A method and system for pulse shaping of nuclear signals

Abstract

The application discloses a kind of pulse shaping method and system of nuclear signal, belong to signal processing technical field, for the problems of existing pulse signal width in prior art Widening, thereby increasing the accumulation event, and there is no better anti-noise effect to Gaussian white noise, the present application includes: the output signal of detector is acquired, and output signal is structured into digital function signal;The Z transform is carried out after the discrete of the digital function signal, and output Z transform signal is obtained;Definition input signal is exponential signal, and the Z transform is carried out to the exponential signal, and input Z transform signal is obtained;According to the input Z transform signal and the output Z transform signal, the transfer function of input signal pulse shaping is obtained;The inverse Z transform is carried out to the transfer function, and the pulse shaping signal of input signal is obtained, and its time domain expression.The purpose is: the pulse shaping signal obtained has better signal-to-noise ratio, and it is convenient to obtain amplitude.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a pulse shaping method and system for nuclear signals. Background Technology

[0002] In radiometric measuring instruments, the pulse signal output from the detector and preamplifier circuit is an exponentially decaying signal based on a time constant. Typically, a pulse shaping circuit is added after the detector and preamplifier circuit output to shape the exponentially decaying signal into a pulse, followed by multichannel pulse amplitude analysis to improve the overall performance of the analytical instrument.

[0003] In existing technologies, exponential pulse signals are typically converted into Gaussian-like signals using a CR-RCm digital filter, and then the Gaussian-like signals are analyzed and processed.

[0004] The existing technology has the following technical problems:

[0005] 1. As m increases, the algorithm of the CR-RCm digital filter becomes more complex and the pulse signal width increases, which in turn increases the likelihood of accumulation events.

[0006] 2. Existing filters do not have a good noise reduction effect against Gaussian white noise. Summary of the Invention

[0007] To address the problems in existing technologies, such as the increased pulse signal width leading to more accumulation events and the lack of effective noise reduction against Gaussian white noise, this invention proposes a pulse shaping method and system for nuclear signals. The aim is to obtain a pulse-shaped signal with a better signal-to-noise ratio and facilitate amplitude acquisition.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is: to provide a pulse shaping method for nuclear signals, comprising:

[0009] S1: Acquire the detector's output signal and construct a digital function signal from the output signal;

[0010] S2: Discretize the digital function signal and perform a Z-transform to obtain the output Z-transform signal;

[0011] S3: Define the input signal as an exponential signal, and perform a Z-transform on the exponential signal to obtain the input Z-transform signal;

[0012] S4: Based on the input Z-transform signal and the output Z-transform signal, obtain the transfer function of the input signal pulse shaping;

[0013] S5: Perform an inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the input signal and its time-domain expression.

[0014] Preferably, S1 of the present invention specifically comprises:

[0015] The output signal is constructed as a sinusoidal signal of the same amplitude, as shown in equation (1):

[0016] in:

[0017] Among them, t c This represents the forming time of a sinusoidal signal, where A is the amplitude of the sinusoidal signal.

[0018] S2 specifically refers to: discretizing the sinusoidal signal and performing a Z-transform to obtain the sinusoidal Z-transform signal, the formula of which is shown in equation (2):

[0019]

[0020] Where, n c =t c / T s T s This represents the ADC sampling time interval.

[0021] Preferably, S1 of the present invention specifically comprises:

[0022] First, the output signal is constructed as a sinusoidal signal of the same amplitude, as shown in equation (1). Then, the sinusoidal signal is integrated to obtain a cosine-like signal, as shown in equation (3).

[0023] in:

[0024]

[0025] The formula is obtained by rearranging:

[0026]

[0027] S2 specifically refers to: discretizing the cosine-like signal and performing a Z-transform to obtain the cosine-like Z-transform signal, the formula of which is shown in equation (5):

[0028]

[0029] Preferably, in S3 of the present invention, the exponential signal is a single exponential signal, and its formula is shown in equation (6):

[0030] v i (t)=V max ·e -t / τ ·u(t), t≥0 (6)

[0031] Among them, V maxLet be the amplitude of the single exponential signal, and τ represent the decay time constant of the single exponential signal.

[0032] The Z-transform of a single exponential signal yields a single exponential Z-transform signal, as shown in equation (7):

[0033]

[0034] in,

[0035] Preferably, in S3 of the present invention, the exponential signal is a double exponential signal, and its formula is shown in equation (8):

[0036]

[0037] Among them, V max The amplitude of the input pulse is represented by τ1 and τ2, which are the decay time constants of the falling edge and rising edge of the pulse, respectively.

[0038] The double exponential signal is transformed by Z to obtain the double exponential Z-transform signal, and its formula is shown in equation (9):

[0039]

[0040] in,

[0041] Preferably, in S4 of the present invention, the transfer function for pulse shaping of the input signal is obtained based on the sinusoidal Z-transform signal and the single exponential Z-transform signal, and its formula is shown in equation (10):

[0042]

[0043] The formula is (11) after simplification:

[0044]

[0045] S5: Perform an inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the single exponential signal, and its time-domain expression is shown in equation (12):

[0046]

[0047] Preferably, in S4 of the present invention, the transfer function for pulse shaping of the input signal is obtained based on the cosine-like Z-transform signal and the single-exponential Z-transform signal, and its formula is shown in equation (13):

[0048]

[0049] Preferably, in S4 of the present invention, the transfer function for pulse shaping of the input signal is obtained based on the sinusoidal Z-transform signal and the double exponential Z-transform signal, and its formula is shown in equation (14):

[0050]

[0051] Simplifying, we get equation (15):

[0052]

[0053] S5: Perform an inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the single exponential signal, and its time-domain expression is shown in equation (16):

[0054]

[0055] Among them, v i [n] represents a discrete double-exponential signal.

[0056] This invention also provides a pulse shaping system for nuclear signals, comprising:

[0057] Detector: Used to acquire the output signal and construct a digital function signal from the output signal;

[0058] Preamplifier: Used to acquire the input signal;

[0059] Z-transform module: Discretizes the digital function signal and performs a Z-transform to obtain the output Z-transform signal; Defines the input signal as an exponential signal and performs a Z-transform on the exponential signal to obtain the input Z-transform signal;

[0060] Pulse shaping module: Based on the input Z-transform signal and the output Z-transform signal, obtain the transfer function of pulse shaping of the input signal; perform inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the input signal and its time-domain expression.

[0061] Compared with the prior art, the technical solution of the present invention has the following advantages / benefits:

[0062] 1. The pulse shaping signal obtained by this invention solves the problem of signal accumulation, has a better signal-to-noise ratio, obvious noise reduction effect, and is convenient for amplitude acquisition.

[0063] 2. The spectral characteristics of the pulse shaping signal of the present invention have been significantly improved compared with the prior art, and it has the characteristics of constant area and bipolar shaping, which can effectively suppress baseline drift. Attached Figure Description

[0064] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0065] Figure 1 This is a schematic diagram of a sinusoidal signal morphology according to Embodiment 1 of the present invention.

[0066] Figure 2 This is a schematic diagram of a sinusoidal pulse shaping signal of a single exponential signal according to Embodiment 1 of the present invention.

[0067] Figure 3 This is a schematic diagram of a sinusoidal pulse shaping signal of a superimposed noise single exponential signal according to Embodiment 1 of the present invention.

[0068] Figure 4 This is a schematic diagram of a sinusoidal pulse shaping signal of superimposed noise double exponential signal in Embodiment 2 of the present invention.

[0069] Figure 5 This is a schematic diagram of the spectral characteristics of a sinusoidal pulse shaping signal according to Embodiment 2 of the present invention.

[0070] Figure 6 This is a schematic diagram of a cosine-like pulse shaping signal for a single exponential signal according to Embodiment 3 of the present invention.

[0071] Figure 7 This is a schematic diagram comparing the cosine-like pulse shaping signal and the Gaussian signal in Embodiment 3 of the present invention.

[0072] Figure 8 This is a schematic diagram illustrating the coherence analysis between a cosine-like pulse shaping signal and a Gaussian signal in Embodiment 3 of the present invention.

[0073] Figure 9 This is a schematic diagram comparing the spectral characteristics of a cosine-like pulse shaping signal and a sine-like pulse shaping signal according to Embodiment 3 of the present invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention are described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of this invention, not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention. Therefore, the detailed description of the embodiments of this invention provided below is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention.

[0075] Example 1:

[0076] This invention proposes a pulse shaping method for nuclear signals, comprising:

[0077] S1: Acquire the detector's output signal and construct a digital function signal from it; S1 specifically includes:

[0078] The output signal is constructed as a sinusoidal signal of the same amplitude, such as... Figure 1 As shown, its formula is as shown in equation (1):

[0079] in:

[0080] Among them, t c This represents the forming time of a sinusoidal signal, where A is the amplitude of the sinusoidal signal.

[0081] S2: Discretize the digital function signal and perform a Z-transform to obtain the output Z-transform signal;

[0082] S2 specifically refers to: discretizing the sinusoidal signal and performing a Z-transform to obtain the sinusoidal Z-transform signal, the formula of which is shown in equation (2):

[0083]

[0084] Where, n c =t c / T s T s This represents the ADC sampling time interval.

[0085] S3: Define the input signal as an exponential signal, and perform a Z-transform on the exponential signal to obtain the input Z-transform signal; In S3, the exponential signal is a single exponential signal, and its formula is shown in equation (6):

[0086] v i (t)=V max ·e -t / τ ·u(t), t≥0 (6)

[0087] Among them, V max Let be the amplitude of the single exponential signal, and τ represent the decay time constant of the single exponential signal.

[0088] The Z-transform of a single exponential signal yields a single exponential Z-transform signal, as shown in equation (7):

[0089]

[0090] in,

[0091] S4: Based on the sinusoidal Z-transform signal and the single exponential Z-transform signal, the transfer function of the input signal pulse shaping is obtained, and its formula is shown in equation (10):

[0092]

[0093] The formula is (11) after simplification:

[0094]

[0095] S5: Perform an inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the single exponential signal, and its time-domain expression is shown in equation (12):

[0096]

[0097] This embodiment 1 also provides a pulse shaping system for nuclear signals, including:

[0098] Detector: Used to acquire the output signal and construct a digital function signal from the output signal;

[0099] Preamplifier: Used to acquire the input signal;

[0100] Z-transform module: Discretizes the digital function signal and performs a Z-transform to obtain the output Z-transform signal; Defines the input signal as an exponential signal and performs a Z-transform on the exponential signal to obtain the input Z-transform signal;

[0101] Pulse shaping module: Based on the input Z-transform signal and the output Z-transform signal, obtain the transfer function of pulse shaping of the input signal; perform inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the input signal and its time-domain expression.

[0102] Simulate a single exponential signal (without added noise) using Matlab, where the maximum pulse amplitude V max =2000, decay time constant τ=100T s Sampling time interval T s =50ns, take n c =300T s The single exponentially decaying signal was shaped into a sinusoidal pulse using equation (12), and the result is as follows. Figure 2 As shown.

[0103] Similarly, Matlab can be used to simulate a single exponential signal superimposed with Gaussian white noise, where the maximum pulse amplitude V... max =2000, decay time constant τ=100T s Sampling time interval T s =50ns, s / n=10dB, take nc =300T s The superimposed noise single exponential signal is subjected to sinusoidal pulse shaping using equation (12), and the result is as follows: Figure 3 As shown. By Figure 3 It is evident that the sinusoidal pulse shaping method exhibits significant noise reduction performance.

[0104] Example 2:

[0105] This invention proposes a pulse shaping method for nuclear signals, comprising:

[0106] S1: Acquire the detector's output signal and construct a digital function signal from it; S1 specifically includes:

[0107] The output signal is constructed as a sinusoidal signal of the same amplitude, such as... Figure 1 As shown, its formula is as shown in equation (1):

[0108] in:

[0109] Among them, t c This represents the forming time of a sinusoidal signal, where A is the amplitude of the sinusoidal signal.

[0110] S2: Discretize the digital function signal and perform a Z-transform to obtain the output Z-transform signal;

[0111] S2 specifically refers to: discretizing the sinusoidal signal and performing a Z-transform to obtain the sinusoidal Z-transform signal, the formula of which is shown in equation (2):

[0112]

[0113] Where, n c =t c / T s T s This represents the ADC sampling time interval.

[0114] S3: Define the input signal as an exponential signal, perform a Z-transform on the exponential signal to obtain the input Z-transform signal; In actual measurement, due to the presence of electronic components such as the feedback capacitor and resistor of the preamplifier, charge will be lost during the charge collection process, so the nuclear pulse signal collected by the ADC usually has double exponential characteristics, that is, it has a fast rising edge and a slow falling edge. Therefore, in S3, the exponential signal is a double exponential signal, and its formula is shown in equation (8):

[0115]

[0116] Among them, V maxThe amplitude of the input pulse is represented by τ1 and τ2, which are the decay time constants of the falling edge and rising edge of the pulse, respectively.

[0117] The double exponential signal is transformed by Z to obtain the double exponential Z-transform signal, and its formula is shown in equation (9):

[0118]

[0119] in,

[0120] S4: Based on the sinusoidal Z-transform signal and the double exponential Z-transform signal, the transfer function of the input signal pulse shaping is obtained, and its formula is shown in equation (14):

[0121]

[0122] Simplifying, we get equation (15):

[0123]

[0124] S5: Perform an inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the single exponential signal, and its time-domain expression is shown in equation (16):

[0125]

[0126] Among them, v i [n] represents a discrete double-exponential signal.

[0127] This embodiment 2 also provides a pulse shaping system for nuclear signals, including:

[0128] Detector: Used to acquire the output signal and construct a digital function signal from the output signal;

[0129] Preamplifier: Used to acquire the input signal;

[0130] Z-transform module: Discretizes the digital function signal and performs a Z-transform to obtain the output Z-transform signal; Defines the input signal as an exponential signal and performs a Z-transform on the exponential signal to obtain the input Z-transform signal;

[0131] Pulse shaping module: Based on the input Z-transform signal and the output Z-transform signal, obtain the transfer function of pulse shaping of the input signal; perform inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the input signal and its time-domain expression.

[0132] Simulate a double exponential signal superimposed with Gaussian white noise using Matlab, where the maximum pulse amplitude V max =2000, decay time constant τ1=100T s τ2=10Ts Sampling time interval T s =50ns, s / n=10dB, the resulting double exponential pulse signal is as follows Figure 4 The superimposed noise double exponential signal, taking n c =300T s The double exponential signal was shaped into a sinusoidal pulse using equation (16), and the result is as follows: Figure 4 The signal shown is a sinusoidal pulse shaping signal. (The signal is derived from...) Figure 4 As can be seen, the sinusoidal pulse shaping signal exhibits significant noise reduction, and with a maximum pulse amplitude of 2000, the amplitude of the input signal was accurately calculated. The frequency characteristics of the sinusoidal digital shaping system are shown below. Figure 5 .

[0133] Example 3:

[0134] This invention proposes a pulse shaping method for nuclear signals, comprising:

[0135] S1: Acquire the detector's output signal and construct a digital function signal from it; S1 specifically includes:

[0136] First, the output signal is constructed as a sinusoidal signal of the same amplitude, as shown in equation (1). Then, the sinusoidal signal is integrated to obtain a cosine-like signal, as shown in equation (3).

[0137] in:

[0138]

[0139] The formula is obtained by rearranging:

[0140]

[0141] S2: Discretize the cosine-like signal and perform a Z-transform to obtain the cosine-like Z-transform signal, the formula of which is shown in equation (5):

[0142]

[0143] S3: Define the input signal as an exponential signal, and perform a Z-transform on the exponential signal to obtain the input Z-transform signal; In S3, the exponential signal is a single exponential signal, and its formula is shown in equation (6):

[0144] v i (t)=V max ·e -t / τ ·u(t), t≥0 (6)

[0145] Among them, V maxLet be the amplitude of the single exponential signal, and τ represent the decay time constant of the single exponential signal.

[0146] The Z-transform of a single exponential signal yields a single exponential Z-transform signal, as shown in equation (7):

[0147]

[0148] in,

[0149] S4: Based on the cosine-like Z-transform signal and the single-exponential Z-transform signal, the transfer function of the input signal pulse shaping is obtained, and its formula is shown in equation (13):

[0150]

[0151] Simulation of cosine-like pulse shaping signals, such as Figure 6 As shown, a comparison between cosine-like pulse-shaped signals and Gaussian signals is given. Figure 7 , Figure 7 The blue signal represents a cosine-like pulse-shaped signal, and the orange signal represents a Gaussian signal. Figure 7 See the data similarity analysis in [the original text]. Figure 8 The linear correlation coefficient R² reached 0.9957. A comparison of the spectral characteristics of the cosine-like pulse shaping signal and the sinusoidal pulse shaping signal is shown in Figure 9. The spectral characteristics of the cosine-like pulse shaping signal are significantly improved. The improved cosine-like pulse shaping has the characteristics of constant area and bipolar shaping, which can effectively suppress baseline drift.

[0152] This embodiment 3 also provides a pulse shaping system for nuclear signals, including:

[0153] Detector: Used to acquire the output signal and construct a digital function signal from the output signal;

[0154] Preamplifier: Used to acquire the input signal;

[0155] Z-transform module: Discretizes the digital function signal and performs a Z-transform to obtain the output Z-transform signal; Defines the input signal as an exponential signal and performs a Z-transform on the exponential signal to obtain the input Z-transform signal;

[0156] Pulse shaping module: Based on the input Z-transform signal and the output Z-transform signal, obtain the transfer function of pulse shaping of the input signal; perform inverse Z-transform on the transfer function to obtain the pulse-shaped signal of the input signal and its time-domain expression.

[0157] The above are merely preferred embodiments of the present invention. It should be noted that the above preferred embodiments should not be considered as limitations on the present invention, and the scope of protection of the present invention should be determined by the scope defined in the claims. For those skilled in the art, several improvements and modifications can be made without departing from the spirit and scope of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method of pulse shaping of a nuclear signal, characterized by, Comprising: S1: obtaining an output signal of a detector, and constructing the output signal into a digital function signal; S2: performing Z transform on the discrete digital function signal to obtain an output Z transform signal; S3: defining an input signal as an exponential signal, and performing Z transform on the exponential signal to obtain an input Z transform signal; S4: obtaining a transfer function of pulse shaping of the input signal according to the input Z transform signal and the output Z transform signal; S5: performing inverse Z transform on the transfer function to obtain a pulse shaping signal of the input signal and a time domain expression thereof; The S1 is specifically: The output signal is constructed into a same-amplitude sinusoid-like signal, and the formula is shown as formula (1): (1) wherein, denotes a shaping time of the quasi-sine signal, is an amplitude of the quasi-sine signal; The S2 is specifically: S2 is specifically: performing Z transform on the discrete sinusoid-like signal to obtain a sinusoid-like Z transform signal, and the formula is shown as formula (2): （2） wherein , is the ADC sampling time interval.

2. The method according to claim 1, wherein, S1 is specifically: The output signal is first constructed into a same-amplitude sinusoid-like signal, and the formula is shown as formula (1), and then the sinusoid-like signal is integrated to obtain a cosine-like signal, and the formula is shown as formula (3): (1) (3) The formula (4) is obtained by arrangement: (4) S2 is specifically: performing Z transform on the discrete cosine-like signal to obtain a cosine-like Z transform signal, and the formula is shown as formula (5): (5)。 3. A method of pulse shaping a nuclear signal according to claim 2, wherein, In S3, the exponential signal is a single exponential signal, and the formula is shown as formula (6): (6) wherein is the amplitude of the mono-exponential signal, denotes the decay time constant of the mono-exponential signal, The single exponential Z transform signal is obtained by performing Z transform on the single exponential signal, and the formula is shown as formula (7): (7) wherein .

4. A method of pulse shaping a nuclear signal according to claim 2, wherein, In S3, the exponential signal is a double exponential signal, and the formula is shown as formula (8): (8) wherein denotes the amplitude of the input pulse, and are the decay time constant of the falling edge and the rise time constant of the rising edge, respectively; The double exponential Z transform signal is obtained by performing Z transform on the double exponential signal, and the formula is shown as formula (9): (9) wherein , .

5. A method of pulse shaping a nuclear signal according to claim 3, wherein, In S4, the transfer function of pulse shaping of the input signal is obtained according to the sinusoid-like Z transform signal and the single exponential Z transform signal, and the formula is shown as formula (10): (10) The formula (11) is obtained by arrangement: (11)； S5: performing inverse Z transform on the transfer function to obtain a pulse shaping signal of the single exponential signal and a time domain expression thereof, and the formula is shown as formula (12): (12)。 6. A method of pulse shaping a nuclear signal according to claim 3, wherein, In S4, the transfer function of pulse shaping of the input signal is obtained according to the cosine-like Z transform signal and the single exponential Z transform signal, and the formula is shown as formula (13): (13)。 7. A method of pulse shaping a nuclear signal according to claim 4, wherein, In S4, the transfer function of pulse shaping of the input signal is obtained according to the sinusoid-like Z transform signal and the double exponential Z transform signal, and the formula is shown as formula (14): (14) The formula (15) is obtained by arrangement: (15) S5: performing inverse Z transform on the transfer function to obtain a pulse shaping signal of the single exponential signal and a time domain expression thereof, and the formula is shown as formula (16): (16) wherein represents a discrete bi-exponential signal.

8. A pulse shaping system for nuclear signals, characterized by Comprising: A detector for obtaining an output signal, and constructing the output signal into a digital function signal, and the formula is: wherein, the shaping time of the quasi-sine signal, is the amplitude of the quasi-sine signal; then the quasi-sine signal is discretized and Z-transformed to obtain a quasi-sine Z-transform signal, whose formula is: wherein , is the ADC sampling time interval; A preamplifier for obtaining an input signal, and the input signal is a single exponential signal, and the formula is: wherein is the amplitude of the mono-exponential signal, denotes the decay time constant of the mono-exponential signal, The single exponential Z transform signal is obtained by performing Z transform on the single exponential signal, and the formula is: wherein ; If the exponential signal is a double exponential signal, the formula is: wherein denotes the amplitude of the input pulse, and are the decay time constant of the falling edge and the decay time constant of the rising edge, respectively; Z transform module: after the digital function signal is discretized, Z transform is made to obtain an output Z transform signal; the input signal is defined as an exponential signal, Z transform is made on the exponential signal to obtain an input Z transform signal, and according to the similar-sine Z transform signal and the single-exponential Z transform signal, a transfer function of pulse shaping of the input signal is obtained, and a formula is: After arrangement, a formula is obtained: ； Pulse shaping module: according to the input Z transform signal and the output Z transform signal, a transfer function of pulse shaping of the input signal is obtained; inverse Z transform is made on the transfer function to obtain a pulse shaping signal of the input signal and a time-domain expression thereof.

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