CN102901853A - Nuclear signal frequency conversion digitization sampling method - Google Patents

Abstract

The invention proposes a new method for nuclear signal frequency conversion digital sampling based on digital extraction technology, which belongs to the technical field of nuclear signals. The method is realized through the following steps: 1. Determination of the optimal sampling frequency: (1) identification and peak-finding of the digital core signal, (2) determination of the optimal sampling frequency for the rising edge of the digital core signal, (3) the optimal sampling frequency for the falling edge of the digital core signal Determination of the best sampling frequency; 2. Frequency conversion sampling of the same digital core signal waveform: (1) digital core signal screening and peak finding, (2) digital low-pass filtering, (3) digital frequency division extraction on the rising edge, ( 4) Carry out digital frequency division extraction on the falling edge, (5) Signal synthesis. Through the method of the invention, the sampling accuracy of the digitized nuclear signal output by the waveform digital nuclear instrument can be ensured without loss, and at the same time, the amount of waveform data of the finally generated digital nuclear signal can be minimized.

Description

A method for nuclear signal frequency conversion digital sampling

technical field

The invention relates to a nuclear signal sampling technology, in particular to a nuclear signal frequency conversion digital sampling method, which belongs to the technical field of nuclear signals.

Background technique

The digital acquisition technology of nuclear information has been developed for half a century. In the past 20 years, with the rapid progress of computer software and hardware technology, digital communication technology and semiconductor technology, digital nuclear instrument technology has also been fully developed. So far, digital nuclear instruments have occupied more than 50% of the nuclear instrument market. To realize any kind of digital nuclear instrument, the waveform digitization system is an essential key part, so the research on the realization principle and method of waveform digitization is also a hot issue in the research of digital nuclear instrument and even all digital instruments. Existing theories, such as Shannon's sampling law and Nyquist's sampling law, all indicate that quantization errors will be introduced in the process of converting analog signals into digital signals through analog/digital conversion technology, and the conversion speed of analog/digital converters (ADCs) will be improved. And converting the number of bits is an effective way to reduce the quantization error. However, there are several contradictions in the digitization of waveforms: First, the contradiction between the performance and price of digital instruments. For example, in 2012, the American Tektronic company launched a high-performance digital oscilloscope with a sampling rate of 80Gbps and an analog frequency band of 33GHz. The price of this product is RMB 3 million. Second, the contradiction between ADC performance and instrument channel density. For example, the digital nuclear energy spectrometer Pixie-500 produced by XIA Corporation of the United States uses an ADC with a sampling rate of 500MSPS to realize a 4-channel digital spectrometer; and the digital nuclear energy spectrometer Pixie-16 realizes a 16-channel digital spectrometer. The sampling rate is 100MSPS ADC. Third, the contradiction between the conversion speed of the ADC and the number of conversion bits. In 2002, the Argonne National Laboratory led 12 research institutions to form a working group of "Digital Electronics in Nuclear Structural Physics", planning to establish a 40-channel fully digital measurement system that can meet most of the measurement tasks of low-energy nuclear physics. Two types of waveform digitization indicators are designed in the plan, one adopts a sampling rate of 100MSPS, 12bitADC, and the other adopts a sampling rate of 1GSPS, 8bitADC. Looking at these contradictions, they can all be attributed to the contradictions between the high precision of ADC conversion and the processing, storage, and transmission of large amounts of data. It is of great significance to solve these contradictions.

Contents of the invention

The purpose of the present invention is aimed at the contradiction between the high-frequency sampling of the analog/digital conversion technology and the large amount of data generated by the waveform digitization link in the existing digital nuclear instrument, and proposes a nuclear signal frequency conversion digital sampling based on digital extraction technology new method. The new method can minimize the data volume of the finally generated digital nuclear signal waveform while ensuring that the sampling accuracy of the digital nuclear signal output by the waveform digitizer is not lost.

In order to achieve the above object, the present invention adopts the following technical measures to realize the technical solution.

A method for nuclear signal frequency conversion digital sampling of the present invention is characterized in that comprising the following specific steps:

(1) Determination of the best sampling frequency

(i) Digital nuclear signal identification and peak finding

From the digitized waveform data output by the waveform digitizer, use traditional discrimination and peak-finding algorithms to find out the start time, end time and peak time of a waveform;

(ii) Determination of the optimal sampling frequency for the rising edge of the digital core signal

Use the signal data between the initial moment and the peak moment of the digital core signal obtained in step (i) as its rising edge part, and design the "best frequency determination algorithm" to find the rising edge that is less than the set rising edge distortion rate The maximum frequency division coefficient M _r , so as to determine the best sampling frequency of the rising edge;

(Ⅲ) Determination of the optimal sampling frequency for the falling edge of the digital core signal

Using the signal data between the peak moment and the end moment of the digital nuclear signal obtained in the (i) step as its falling edge part, design "best frequency determination algorithm", find the falling edge maximum value less than the set falling edge distortion rate Frequency division coefficient M _f , so as to determine the best sampling frequency of the falling edge;

(2) Frequency conversion sampling of the digital core signal data stream output by the waveform digitizer

(i) Digital nuclear signal identification and peak finding

According to the digital core signal waveform obtained in step (1) and step (i), the waveform is divided into two parts: rising edge and falling edge;

(ii) Digital low-pass filtering

Design an anti-aliasing digital filter according to the optimal sampling frequency of the rising edge obtained in step (1) and (ii) and the minimum sampling frequency in the Nyquist sampling law, and perform anti-aliasing digital filtering on the rising edge of the digital core signal Low-pass filtering, design an anti-aliasing digital filter according to the optimal sampling frequency of the falling edge obtained in step (1) (iii) and the minimum sampling frequency in the Nyquist sampling law, and reverse the falling edge of the digital nuclear signal Aliasing digital low-pass filtering;

(Ⅲ) Perform digital frequency division extraction on the rising edge

Use the maximum frequency division coefficient M _r of the rising edge obtained in step (1) (ii) to perform frequency conversion extraction on the rising edge signal obtained in step (2) (ii) after anti-aliasing and low-pass filtering;

(ⅳ) Perform digital frequency division extraction on the falling edge

Use the maximum frequency division coefficient M _f of the falling edge obtained in step (1) (iii) to perform frequency conversion extraction on the falling edge signal obtained in step (2) (ii) after anti-aliasing and low-pass filtering;

(v) Signal synthesis

Synthesize the frequency-divided rising edge signal obtained in step (2) (iii) and the frequency-divided falling edge signal obtained in step (2) (iv) to form a complete digital core signal waveform.

值即为上升沿的最佳采样频率。In the above scheme, the determination of the optimal sampling frequency of the rising edge of the digital nuclear signal, the sampling frequency of the output digitized nuclear signal data is recorded as f ₀ , and the positive value of the maximum frequency division coefficient M _r of the rising edge is found through the optimal frequency iterative algorithm Integer value, and ensure that the rising edge part x _ir (n) is subjected to M _r times frequency division and extraction with this M _r value, and the signal is smaller than the rising edge distortion rate set by the measurement, this

The value is the optimal sampling frequency of the rising edge.

In the above scheme, the specific steps for determining the optimal sampling frequency on the rising edge of the digital core signal are as follows:

1) Digital low-pass filtering

Carry out digital low-pass filtering to the rising edge part x _ir (n) of the digitized waveform data of the output, and the filtering result is x _irp (n);

2) Digital frequency division extraction

The frequency division coefficient M _r starts to increase from 2, and the rising edge x _irlp (n) of the waveform is extracted by M _r times of frequency division to obtain the rising edge x _irlp (M _r n) of the waveform after the frequency division extraction;

3) Evaluation of signal accuracy after digital frequency division extraction

Define the distortion rate of the rising edge: the ratio of the difference between the rise time t _ra of the digital signal after frequency division and extraction and the signal rise time t _rb before frequency division and extraction ε _r to t _rb , as shown in formula (1),

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ra</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

(1) where s _n is the sampling rate of the digital nuclear signal after frequency division, δ(s _n ) is the shape distortion rate of the rising edge of the signal at the corresponding sampling rate, and the rise time t _ra of the signal involved in the formula (1) is divided before and after frequency division The calculation method of t _{rb and t rb} is summarized as the calculation method of t _r : suppose the i-th digital nuclear signal start time and corresponding amplitude value are (t _is , v _i0 ), the peak time and corresponding amplitude value are (t _im , vi _im ), the rise time of the signal is determined by formula (2),

t _ir =t(0.9v _im )-t(0.1v _im ) (2)

In the formula (2), t(0.1v _im ) and t(0.9v _im ) represent the positions of 10% and 90% of the peak value of the nuclear signal waveform during the rising edge of the signal, that is, during the time period from t _i0 to t _im corresponding time value;

Set the rising edge distortion rate δ ₀ according to the measurement accuracy requirements, and compare the δ(s _n ) obtained in formula (1) with δ ₀ : when δ(s _n )<δ ₀ , continue to increase the rising edge frequency division coefficient M _r value, repeat the above steps 1) to 3), until finding the largest positive integer value of the rising edge frequency division coefficient M _r under the condition of δ(s _n )<δ ₀ , at this time

值即为下降沿的最佳采样频率。In the above scheme, the sampling frequency _f0 finds the positive integer value of the maximum frequency division coefficient M _f on the falling edge through the optimal frequency iterative algorithm, and ensures that the falling edge part x _if (n) is multiplied by M _f with this value of M _f The signal after frequency division and extraction is less than the falling edge distortion rate set by the measurement.

The value is the optimal sampling frequency of the falling edge.

In the above scheme, the specific steps for determining the optimal sampling frequency on the falling edge of the digital core signal are as follows:

1) Digital low-pass filtering

Perform low-pass filtering on a complete signal x _i (n) of the output i-th digitized waveform data, and the filtering result is x _ilp (n), that is, x _ilp (n) is divided into rising edge filtering results x _irlp (n) and the falling edge filtering result x _iflp (n) two parts;

2) Digital frequency division extraction

The frequency division coefficient M _f starts to increase from 2, and the waveform falling edge x _iflp (n) is extracted by M _f times of frequency division, and the waveform falling edge x _iflp (M _f n) after frequency division extraction is obtained;

3) Evaluation of signal accuracy after digital frequency division extraction

Define the distortion rate of the falling edge of the digital core signal: the ratio of the difference between the falling time t _fa of the digital signal after frequency division and extraction and the signal falling time t _fb before frequency division and extraction ε _f to t _fb , as shown in formula (3):

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fa</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The definition of δ(s _n ) in the formula (3) refers to the formula (1), and the formula (3) indicates the shape distortion rate of the falling edge of the digital nuclear signal when the sampling rate is s _n after the falling edge of the digital nuclear signal is divided, (3 The calculation method of the fall time t _f involved in the formula is as follows: set the i-th digital nuclear signal peak moment and the corresponding amplitude value as (t _im , v _im ), the termination time and the corresponding amplitude value as (t _ie , v _ie ), then the falling time of the signal is determined by formula (4):

t _if ＝t(0.9v _im )-t(0.1v _im ) (4)

(4) In the formula, t(0.9v _im ) and t(0.1v _im ) respectively represent the corresponding 90% and 10% of the peak value v _im of the digital core signal in the falling edge of the signal, that is, in the time period from t _im to t _ie time;

Set the falling edge distortion rate δ ₀ according to the measurement accuracy requirements, and compare the δ(s _n ) obtained in formula (3) with δ ₀ : when δ(s _n )<δ ₀ , continue to increase the falling edge frequency division coefficient M _f value, repeat the above steps 1) to 3), until finding the positive integer value of the maximum falling edge frequency division coefficient M _f under the condition of δ(s _n )<δ ₀ , at this time

对第i个数字核信号的整个信号x_i(n)进行低通滤波，得到其滤波结果为x_iflp(n)。In the above scheme, the best frequency obtained by the rising edge Carry out low-pass filtering to the rising edge part x _ir (n) of the i-th digital core signal, and obtain the filtering result as x _irp (n); the obtained falling edge optimal frequency

Low-pass filtering is performed on the entire signal x _i (n) of the i-th digital core signal, and the filtering result is obtained as x _iflp (n).

In the above scheme, the waveform rising edge signal x _irlp (M _r n ) and the waveform falling edge signal x _iflp (M _f n ) after frequency division and extraction are recombined into a new signal x _iext (n), and the synthesis algorithm is : x _iext (n)=M _r x _irlp (M _r n)+M _f x _iflp (M _f n), the signal x _iext (n) is the waveform data of a nuclear signal obtained at the optimal sampling frequency.

The digital nuclear signal discrimination of the present invention and its realization process of peak-seeking are:

1) Waveform screening

Set the signal threshold as x ₀ , and the digital core signal sequence output by the waveform digitizer is expressed as x(n), where n=1,2,3,..., to judge the size of x(n), when x( t _si )>x ₀ , t _si =n _si T time is the starting time of the i-th nuclear signal waveform in this measurement; where, T is the sampling period of the analog-to-digital converter in the waveform digitizer, when x When (t _ei )<x ₀ , t _ei =n _ei T is the termination moment of the i-th nuclear signal waveform in this measurement, then the i-th digital nuclear signal waveform data screened out in this measurement can be recorded as: x _i (n)={x(t _si ),x(t _si +1),...,x(t _ei )};

2) Determination of peak position

Use the point-by-point comparison method of sampling data to obtain the peak position of the signal. If the amplitude value of a certain point in the signal is greater than the amplitude values of m points adjacent to it, then this point is the peak value of the waveform, expressed as:

x _i (t _p )＞ _xi (t _p +j),j=-m,-m+1,-m+2,…,m-2,m-1,m; then x _i (t _p ) In order to measure the peak value of the i-th digital core signal waveform this time, t _p is the moment when it reaches the peak value. Take t _p as the dividing point to divide a nuclear signal into two parts, the rising edge and the falling edge. The part from t _si to t _p is the rising edge of the nuclear signal waveform, and the data sequence of the rising edge of the signal waveform is recorded as x _ir (n); t The part from _p to t _ei is the falling edge of the nuclear signal waveform, and the data sequence of the falling edge of the signal waveform is recorded as x _if (n), x _i (n)=xi _ir (n)+xi _if (n).

和

的数字反混叠低通滤波器，其次根据完成信号甄别，确定第i个数字核信号已出现；再根据寻峰原理找到第i个数字核信号的达峰时刻，将第i个信号分为上升沿和下降沿两部分；最后，将第i个数字核信号上升沿波形数据输入截至频率为

的数字反混叠低通滤波器，再将滤波后的波形数据x_irlp(n)以M_r倍进行数据抽取，从而得到第i个数字核信号的上升沿部分处理后的数据序列x_irlp(M_rn)，与此同时将第i个数字核信号的下降沿波形数据输入截至频率为

的数字反混叠低通滤波器，再将滤波后的波形数据x_iflp(n)以M_f倍进行数据抽取，从而得到第i个数字核信号的下降沿部分处理后的数据序列x_iflp(M_fn)。The principle of the frequency conversion sampling of the waveform digitizer output digital core signal data stream of the present invention: at first by the determined optimal frequency division coefficients M _r and M _f of the rising edge and the falling edge, respectively design the cut-off frequency as

and

The digital anti-aliasing low-pass filter of the digital anti-aliasing low-pass filter, and then according to the completion of signal screening, it is determined that the i-th digital core signal has appeared; then according to the peak-seeking principle, the peak-reaching moment of the i-th digital core signal is found, and the i-th signal is divided into There are two parts: rising edge and falling edge; finally, input the rising edge waveform data of the i-th digital core signal until the frequency is

The digital anti-aliasing low-pass filter of the digital anti-aliasing low-pass filter, and then perform data extraction on the filtered waveform data x _irlp (n) by M _r times, so as to obtain the data sequence x _irlp ( M _r n), at the same time, the falling edge waveform data of the i-th digital core signal is input and the cut-off frequency is

The digital anti-aliasing low-pass filter of the digital anti-aliasing low-pass filter, and then the waveform data x _iflp (n) after filtering is carried out data extraction with M _f times, thereby obtain the data sequence x _iflp ( M _f n).

The working principle of the whole system of the present invention is: 1. after setting up the nuclear detector, the waveform digitizer and the digital nuclear signal processing system, start the waveform digitizer to sample the nuclear detector signal; 2. the digital nuclear signal processing system according to the steps (1 ) The method described in step (i) first discriminates a complete nuclear signal waveform from the output result of the waveform digitizer; then according to step (1) (ii) and step (1) (iii) Determine the optimum sampling frequency of the rising edge and falling edge of the nuclear signal waveform in this measurement according to the method described above; ③ start to continuously process the data stream of the digital nuclear signal obtained by the waveform digitizer according to the optimal sampling frequency obtained in the aforementioned ②; Step (2) The appearance of the nuclear signal waveform screened in step (i); then according to the method described in step (2) step (ii), the optimal sampling frequency of the rising edge and the optimal sampling frequency of the falling edge are used as filtering parameters for the Perform anti-aliasing low-pass filtering on the rising and falling edges of the waveform; ④The digital nuclear signal processing system performs anti-aliasing low-pass filtering according to the method described in step (2) (iii) and step (2) (iv). The rising edge and falling edge of the signal output by the pass filter are respectively frequency-divided and extracted; ⑤ According to the method described in step (2) (v), the extracted rising edge signal and falling edge signal are combined into a new complete The digital nuclear signal is transmitted to the next link of the system.

Features and beneficial technical effects of the present invention:

1. The present invention proposes to use the method of digital signal processing to determine the optimal digital sampling frequency in a certain nuclear measurement, which is used for digital nuclear signal frequency conversion digital sampling of digital nuclear instruments, and uses this as the basis and basis for establishing intelligent nuclear signal digital sampling in accordance with.

2. The present invention proposes a method of sampling digital extraction to realize extraction at different extraction frequencies of the rising edge and falling edge sampling of the same digital nuclear signal, and then synthesize a complete digital nuclear signal; it realizes the output without damaging the waveform digitizer. The data volume of the digital nuclear signal is minimized without compromising the accuracy of the digital nuclear signal.

3. The present invention proposes an algorithm for realizing digital low-pass anti-aliasing filtering on different parts of the same core signal. This principle is applicable to both digital core signal processing and digital low-pass anti-aliasing processing of other signals. .

4. After digital low-pass filtering, the digital nuclear signal may have different degrees of distortion on the waveform. The present invention defines the distortion evaluation method of the rising edge and falling edge of the filtered signal in the time domain, which is the frequency conversion sampling proposed by the present invention. The specific implementation of the algorithm provides a theoretical basis.

5. The shape of the rising edge and falling edge of the nuclear signal in the present invention after frequency conversion sampling is consistent with the original signal, but the amount of data is greatly reduced.

Description of drawings

Fig. 1 is the amplitude-frequency characteristic of the Butterworth filter that the present invention designs;

Fig. 2 is the determination process of the optimum frequency of the signal rising edge or falling edge of the present invention;

Fig. 3 is the frequency conversion sampling process of the same digital core signal waveform of the present invention;

Fig. 4 is the experimental result that the best sampling frequency shown in the present invention is determined, and wherein, A is to obtain a group of 120MHz after signal is extracted and compared with the original signal, B is a group of 30MHz after the signal is extracted and compared with the original signal, C is a group of 5MHz The digitized waveform of the extracted signal compared with the original signal; the black is the original signal, and the white is the extracted signal; it can be seen from the figure that the rising edge of 5MHz does not coincide with the original signal. Using the distortion rate evaluation algorithm, the core signal can be obtained The sampling frequency of the rising edge should be at least 30MHz, and the sampling frequency of the falling edge should be at least 10MHz;

Fig. 5 is the waveform comparison result before and after frequency conversion sampling in the present invention, the black is the original signal, the white is the extracted signal, the sampling frequency of the rising edge is 30MHz, and the sampling frequency of the falling edge is 10MHz.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings, but it should not be construed as any limitation to the protection content of the present invention.

1. Build a measurement system.

① Dysprosium-zinc-chromium (CdZnTd) detectors and charge-sensitive preamplifiers provided by Tsinghua Tongfang Nuctech Co., Ltd. detect ²⁴¹ Am gamma rays and output analog signals. The waveform digitization system uses a high-performance digital oscilloscope with a maximum analog bandwidth of 1GHz and a maximum sampling rate of 10Gsps Lecroy WaveRunner 104MXi-A acquires digitized nuclear signal waveforms.

2. Digital nuclear signal identification and peak finding

Signal discrimination: set the signal threshold to x ₀ =150 (millivolts), and the digital core signal sequence output by the waveform digitizer is expressed as x(n), where n=1,2,3,..., to judge The size of x(n), when x(t _si )>x ₀ , t _si =n _si T time is the starting time of the i-th nuclear signal waveform in this measurement; where, T is the waveform digitizer The sampling period of the analog-to-digital converter, when x(t _ei )<x ₀ , t _ei =n _ei T is the termination moment of the i-th nuclear signal waveform in this measurement, then the i-th nuclear signal waveform identified in this measurement The digital core signal waveform data can be recorded as: x _i (n)={x(t _si ),x(t _si +1),…,x(t _ei )};

(2) Determination of the peak position: Use the point-by-point comparison method of sampling data to obtain the peak position of the signal. If the amplitude value of a certain point in the signal is larger than the amplitude values of m points adjacent to it, then this point is the peak value of the waveform, expressed as:

x _i (t _p )＞ _xi (t _p +j),j=-m,-m+1,-m+2,…,m-2,m-1,m; then x _i (t _p ) In order to measure the peak value of the i-th digital core signal waveform this time, t _p is the moment when it reaches the peak value. Take t _p as the dividing point to divide a nuclear signal into two parts: rising edge and falling edge. The part from t _si to t _p is the rising edge of the nuclear signal waveform, which is recorded as x _ir (n); the part from t _p to t _ei is The falling edge of the nuclear signal waveform is denoted as x _if (n), where x _i (n)=xi _ir (n)+xi _if (n).

3. Determination of the best sampling frequency on the rising edge of the digital core signal

In this example, the sampling frequency of the digitized waveform data output by the waveform digitizer is 1200MHz, and the distortion rate δ ₀ of the nuclear signal is set as 20%, and the initial value of _M is 2; the optimal sampling frequency of the rising edge of the digital nuclear signal is determined , the specific steps are as follows:

1) Digital low-pass filtering

Perform digital low-pass filtering on the rising edge part x _ir (n) of the digitized waveform data output by the waveform digitizer: the rising edge of the nuclear signal x _i (n) is expressed as: $x_{\mathrm{ir}}\left(\mathrm{no}\right)=\left\{\begin{array}{c}{x}_i\left(\mathrm{no}\right),\mathrm{no}\&le;t_p\\ 0,\mathrm{no}>t_p\end{array}\right.,$ where t _p is the peak moment of the nuclear signal,

Anti-aliasing filtering is implemented on the rising edge of x _ir (n), and the rising edge x _irlp (n) of the filtered nuclear signal is:

x _irlp (n)＝x _ir (n)*h ₁ (n)＝ _xi (n)*h ₁ (n) (n≤t _p ), h ₁ (n) is the rising edge Butterworth low-pass filter Shock response;

2) Digital frequency division extraction

The frequency division coefficient M _r starts to increase from 2, and the rising edge x _irlp (n) of the waveform is extracted by M _r times of frequency division to obtain the rising edge x _irlp (M _r n) of the waveform after the frequency division extraction;

3) Evaluation of signal accuracy after digital frequency division extraction

Define the distortion rate of the rising edge: the ratio of the difference between the rise time t _ra of the digital signal after frequency division and extraction and the signal rise time t _rb before frequency division and extraction ε _r to t _rb , as shown in formula (1),

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ra</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

(1) where s _n is the sampling rate of the digital nuclear signal after frequency division, δ(s _n ) is the shape distortion rate of the rising edge of the signal at the corresponding sampling rate,

The calculation method of the rise time t _ra and t _rb of the signals involved in the formula (1) before and after frequency division can be summarized as the calculation method of t _r : Assume that the starting moment of the i-th digital core signal and the corresponding amplitude value are (t _is , v _i0 ), the peak moment and the corresponding amplitude value (t _im , v _im ), then the rise time of the signal is determined by formula (2),

t _ir =t(0.9v _im )-t(0.1v _im ) (2)

In the formula (2), t(0.1v _im ) and t(0.9v _im ) represent the positions of 10% and 90% of the peak value of the nuclear signal waveform during the rising edge of the signal, that is, during the time period from t _i0 to t _im corresponding time value;

这里计算的该核信号上升沿的采样频率最小应为30MHz。图2所示描述了信号上升沿最佳频率的确定流程。Set the rising edge distortion rate δ ₀ according to the measurement accuracy requirements, and compare the δ(s _n ) obtained in formula (1) with δ ₀ : if δ(s _n )<δ ₀ , continue to increase the rising edge frequency division coefficient M value of _r , repeat the above steps 1) to 3), until the maximum positive integer value of the rising edge frequency division coefficient M _r is found under the condition of δ(s _n )<δ ₀ , at this time

The sampling frequency of the rising edge of the nuclear signal calculated here should be at least 30MHz. Figure 2 shows the process of determining the optimum frequency of the rising edge of the signal.

4. Determination of the best sampling frequency on the falling edge of the digital core signal

In this example, the sampling frequency of the digitized waveform data output by the waveform digitizer is 1200MHz, and the distortion rate δ ₀ of the nuclear signal is set as 20%, and the initial value of _M is 2; the optimal sampling frequency is determined on the falling edge of the digital nuclear signal , the specific steps are as follows:

1) Digital low-pass filtering

The falling edge of the nuclear signal is x _if (n), expressed as: $x_{\mathrm{if}}\left(\mathrm{no}\right)=\left\{\begin{array}{c}0,\mathrm{no}\&le;t_p\\ x_i\left(\mathrm{no}\right),\mathrm{no}>t_p\end{array}\right.,$ Where t _p is the peak moment of the nuclear signal. Since, when t>t _p , x _i (n)*h ₂ (n)≠0, in order not to lose the effective information in the original signal after low-pass filtering, the falling edge x _flp (n ), the falling edge Butterworth low-pass filter needs to be performed on the entire signal, and the falling edge x _iflp (n) of the filtered signal is x _iflp (n)= _xi (n)*h ₂ (n) (n＞t _p ) , h ₂ (n) is the impulse response of the falling edge Butterworth low-pass filter.

2) Digital frequency division extraction

The frequency division coefficient M _f starts to increase from 2, and the waveform falling edge x _iflp (n) is extracted by M _f times of frequency division, and the waveform falling edge x _iflp (M _f n) after frequency division extraction is obtained;

3) Evaluation of signal accuracy after digital frequency division extraction

Define the distortion rate of the falling edge of the digital core signal: the ratio of the difference between the falling time t _fa of the digital signal after frequency division and extraction and the signal falling time t _fb before frequency division and extraction ε _f to t _fb , as shown in formula (3):

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fa</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The definition of δ(s _n ) in formula (3) refers to formula (1), which means that after the falling edge of the digital nuclear signal is divided, when the sampling rate is s _n , the shape distortion rate of the falling edge of the nuclear signal, in formula (3) involves The calculation method of the fall time t _f is as follows: Assume that the i-th digital core signal reaches its peak moment and the corresponding amplitude value is (t _im , v _im ), the end time and the corresponding amplitude value is (t _ie , vi _ie ), Then the falling time of the signal is determined by formula (4):

t _if ＝t(0.9v _im )-t(0.1v _im ) (4)

(4) In the formula, t(0.9v _im ) and t(0.1v _im ) respectively represent the corresponding 90% and 10% of the peak value v _im of the digital core signal in the falling edge of the signal, that is, in the time period from t _im to t _ie time;

这里计算的该核信号下降沿的采样频率最小应为10MHz。图2所示描述了信号下降沿最佳频率的确定流程。Set the falling edge distortion rate δ ₀ according to the measurement accuracy requirements, and compare the δ(s _n ) obtained in formula (3) with δ ₀ : if δ(s _n )<δ ₀ , continue to increase the falling edge frequency division coefficient M For the value of _f , repeat the above steps 1) to 3), until finding the positive integer value of the largest falling edge frequency division coefficient M _f under the condition of δ(s _n )<δ ₀ , at this time

The sampling frequency of the falling edge of the nuclear signal calculated here should be at least 10MHz. Figure 2 describes the process of determining the optimum frequency of the falling edge of the signal.

5. Anti-aliasing low-pass filtering of digital signals

After obtaining the optimal sampling frequency of the rising edge and the optimal sampling frequency of the falling edge of the nuclear signal waveform according to the above steps, all waveforms can be identified from the data output by the waveform digitizer, according to the optimal sampling frequency of the rising edge and the optimal sampling frequency of the falling edge The sampling frequency performs anti-aliasing low-pass filtering on the rising edge part and the falling edge part of the nuclear signal respectively.

Let the rising edge of the core signal x _i (n) be x _ir (n), and the falling edge be x _if (n), expressed as:

$x_{\mathrm{ir}}\left(\mathrm{no}\right)=\left\{\begin{array}{c}{x}_i\left(\mathrm{no}\right),\mathrm{no}\&le;t_p\\ 0,\mathrm{no}>t_p\end{array}\right.,$ $x_{\mathrm{if}}\left(\mathrm{no}\right)=\left\{\begin{array}{c}0,\mathrm{no}\&le;t_p\\ x_i\left(\mathrm{no}\right),\mathrm{no}>t_p\end{array}\right.,$ where t _p is the peak moment of the nuclear signal,

Anti-aliasing filtering is implemented with a rising edge filter for x _ir (n), and the rising edge x _irlp (n) of the filtered nuclear signal is:

x _irlp (n)＝x _ir (n)*h ₁ (n)＝ _xi (n)*h ₁ (n) (n≤t _p ), h ₁ (n) is the rising edge Butterworth low-pass filter shock response.

Since, when t>t _p , x _i (n)*h ₂ (n)≠0, in order not to lose the effective information in the original signal after low-pass filtering, the falling edge x _flp (n ), the falling edge Butterworth low-pass filter needs to be performed on the entire signal, and the falling edge x _iflp (n) of the filtered signal is x _iflp (n)= _xi (n)*h ₂ (n) (n＞t _p ) , h ₂ (n) is the impulse response of the falling edge Butterworth low-pass filter.

6. Frequency division and extraction of digitized waveform

After the rising and falling edges of the nuclear signal waveform are anti-aliased and low-pass filtered, the frequency division coefficient corresponding to the optimal sampling frequency of the rising edge is M _r , and the frequency division coefficient corresponding to the optimal sampling frequency of the falling edge is M _f ; Perform M _r times frequency division and extraction on the rising edge x _irlp (n) of the waveform, and obtain the rising edge of the waveform after frequency division and extraction as x _irlp (M _r n); perform M _f frequency division on the falling edge x _iflp (n) of the waveform Extraction, the falling edge of the waveform obtained after frequency division and extraction is x _iflp (M _f n).

7. Synthesis of digital waveform after frequency division and extraction

Since the low-pass filter attenuates the amplitudes of the rising edge and falling edge signals of the original signal to different degrees, when recombining the rising edge signal and falling edge signal after frequency division and extraction into a new signal x _iext (n), it is necessary The corresponding amplitude compensation, the synthesis algorithm is: x _iext (n) = M _r x _{irlp (} M _r n) + M _f x _iflp (M _f n ₎ ; Draw multiples. As shown in Figure 3, it illustrates the frequency conversion sampling process of the same digital core signal waveform. Figure 4 shows the experimental results of determining the optimal sampling frequency. Figure 4 shows a group of digitalization of the entire waveform at 1/10 times (120MHz), 1/40 (30MHz), and 1/240 (5MHz). The result of frequency division extraction, where the black curve represents the original signal, and the white curve represents the extracted signal; it can be seen from Figure 4 that the rising edge of 5MHz is significantly distorted compared with the original signal. Figure 5 shows the comparison of the waveforms after frequency-conversion sampling and the waveforms before frequency-conversion sampling on the rising edge and falling edge respectively at their respective optimal sampling frequencies. Among them, the black curve represents the original signal, and the white curve represents the extracted signal; it can be seen that the frequency conversion The shape of the rising edge and falling edge after sampling is consistent with the original signal, but the amount of data is reduced to 0.85% of the original. The calculation method is as follows: the sampling frequency of the original signal is 1200MHz; the optimal sampling frequency of the rising edge is 30MHz, and the width of the rising edge accounts for 1% of the entire waveform width; the optimal sampling frequency of the falling edge is 10MHz, and the width of the falling edge accounts for 99% of the entire waveform width %; then the amount of waveform data is reduced to the original (30/1200*0.01+10/1200*0.99)=0.85%.

Claims (7)

1. a method for digital sampling of nuclear signal frequency conversion is characterized in that comprising the following concrete steps: (1) Determination of the best sampling frequency (i) Digital nuclear signal identification and peak finding Use traditional discrimination and peak-finding operations to find out the start time, end time and peak time from the digitized waveform data output by the waveform digitizer; (ii) Determination of the optimal sampling frequency for the rising edge of the digital core signal Use the signal data between the initial moment and the peak moment of the digital core signal obtained in step (i) as its rising edge part, and design the "best frequency determination algorithm" to find the rising edge that is less than the set rising edge distortion rate The maximum frequency division coefficient M _r , so as to determine the best sampling frequency of the rising edge; (Ⅲ) Determination of the optimal sampling frequency for the falling edge of the digital core signal Using the signal data between the peak moment and the end moment of the digital core signal obtained in the (i) step as its falling edge part, design "best frequency iterative algorithm", find the falling edge maximum value less than the set falling edge distortion rate Frequency division coefficient M _f , so as to determine the best sampling frequency of the falling edge; (2) Frequency conversion sampling of the digital core signal data stream output by the waveform digitizer (i) Digital nuclear signal identification and peak finding The digital nuclear signal waveform obtained in the step (i) of step (1) is divided into two parts: rising edge and falling edge; (ii) Digital low-pass filtering Design an anti-aliasing digital filter based on the optimal sampling frequency of the rising edge obtained in step (1) and (ii) and the minimum sampling frequency specified in the Nyquist sampling law, and perform anti-aliasing digital filtering on the rising edge of the digital core signal Low-pass filtering, obtain the optimal sampling frequency of the falling edge in step (1) (Ⅲ) and design the anti-aliasing digital filter to the regulation of the minimum sampling frequency in the Nyquist sampling law, and reverse the falling edge of the digital nuclear signal Aliasing digital low-pass filtering; (Ⅲ) Perform digital frequency conversion extraction on the rising edge Use the maximum frequency division coefficient M _r of the rising edge obtained in step (1) (ii) to perform frequency conversion extraction on the rising edge signal obtained in step (2) (ii) after anti-aliasing and low-pass filtering; (ⅳ) Perform digital frequency conversion extraction on the falling edge Using the falling edge maximum frequency division coefficient M _f obtained in step (1) step (iii), perform frequency conversion extraction on the falling edge signal obtained in step (2) step (ii) after anti-aliasing and low-pass filtering; (v) Signal synthesis Synthesize the frequency-divided rising edge signal obtained in step (2) (iii) and the frequency-divided falling edge signal obtained in step (2) (iv) to form a complete digital core signal waveform. 2. method according to claim 1, it is characterized in that described rising edge optimal sampling frequency is determined, and waveform digitizer obtains digitization nuclear signal waveform with f ₀ sampling frequency, and is output in this optimal sampling frequency determining system, Use the "best frequency determination algorithm" to find the positive integer value of the maximum frequency division coefficient M _r on the rising edge, then

The value is the optimal sampling frequency of the rising edge. 3. according to the described method of claim 1 or 2, it is characterized in that the concrete steps that described digital core signal rising edge optimal sampling frequency determine are as follows: 1) Digital low-pass filtering Carry out digital low-pass filtering to the rising edge part x _ir (n) of the digitized waveform data of the output, and the filtering result is x _irp (n); 2) Digital frequency division extraction The maximum frequency division coefficient M _r starts to increase from 2, and M _r multiple frequency division extraction is performed on the waveform rising edge x _irlp (n), and the waveform rising edge x _irlp (M _r n) after frequency division extraction is obtained; 3) Evaluation of signal accuracy after digital frequency division extraction Define the distortion rate of the rising edge: the ratio of the difference between the rise time t _ra of the digital signal after frequency division and extraction and the signal rise time t _rb before frequency division and extraction ε _r to t _rb , as shown in formula (1), $\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ra</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; rb</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ (1) where s _n is the sampling rate of the digital nuclear signal after frequency division, δ(s _n ) is the shape distortion rate of the rising edge of the signal at the corresponding sampling rate, and the rise time t _ra of the signal involved in the formula (1) is divided before and after frequency division The calculation method of t _{rb and t rb} is summarized as the calculation method of t _r : suppose the i-th digital nuclear signal start time and corresponding amplitude value are (t _is , v _i0 ), the peak time and corresponding amplitude value are (t _im , vi _im ), the rise time of the signal is determined by formula (2), t _ir =t(0.9v _im )-t(0.1v _im ) (2) In the formula (2), t(0.1v _im ) and t(0.9v _im ) represent the positions of 10% and 90% of the peak value of the nuclear signal waveform during the rising edge of the signal, that is, during the time period from t _i0 to t _im corresponding time value; Set the rising edge distortion rate δ ₀ according to the measurement accuracy requirements, and compare the δ(s _n ) obtained in formula (1) with δ ₀ : when δ(s _n )<δ ₀ , continue to increase the rising edge frequency division coefficient M _r value, repeat the above steps 1) to 3), until finding the largest positive integer value of the rising edge frequency division coefficient M _r under the condition of δ(s _n )<δ ₀ , at this time

4. method according to claim 1, it is characterized in that the determination of said falling edge sampling frequency, the nuclear signal data sampling frequency _f of output is found falling edge maximum frequency division coefficient M _f by " optimal frequency iterative algorithm " The positive integer value of , and with this M _f value, the signal after performing M _f frequency division and extraction on the falling edge part x _if (n) satisfies the falling edge distortion rate that is less than the measurement setting, this

The value is the optimal sampling frequency of the falling edge. 5. according to the described method of claim 1 or 4, it is characterized in that the concrete steps that described digital nuclear signal falling edge optimal sampling frequency determine are as follows: 1) Digital low-pass filtering Perform low-pass filtering on a complete signal x _i (n) of the output i-th digitized waveform data, and the filtering result is x _ilp (n), that is, x _ilp (n) is divided into rising edge filtering results x _irlp (n) and the falling edge filtering result x _iflp (n) two parts; 2) Digital frequency division extraction The maximum frequency division coefficient M _f starts to increase from 2, and the waveform falling edge x _iflp (n) is extracted by M _f times frequency division, and the waveform falling edge x _iflp (M _f n) after frequency division extraction is obtained; 3) Evaluation of signal accuracy after digital frequency division extraction Define the distortion rate of the falling edge of the digital core signal: the ratio of the difference between the falling time t _fa of the digital signal after frequency division and extraction and the signal falling time t _fb before frequency division and extraction ε _f to t _fb , as shown in formula (3): $\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fa</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; fb</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ The definition of δ(s _n ) in the formula (3) refers to the formula (1), and the formula (3) indicates the shape distortion rate of the falling edge of the digital nuclear signal when the sampling rate is s _n after the falling edge of the digital nuclear signal is divided, (3 The calculation method of the fall time t _f involved in the formula is as follows: set the i-th digital nuclear signal peak moment and the corresponding amplitude value as (t _im , v _im ), the termination time and the corresponding amplitude value as (t _ie , v _ie ), then the falling time of the signal is determined by formula (4): t _if ＝t(0.9v _im )-t(0.1v _im ) (4) (4) In the formula, t(0.9v _im ) and t(0.1v _im ) respectively represent the corresponding 90% and 10% of the peak value v _im of the digital core signal in the falling edge of the signal, that is, in the time period from t _im to t _ie time; Set the falling edge distortion rate δ ₀ according to the measurement accuracy requirements, and compare the δ(s _n ) obtained in formula (3) with δ ₀ : when δ(s _n )<δ ₀ , continue to increase the falling edge frequency division coefficient M _f value, repeat the above steps 1) to 3), until finding the positive integer value of the maximum falling edge frequency division coefficient M _f under the condition of δ(s _n )<δ ₀ , at this time

6. The method according to claim 2 or 4, characterized in that the obtained rising edge optimum frequency

Carry out low-pass filtering to the rising edge part x _ir (n) of the i-th digital core signal, and obtain the filtering result as x _irp (n); the obtained falling edge optimal frequency Low-pass filtering is performed on the entire signal x _i (n) of the i-th digital core signal, and the filtering result is obtained as x _iflp (n). 7. The method according to claim 2 or 4, characterized in that the waveform rising edge signal x _irlp (M _r n ) and the waveform falling edge signal x _iflp (M _f n) after frequency division extraction are recombined into a new signal x _iext (n), the synthesis algorithm is: x _iext (n)＝M _r x _irlp (M _r n)+M _f x _iflp (M _f n), the signal x _iext (n) is the best sampling Waveform data of a nuclear signal is obtained at the frequency.

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