forming;
and S2, performing second convolution processing on the signal obtained in the S1 to realize Gaussian-like forming.
According to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: the first convolution is processed as follows:
y(t)＝x(t)*H1(t)＝x(t)-x(t-tc)。
according to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: h1 (t) is the systematic convolution function, which is defined as follows:
H1(t)＝δ(t)-δ(t-tc)，
tc in the above equation is the pulse cut-off width.
According to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: the process of the second convolution is as follows:
z(t)＝y(t)*H2(t)/nc＝y (-1) (t)/nc
where nc = tc/Δ t, H2 (t) = ∈ (t), and is a step function.
According to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: the integral convolution and normalization again on the basis of the bipolar formation can be described by the following formula:
according to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows:
wherein the gaussian-like shaped filter convolution is defined as follows:
in the above equation, tc represents a pulse cut width, and nc = tc/Δ t.
According to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: the Gaussian-like shaping filtering convolution processing is full digitalization processing.
According to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: the gaussian-like shaped filter convolution process can be performed in real time.
According to the invention, a further preferable technical scheme of the Gaussian-like forming method is as follows: the gaussian-like shaped filter convolution process may be in parallel with the AD sampling.
According to the Gaussian-like forming method, the further preferable technical scheme is as follows: repeating S1-S2 twice to improve the filtering effect so as to achieve better effect.
Compared with the prior art, the technical scheme of the invention has the following advantages/beneficial effects:
the convolution-based Gaussian-like forming filtering method is from digital trapezoid forming and bipolar forming, has the advantages of Gaussian forming and bipolar forming, has better anti-noise capability while realizing high-resolution energy spectrum, and also has baseline drift resistance compared with a common digital forming method. Because the digital Gaussian-like shaping method is fully digital, parameters for digital Gaussian-like shaping compared with analog Gaussian shaping are easy to adjust, trailing symmetry of pulses of a comparative digital S-K filter is better after being removed, the pulse width is narrower and suitable for energy spectrum measurement at high counting rate, the algorithm is much simpler when a real-time digital system is realized, the digital Gaussian-like shaping method can be parallel to an AD sampling system at high speed, and the method is simpler compared with a Gaussian-like shaping method realized based on concave-convex shaping combination. The digital Gaussian-like forming filtering method can be reused for two times in order to improve the filtering effect, and a better effect is achieved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a flow chart of a Gaussian-like forming method of the present invention.
FIG. 2 is a comparative schematic of various forming processes.
Fig. 3 is a simulation schematic diagram of a single exponential signal bipolar shaping.
Fig. 4 is a schematic diagram of a bipolar shaped signal integral convolution simulation.
FIG. 5 is a schematic diagram of a forward sawtooth signal twice convolved simulation.
FIG. 6 is a schematic diagram of a simulation of the two-fold convolution of an inverted sawtooth signal.
Fig. 7 is a schematic diagram of gaussian-like shaped digital simulation.
Fig. 8 is a diagram of a flat-top gaussian-like shaped digital simulation.
Fig. 9 is a schematic diagram of a gaussian-like shaped baseline digital simulation.
Fig. 10 is a schematic diagram of a modified gaussian-like shaped baseline digital simulation.
Fig. 11 is a schematic diagram of a simulation of two convolutions of a CUSP signal.
FIG. 12 is a schematic diagram of a Gaussian-like cascade shaping simulation.
Fig. 13 is a comparison diagram of the frequency characteristics of three filters.
FIG. 14 is a schematic diagram of a trapezoidal Gaussian shaped detector signal test (NaI detector, 3.2 μ s digital pulse width).
FIG. 15 is a schematic representation of a Gaussian-like shaped spectrum test (NaI probe Cs-137 FWHM.
FIG. 16 is a schematic of a Gaussian-like shaped spectrum test (NaI probe, co-60).
FIG. 17 is a schematic of a Gaussian-like shaped spectrum test (NaI detector, cs-137+ Co-60).
The labels in the figure are respectively: 1. inputting a signal; 2. forming a Gaussian-like pulse; 3. trapezoidal pulse forming; 4. cusp-like forming; 5. CUSP gaussian-like frequency response curve; 6. trapezoidal shaped gaussian-like spectral responses; 7. The spectral response is shaped in a trapezoid.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the embodiments of the present invention are clearly and completely described below, and it is obvious that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention. Thus, the detailed description of the embodiments of the present invention provided below is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it may not be further defined and explained in subsequent figures. As shown in fig. 1, the present invention provides a gaussian-like shaping method, based on which a gaussian-like shaping filter can be constructed, specifically, it is used for performing a gaussian-like shaping filtering convolution process on an input signal, through a convolution method, a bipolar shaping can be constructed on the basis of a single exponential signal in fig. 3, equation (1) is a system convolution function, tc (nc = tc/Δ t) in the equation is a pulse truncation width, the convolved function is, for example, equation (2), a digital solution of equation (3) is obtained by sorting, a simulation result is shown in fig. 3, integral convolution is performed once again on the basis of the bipolar shaping, for example, equation (6), equations (1) to (5) can be sorted into a bipolar gaussian-like shaping filtering convolution equation (7), and if an integral area of the bipolar shaping is zero, stable baseline shaping as shown in fig. 4 can be achieved.
H1(t)＝δ(t)-δ(t-tc)
(1)
y(t)＝x(t)*H1(t)＝x(t)-x(t-tc)
(2)
y(t)＝x(t)-x(t-tc)
(3)
H2(t)＝ε(t)
(4)
z(t)＝y(t)*H2(t)/nc＝y (-1) (t)/nc
(5)
Fig. 5 and 6 show the effect of the bipolar shaping and the integral shaping simulated based on the positive direction sawtooth signal and the negative direction sawtooth signal by using the same algorithm, which is obviously improved compared with the effect of the shaping shown in fig. 4.
By directly replacing the input signal with a triangular shaped or trapezoidal shaped signal, the same algorithm can construct a gaussian-like shaped simulation result, see fig. 7. Extending the truncation time beyond the pulse width allows for a flat-top gaussian-like shaping as shown in fig. 8.
Fig. 9 shows a condition that a baseline is not zero due to accumulation of non-zero baseline values of trapezoidal shaped data at an initial stage when a simulated input signal baseline is not at zero, fig. 10 shows an improved simulation by proper integration and zero clearing, wherein an input single exponential signal is firstly shaped into a trapezoidal shaped signal, then bipolar shaped, and finally integrated shaped, and the improved baseline is stabilized at zero.
Fig. 11 shows that the same algorithm can be used to achieve baseline-stabilized gaussian-like shaping based on the peaked CUSP signal, which has a somewhat different shape from the gaussian-like shaped signal with trapezoidal shaped structure and flatter top.
Fig. 12 shows that the same algorithm is used to obtain a signal quality further improved by using a gaussian-like signal as a basis for cascading gaussian-like shaping simulation (the truncation time is slightly narrower than the pulse width, and a part of the flat top width can be compressed), and certainly, the resources consumed by a digital system can be doubled, and the width of the shaped signal can be widened.
In addition, a primary digital Gaussian-like forming object formed on the basis of digital trapezoid forming is firstly constructed and analyzed from a time domain signal construction of trapezoid forming, a Gaussian-like forming time domain signal expression is constructed on the basis of the trapezoid forming time domain signal, then the time domain signal is Z-transformed, finally a Z-domain system response function based on a single exponential signal is constructed, and then the frequency characteristic of the system is analyzed.
Equations (8) - (12) are the time domain synthesis description and the four-part time domain description of the trapezoidal signal; formula (13) is a Z-domain description of the trapezoidal signal; equations (14) - (15) are time-domain Z-domain descriptions of single exponential signals; equation (16) is the Z-domain system response function for trapezoidal shaping of the single exponential signal; formula (17) is a gaussian-like signal described by a time-domain function of a trapezoidal signal; equation (18) is a gaussian-like signal segment signal time domain description; equation (19) is a gaussian-like signal segmentation signal time domain solution; equations (20) - (23) are time domain descriptions of the gaussian-like signal divided into four parts; equations (24) - (27) are a Z-domain description of the Gaussian-like signal divided into four parts; equation (28) is a Z-domain description of gaussian-like signal synthesis; equation (29) is a single exponential signal gaussian-like shaped Z-domain system response function.
The frequency domain characteristics of the system can be obtained by the formula (16) and the formula (29) as shown in fig. 12.
V2(t)＝-V1(t-t a )
(10)
V3(t)＝-V1(t-t b )
(11)
V4(t)＝V1(t-t c )
(12)
Y(t)＝(Vo(t)-Vo(t-tc)) (-1) ＝Vo(t) (-1) -Vo(t-tc) (-1)
(17)
Y(t)＝V1(t) (-1) +V2(t) (-1) +V3(t) (-1) +V4(t) (-1) -V1(t-tc) (-1) +
V2(t-tc) (-1) +V3(t-tc) (-1) +V4(t-tc) (-1) )
(18)
Y 1 (t)＝V1(t) (-1) -(V1(t-tc) (-1)
(20)
Y 2 (t)＝V2(t) (-1) -(V2(t-tc) (-1)
(21)
Y 3 (t)＝V3(t) (-1) -(V3(t-tc) (-1）
(22)
Y 4 (t)＝V4(t) (-1) -(V4(t-tc) (-1)
(23)
As can be seen from comparison in fig. 13, for the same single-exponential input signal, the frequency characteristics of the digital trapezoidal gaussian shaping filter and the digital trapezoidal gaussian shaping filter almost coincide at the front portion, but the performance is better at the rear end of the high-frequency cutoff portion, the performance of the digital trapezoidal gaussian shaping filter has a significant advantage over the digital trapezoidal filter, the simulation effect of the steeple CUSP gaussian shaping filter is almost equivalent to that of the trapezoidal gaussian shaping filter, and the steeple CUSP gaussian shaping filter Z-domain system function can be constructed by using a method similar to that of the foregoing.
FIG. 14 shows the signal test of a trapezoidal Gaussian-like forming detector, the 20MHZ 12-bit ADC sampling, the 32-point double-exponential trapezoidal forming is adopted to generate 64-point bipolar forming, and the integral forming is performed to generate 64-point Gaussian-like forming, so that the symmetry of signals is good, the approximation degree with Gaussian signals is high, and the noise is low; fig. 15 shows a gaussian-like shaped Cs-137 spectrum test (Φ 75 x 100NaI detector, 3.2 μ s digital pulse width) FWHM =6.62%, and also FWHM =6.75% when the pulse width is trapezoidal shaped, which realizes a narrow-pulse gaussian shaped high-resolution spectrum of the NaI scintillation detector; FIG. 16 is a Co-60 energy spectrum test; fig. 17 is a spectrum test with Cs-137 added under the same measurement conditions as fig. 15, and the peak positions of Co in fig. 16 and fig. 17 are almost completely overlapped, the baseline of the system is stable, the bipolar forming characteristic is inherited, and the integral linearity of the three peaks is good (R2 = 0.999994). In the testing process, the bias voltage of the signal is artificially adjusted, the digital forming baseline value measured by the system is always zero as the same as the measured value when the bipolar forming is adopted, and the system baseline is stable.
The convolution-based Gaussian-like forming filtering method is from digital trapezoid forming and bipolar forming, has the advantages of Gaussian forming and bipolar forming, has better anti-noise capability while realizing high-resolution energy spectrum, and also has baseline drift resistance compared with a common digital forming method. Because the digital Gaussian-like shaping method is fully digital, parameters of digital Gaussian-like shaping compared with analog Gaussian shaping are easy to adjust, the trailing symmetry of pulses of the digital S-K filter is better removed, the pulse width is narrower, and the digital S-K filter is suitable for energy spectrum measurement at high counting rate. In order to improve the filtering effect, the digital Gaussian-like forming filtering method can be repeatedly used for two times, and a better effect is achieved.
The above is only a preferred embodiment of the present invention, and it should be noted that the above preferred embodiment should not be considered as limiting the present invention, and the protection scope of the present invention should be subject to the scope defined by the claims. It will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the spirit and scope of the invention, and should be considered to be within the scope of the invention.
Claims (5)
1. A Gaussian-like shaping method is characterized in that the input signal is processed by the convolution processing of Gaussian-like shaping filtering, the convolution processing comprises two times of convolution processing, and the steps are as follows:
s1, performing first convolution processing on an input signal to realize bipolar forming;
the process of the first convolution is as follows:
y(t)＝x(t)*H1(t)＝x(t)-x(t-tc)；
wherein x (t) is an input signal; h1 (t) is the impulse response function of the first convolution; y (t) is an output result of the convolution of the input signal and the impulse response function; t denotes time, tc denotes pulse truncation width, and H1 (t) is defined as follows:
H1(t)＝δ(t)-δ(t-tc)；
wherein, δ (t) represents impulse signal, δ (t-tc) represents impulse signal delay tc time;
s2, performing second convolution processing on the signal obtained in the S1 to realize Gaussian-like forming;
the process of the second convolution is as follows:
Z(t)＝y(t)*H2(t)/tc＝y (-1) (t)/tc
wherein y (t) is an output signal after the first convolution; h2 (t) is the impulse response function of the second convolution; h2 (t) = epsilon (t), epsilon (t) represents a step signal; z (t) is the output signal after the second convolution;
discretizing the above formula to obtain
Wherein t = n · Δ t, n =1,2,3,4 …, Δ t being the ADC sampling time; nc = tc/Δ t
Finally, the transfer function H (t) of the Gaussian-like shaping method can be written as
Wherein, H1 (t) is the impulse response function of the first convolution, H2 (t) is the impulse response function of the second convolution, and tc represents the pulse truncation width.
2. The gaussian-like shaping method according to claim 1, wherein the gaussian-like shaping filter convolution process is a fully digital process.
3. The gaussian-like shaping method as recited in claim 1, wherein the gaussian-like shaping filtering convolution process is performed in real time.
4. The gaussian-like shaping method according to claim 1, wherein the gaussian-like shaping filtering convolution process and the ADC sampling can be performed in parallel.
5. The gaussian-like shaping method as claimed in claim 1, wherein S1-S2 are repeated twice to improve filtering effect.
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