Gamma energy spectrum data peak center offset correction method based on Sallen-Key filtering function

Abstract

The invention provides a gamma energy spectrum data peak center offset correction method based on a Sallen-Key filtering function, which is used for solving the technical problem of peak center offset in the process of smoothing gamma energy spectrum data based on the Sallen-Key filtering function at present. The invention provides a gamma energy spectrum data peak center offset correction method based on a Sallen-Key filtering function, and the method comprises the steps: constructing a digital filter circuit based on a second-order Sallen-Key filtering function, carrying out the time domain conversion of the digital filter circuit, and obtaining a reverse Sallen-Key filtering function in a time domain; a reverse Sallen-Key filtering function in a time domain is adopted to carry out offset correction on peak center offset caused in the smoothing process of gamma energy spectrum data through the Sallen-Key filtering function, high fidelity of the Sallen-Key filtering function is achieved, and algorithm support is provided for data processing.

Description

TECHNICAL FIELD

[0001] The present application relates to a peak center offset correction method of gamma spectrum data, and particularly relates to a peak center offset correction method of gamma spectrum data based on a Sallen-Key filter function. BACKGROUND

[0002] Since the measurement of gamma spectrum data has randomness and statistics, a gamma spectrum with counting statistical fluctuation is formed, which not only affects the determination of full energy peak position and the calculation of net peak area, but also hides weak peaks, misses the judgment of detectable nuclides, and even identifies non-existing nuclides. In order to reduce the influence of statistical fluctuation of gamma spectrum data and as much as possible to retain all important features of gamma spectrum peaks, so as to more reliably analyze the gamma spectrum, it is necessary to first smooth or denoise the measured gamma spectrum data.

[0003] At present, the research on smoothing or denoising of gamma spectrum data mainly focuses on the application of filter functions, such as the widely used Sallen-Key filter function. However, in the process of smoothing the gamma spectrum data based on the Sallen-Key filter function, the peak center will be offset, and how to correct the peak center offset is a research difficulty. At present, there is no report on the peak center offset correction method based on the Sallen-Key filter function in the industry, so it is necessary to study the gamma spectrum data peak center correction method based on the Sallen-Key filter function. SUMMARY

[0004] The purpose of the present application is to solve the technical problem that the peak center will be offset in the process of smoothing the gamma spectrum data based on the Sallen-Key filter function at present, and to provide a gamma spectrum data peak center offset correction method based on the Sallen-Key filter function.

[0005] In order to achieve the above purpose, the technical scheme provided by the present application is as follows:

[0006] A gamma spectrum data peak center offset correction method based on a Sallen-Key filter function, characterized in that it comprises the following steps:

[0007] Step 1, constructing a digital filter circuit based on a second-order Sallen-Key filter function;

[0008] Step 2, constructing a differential equation representing the relationship between the input signal V in and the output signal V o of the digital filter circuit according to Kirchhoff's law;

[0009] Step 3, substituting the input signal V inThe differential equation of the relationship between the input signal V o is converted into a corresponding time-domain equation;

[0010] Step 4, the time-domain equation is converted by using a differential numerical method to obtain a forward Sallen-Key filter function in the time domain;

[0011] Step 5, according to the forward Sallen-Key filter function in the time domain, a reverse Sallen-Key filter function in the time domain is constructed;

[0012] Step 6, first, the gamma spectrum data is input into the Sallen-Key filter function for filtering processing, and then the output of the Sallen-Key filter function is input into the reverse Sallen-Key filter function in the time domain for reverse filtering processing, after the reverse filtering is completed, the output of the reverse Sallen-Key filter function in the time domain is the signal after the peak center offset correction of the gamma spectrum data.

[0013] Further, in step 1, the digital filter circuit includes an amplifier A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a capacitor C1 and a capacitor C2; the resistor R3 and the resistor R4 are gain resistors;

[0014] One end of the resistor R1 is used as an input end of the digital filter circuit, and is used for receiving an input signal V in The other end of the resistor R1 is connected to one end of the resistor R2; the other end of the resistor R2 is connected to one end of the capacitor C2 and a non-inverting input end of the amplifier A respectively; the other end of the capacitor C2 is grounded;

[0015] One end of the resistor R3 is grounded, and the other end of the resistor R3 is connected to one end of the resistor R4 and an inverting input end of the amplifier A respectively; the other end of the resistor R4 is connected to an output end of the amplifier A;

[0016] One end of the capacitor C1 is connected between the resistor R1 and the resistor R2, and the other end of the capacitor C1 is connected to the output end of the amplifier A and used as an output end of the digital filter circuit.

[0017] Further, in step 2, the differential equation of the relationship between the input signal V in and the output signal V o is:

[0018]

[0019] Wherein, t represents a sampling time, and D represents a voltage gain of the amplifier A.

[0020] Further, in step 3, the time-domain equation is:

[0021]

[0022] Where A1=C1C2R1R2,A2=C1R1(1-D)+C2R1+C2R2;x i is the time domain input signal at time i, y i 、y i-1 、y i-2 are the time domain output signals at time i, time i-1, and time i-2 respectively, where i is a positive integer greater than or equal to 3, and Δt represents the sampling time interval.

[0023] Furthermore, step 4 is specifically as follows:

[0024] Let R1=mR, R2=R, C1=nC, C2=C, k=RC / Δt in the time domain equation, and m and n be any positive numbers to obtain the forward Sallen-Key filter function in the time domain; the forward Sallen-Key filter function in the time domain is:

[0025]

[0026] Furthermore, in step 5, the reverse Sallen-Key filtering function in the time domain is:

[0027]

[0028] Among them, y i+1 、y i+2 They are the time domain output signals at time i+1 and time i+2 respectively.

[0029] The beneficial effects of the present invention compared to the prior art are as follows:

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. The present invention provides a method for correcting the peak center offset of gamma spectrum data based on the Sallen-Key filter function. By constructing a digital filter circuit based on a second-order Sallen-Key filter function and then performing time domain conversion on it, an inverse Sallen-Key filter function in the time domain is obtained. The inverse Sallen-Key filter function in the time domain is used to correct the peak center offset caused by the smoothing of the gamma spectrum data by the Sallen-Key filter function. This method can achieve high fidelity of the Sallen-Key filter function and provide algorithm support for data processing.

[0032] 2. The reverse Sallen-Key filtering function in the time domain constructed by the present invention can achieve controllable and optimized filtering effect through multi-parameter adjustment of m, n, k, and D. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A topology diagram of the digital filter circuit in step 1 of the peak center offset correction method for gamma spectrum data based on a Sallen-Key filter function;

[0034] Figure 2 A waveform diagram at different time points when the gamma spectrum data is filtered and offset corrected by the embodiment of the peak center offset correction method for gamma spectrum data based on a Sallen-Key filter function; wherein the red curve is the original waveform of the gamma spectrum data, the black curve is the waveform offset after the Sallen-Key filter function, and the blue curve is the waveform offset corrected after the inverse Sallen-Key filter function in the time domain;

[0035] Figure 3 A Figure 2 The horizontal coordinate is a partial enlargement of 200 channels to 250 channels. DETAILED DESCRIPTION

[0036] In order to make the advantages and characteristics of the present application clearer, the present application will be further described in detail below in combination with the drawings and specific embodiments.

[0037] A peak center offset correction method for gamma spectrum data based on a Sallen-Key filter function, comprising the following steps:

[0038] Step 1, constructing a digital filter circuit based on a second-order Sallen-Key filter function, as shown in Figure 1 , including an amplifier A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a capacitor C1 and a capacitor C2. One end of the resistor R1 is used as the input end of the digital filter circuit, for receiving an input signal V in , the other end of which is connected to one end of the resistor R2; the other end of the resistor R2 is respectively connected to one end of the capacitor C2 and the non-inverting input end of the amplifier A; the other end of the capacitor C2 is grounded. One end of the resistor R3 is grounded, and the other end is respectively connected to one end of the resistor R4 and the inverting input end of the amplifier A; the other end of the resistor R4 is connected to the output end of the amplifier A. One end of the capacitor C1 is connected between the resistor R1 and the resistor R2, and the other end is connected to the output end of the amplifier A and used as the output end of the digital filter circuit.

[0039] Step 2, constructing a differential equation according to the Kirchhoff's law, which characterizes the relationship between the input signal V in and the output signal V o , and the expression is:

[0040]

[0041] Let A1=C1C2R1R2, A2=C1R1(1-D)+C2R1+C2R2

[0042]

[0043] Where t is the sampling time and D is the voltage gain of amplifier A.

[0044] Step 3: Characterize the input signal V in the digital filter circuit in With the output signal V o The differential equation of the relationship is converted into the corresponding time domain equation, that is, the input signal V in and the output signal V o The time domain input signal and the time domain output signal at time i are respectively denoted as x i and y i , then the corresponding time domain equation is:

[0045]

[0046] Among them, y i-1 、y i-2 are the time domain output signals at time i, i-1, and i-2 respectively, and x i is the time domain input signal at time i, i is a positive integer greater than or equal to 3, and Δt represents the sampling time interval.

[0047] Step 4: Use the differential numerical method to transform the time domain equation. Specifically, let R1=mR, R2=R, C1=nC, C2=C, k=RC / Δt in the time domain equation, where m and n are any positive numbers, R is any resistance value, and C is any capacitance value. Then the forward Sallen-Key filter function in the time domain is obtained as a function based on m, n, k, and D, and its expression is:

[0048]

[0049] Step 5: Based on the forward Sallen-Key filter function in the time domain, a reverse Sallen-Key filter function in the time domain is constructed. The constructed reverse Sallen-Key filter function in the time domain is:

[0050]

[0051] Among them, y i+1 、y i+2 They are the time domain output signals at time i+1 and time i+2 respectively.

[0052] In step 6, the gamma spectrum data is first input into the Sallen-Key filter function for filtering. This process will cause the peak center of the original waveform of the gamma spectrum data to shift. Therefore, the present invention then uses an inverse Sallen-Key filter function in the time domain to perform inverse filtering on the output of the Sallen-Key filter function. After the reverse filtering is completed, the output of the inverse Sallen-Key filter function in the time domain is the signal after the peak center shift of the gamma spectrum data is corrected.

[0053] It is worth noting that the Sallen-Key filter function used to filter the gamma energy spectrum data in step 6 of the present invention can be second-order, third-order or higher-order, while when constructing a digital filter circuit in step 1, a second-order Sallen-Key filter function is required.

[0054] The present invention can modify the output of the inverse Sallen-Key filter function in the time domain by modifying m, n, k, and D, thereby achieving controllable and optimized filtering effects, that is, correcting the offset of the gamma spectrum data peak center. In this embodiment, when correcting the offset of the gamma spectrum data peak center, m = 1, n = 2, k = 1.5, and D = 1.

[0055] like Figure 2 As shown in FIG. 1 , a schematic diagram of waveforms at different times when the gamma spectrum data is filtered and offset corrected using the peak center offset correction method based on the Sallen-Key filter function of this embodiment is used. The red curve is the original waveform of the gamma spectrum data, the black curve is the waveform offset after passing through the Sallen-Key filter function, and the blue curve is the waveform offset corrected after passing through the inverse Sallen-Key filter function in the time domain. Figure 3 for Figure 2 The local enlarged view of the horizontal coordinate between channel addresses 200 and 250 clearly shows that the peak center of the original waveform of the gamma energy spectrum data is offset to the right after the Sallen-Key filtering function. However, after passing through the inverse Sallen-Key filtering function in the time domain, the peak center of the gamma energy spectrum data is offset to the left again and basically coincides with the original waveform of the gamma energy spectrum data. Therefore, the present invention can accurately correct the peak center offset of the gamma energy spectrum data.

[0056] The above description is only used to illustrate the technical solution of the present invention, rather than to limit it. For ordinary professional and technical personnel in this field, the specific technical solutions recorded in the above embodiments can be modified, or some of the technical features therein can be replaced by equivalents. These modifications or replacements do not cause the essence of the corresponding technical solution to deviate from the scope of the technical solution protected by the present invention.

Claims

1. A method for correcting the peak center offset of gamma energy spectrum data based on the Sallen-Key filter function, characterized in that: The following steps are involved: Step 1: construct a digital filter circuit based on the second-order Sallen-Key filter function; Step 2: According to Kirchhoff's law, construct a digital filter circuit to represent the input signal V in With the output signal V o differential equations of relations; Step 3: Characterize the input signal V in the digital filter circuit in With the output signal V o The differential equation of the relationship is converted into the corresponding time domain equation; Step 4: Use the differential numerical method to transform the time domain equation to obtain the forward Sallen-Key filter function in the time domain; Step 5: construct a reverse Sallen-Key filter function in the time domain based on the forward Sallen-Key filter function in the time domain; In step 6, the gamma energy spectrum data is first input into the Sallen-Key filter function for filtering, and then the output of the Sallen-Key filter function is input into the inverse Sallen-Key filter function in the time domain for reverse filtering. After the reverse filtering is completed, the output of the inverse Sallen-Key filter function in the time domain is the signal after the peak center offset of the gamma energy spectrum data is corrected.

2. The method for correcting the peak center offset of gamma energy spectrum data based on the Sallen-Key filter function according to claim 1, characterized in that: In step 1, the digital filter circuit includes an amplifier A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a capacitor C1, and a capacitor C2; the resistor R3 and the resistor R4 are gain resistors; One end of the resistor R1 serves as the input end of the digital filter circuit, and is used to receive the input signal V in , the other end of which is connected to one end of the resistor R2; the other end of the resistor R2 is respectively connected to one end of the capacitor C2 and the non-inverting input terminal of the amplifier A; the other end of the capacitor C2 is grounded; One end of the resistor R3 is grounded, and the other end is connected to one end of the resistor R4 and the inverting input end of the amplifier A respectively; the other end of the resistor R4 is connected to the output end of the amplifier A; One end of the capacitor C1 is connected between the resistor R1 and the resistor R2 , and the other end is connected to the output end of the amplifier A and serves as the output end of the digital filter circuit.

3. The method for correcting the peak center offset of gamma energy spectrum data based on the Sallen-Key filter function according to claim 2, characterized in that: In step 2, the input signal V in the characterization digital filter circuit in With the output signal V o The differential equation of the relationship is: Where t is the sampling time and D is the voltage gain of amplifier A.

4. The method for correcting the peak center offset of gamma energy spectrum data based on the Sallen-Key filter function according to claim 3, characterized in that: In step 3, the time domain equation is: Where A1=C1C2R1R2,A2=C1R1(1-D)+C2R1+C2R2;x i is the time domain input signal at time i, y i 、y i-1 、y i-2 are the time domain output signals at time i, time i-1, and time i-2 respectively, where i is a positive integer greater than or equal to 3, and Δt represents the sampling time interval.

5. The method for correcting the peak center offset of gamma energy spectrum data based on the Sallen-Key filter function according to claim 4, characterized in that: Step 4 is as follows: Let R1=mR, R2=R, C1=nC, C2=C, k=RC / Δt in the time domain equation, and m and n be any positive numbers to obtain the forward Sallen-Key filter function in the time domain; the forward Sallen-Key filter function in the time domain is:

6. The method for correcting the peak center offset of gamma energy spectrum data based on the Sallen-Key filter function according to claim 5, characterized in that: In step 5, the reverse Sallen-Key filter function in the time domain is: Among them, y i+1 、y i+2 They are the time domain output signals at time i+1 and time i+2 respectively.

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