A method for identifying pulse signal parameters based on spectrum transition

Abstract

The present invention discloses a method for identifying pulse signal parameters based on spectrum transition. Aiming at the problems encountered in obtaining the parameters of high-order complex nuclear pulse signals by using existing digital waveform shaping, the pulse signal is subjected to spectrum shift, and a matching filter bank is designed for filtering; the center frequency point is tracked in real time to overcome the inconsistency of subsequent parameter identification caused by circuit parameter fluctuations; it overcomes the high sensitivity of the existing digital waveform shaping method to the order and complexity of pulses; it is convenient to effectively combine the non-delay characteristic of analog signal processing with the flexibility of digital signal processing; it is convenient to transmit analog signals over long distances for further analysis and processing; ultimately, it provides guarantee for accurate measurement of energy spectrum.

Description

Technical Field

[0001] The present invention relates to a method for identifying pulse signal parameters based on spectral transition. Background Art

[0002] In radioactive measurement, the front-end analog system of a nuclear radiation detector is jointly composed of a detector, a preamplifier, a C-R / R-C network, an amplifier circuit, and a conditioning circuit designed to adapt to specific radiation scenarios. When there are many circuit links and the composition methods are complex and diverse, the form of the pulse signal output by the system has the characteristics of diversity and complex waveform, that is, it shows complex high-order characteristics.

[0003] In fact, the complex diversity of the pulses output by the front-end analog system is manifested as follows: the mathematical model order of the pulse signal is relatively high (possibly infinitely high); when performing digital waveform shaping on the pulse signal subsequently (for example, standard Gaussian, quasi-Gaussian S-K, trapezoidal, bullet-shaped, and other newly emerging shaping methods, etc.) to obtain the pulse amplitude, due to the high-order complexity of the pulse signal model and the large difference in the time constants of the components contained in the pulse, it is difficult to design the digital waveform shaping algorithm or it is difficult to ensure the standardization of the pulse after shaping, thereby leading to a reduction or even failure in the accuracy of energy spectrum measurement. For example, in the case of too high an order of the pulse signal, the shaping method based on the mathematical model has difficulties in recursion or poor consistency after shaping due to too many coefficients, too large a coefficient difference, pulse tailing, and too short a pulse; and incomplete acquisition of the "high-order information" of the signal during sampling leads to a reduction or even failure in the recognition accuracy, etc.

[0004] In energy spectrum measurement, in view of the above difficulties in using the existing digital waveform shaping to obtain the amplitude of high-order complex nuclear pulse signals, it is necessary to develop a new and effective method. The present invention adopts a method for identifying pulse signal parameters based on spectral transition to solve the above problems and ultimately provide guarantee for the accurate measurement of energy spectrum. Summary of the Invention

[0005] The purpose of the present invention is to disclose a method for identifying pulse signal parameters based on spectral transition, which performs spectral shift on the high-order complex pulse signal output by the front-end analog system of a nuclear radiation detector, filters the pulse signal in a higher frequency band, and finally estimates and identifies the amplitude, overcoming the specific difficulties of the existing digital waveform shaping method for high-order complex, short-time, and tailed pulse signals, and providing guarantee for the accurate measurement of energy spectrum.

[0006] The present invention relates to a method for identifying pulse signal parameters based on spectral transition, which is realized through the following steps ① to ⑥.

[0007] Step ① Multiply the nuclear pulse signal f(t) by the oscillating signal g(t; ω0) to obtain the expression of the noisy oscillating signal x(t).

[0008] In step ②, the performance function p[x(t)|ω0] is obtained for the high-frequency signal x(t) with noise, and is implemented according to the following steps (1) to (2):

[0009] (1) Design the orthogonal function set φ M,k (t), and find the orthogonal projection of the signal x(t) in this function set φ M,k (t);

[0010] (2) Based on the angular frequency ω0 and the phase θ, obtain the probability density function p[x(t)|ω0,θ] of x(t):

[0011] First, obtain the joint probability density function of the orthogonal projection vector ;

[0012] Then, obtain the probability density function p[x(t)|ω0,θ] of the signal x(t) based on ω0 and θ;

[0013] Finally, obtain the probability density function of the signal x(t) based on ω0, that is, the performance function p[x(t)|ω0].

[0014] In step ③, based on the performance function, search for the optimal value of the angular frequency ω0, and implement it according to the following steps (1) to (2):

[0015] (1) Judge the monotonic increase of the performance function p[x(t)|ω0] with respect to ρ;

[0016] (2) Search for the optimal value of the angular frequency ω0, and implement it according to the following steps A to D:

[0017] Step A: Design the filter bank;

[0018] Step B: Obtain the output y m (t) of the filter bank h m (t);

[0019] Step C: Obtain the envelope of the output y m (t) of the filter bank at the value at time T

[0020] Step D: Select the maximum value from the values , and use the filter angular frequency corresponding to it as the optimal angular frequency ω opt .

[0021] In step ④, based on the optimal angular frequency ω opt obtained in step ③, perform a further fine search on the angular frequency, and implement it according to the following steps 4S1 to 4S5:

[0022] Step 4S1: Design a filter bank in the following way;

[0023] Step 4S2: Obtain the output of the filter bank

[0024] Step 4S3: Obtain the output of the filter bank The inclusion of at time T;

[0025] Step 4S4: Select the maximum value from the values obtained in Step 4S3 and use the corresponding filter angular frequency as the optimal angular frequency

[0026] Step 4S5: Calculate the angular frequency error E between two adjacent iterations ω ; If E ω ≤ E0 or i ≥ I0, proceed to Step ⑤; If E ω > E0 and i < I0, then return to Step 4S1 to continue the search; E0 and I0 respectively represent the allowed error and the maximum number of iterations.

[0027] Step ⑤: Search for the optimal phase of x(t) in the following way:

[0028] (1) Modify the value range of x(t);

[0029] (2) Construct the error between the true phase θ and the estimated phase

[0030] (3) The phase search process of x(t) is carried out according to the following steps A, B, and C:

[0031] A. Set Initialize the number of iterations and calculate the mean phase error

[0032] B. Modify and recalculate the mean phase error

[0033] C. If the error or the number of iterations meets the condition, obtain the optimal phase of x(t) and then proceed to Step ⑥; otherwise, return to Step B.

[0034] Step ⑥: Obtain the optimal amplitude of x(t) according to the optimization algorithm.

[0035] In summary, through Steps ① to ⑥, using the method of spectrum shifting, the parameter identification of high-order complex nuclear pulse signals is achieved.

[0036] The beneficial effects of the present invention are:

[0037] In radioactive measurement, the front-end analog system of a nuclear radiation detector is jointly composed of a detector, a preamplifier, a C-R / R-C network, an amplifier circuit, and a conditioning circuit designed to adapt to specific radiation scenarios. When there are many circuit links and their composition methods are complex and diverse, the form of the pulse signal output by the system is diverse and the waveform is complex, that is, it shows complex high-order characteristics. This high-order complexity is manifested as follows: the mathematical model order of the pulse signal is relatively high (possibly infinitely high); when digitally wave-forming the pulse signal subsequently to obtain the pulse amplitude, due to the high-order complexity of the pulse signal model and the large difference in the time constants of the components contained in the pulse, it is difficult to design and operate the digital wave-forming algorithm or it is difficult to ensure the standardization of the pulse after shaping, thereby reducing the accuracy of energy spectrum measurement or even causing failure. For example, when the order of the pulse signal is too high, the shaping method based on the mathematical model has problems such as difficult recurrence or poor consistency after shaping due to too many coefficients, too large coefficient differences, pulse tailing, and too short pulses; and incomplete acquisition of the "high-order information" of the signal during sampling leads to reduced recognition accuracy or even failure, etc.

[0038] Aiming at the above difficulties in using the existing digital wave-forming to obtain the parameters of high-order complex nuclear pulse signals, the present invention adopts a method for identifying pulse signal parameters based on spectrum transition to solve the above problems. The beneficial effects of this method are as follows: (1) Shift the spectrum of the high-order complex pulse signal, and design a filter bank matching the signal in a suitable higher frequency band to filter out noise; (2) Track the center frequency point of the shifted spectrum in real time to overcome the inconsistency of subsequent parameter recognition caused by the frequency change due to the parameter fluctuation of the front-end oscillation circuit; (3) The recognition of the signal amplitude by this method is hardly affected by the order and complexity of the pulse signal, overcoming the high sensitivity of the existing digital wave-forming method to the order and complexity of the pulse; (4) Facilitate the effective combination of the non-delay characteristic of analog signal processing and the flexibility of digital signal processing; (5) For the situation where the pulse complexity is too high and it is not convenient to process immediately on-site, it is convenient to transmit the analog signal over a long distance for further analysis and processing. Ultimately, it provides guarantee for the accurate measurement of the energy spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0040] The following will describe the embodiments of the present invention in detail with reference to the drawings. These embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation manners and processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0041] The present invention relates to a method for identifying pulse signal parameters based on spectrum transition, which is realized through the following steps ① to ⑥.

[0042] Step ① Multiply the nuclear pulse signal f(t) by the oscillation signal g(t; ω0) to obtain the expression of the oscillatory signal x(t) with noise:

[0043] In this invention, taking the nuclear pulse signal f(t) as a high-order exponential signal shown in the following formula (1) as an example, that is

[0044]

[0045] where τ i is the time constant, A is the amplitude, and N is the order;

[0046] The oscillation signal g(t; ω0) is:

[0047] g(t; ω0) = cos(ω0t + θ) (2)

[0048] where θ is uniformly distributed in the interval (-π, π);

[0049] Define the signal s(t; ω0) as:

[0050]

[0051] Multiply the signal s(t; ω0) by the oscillation signal g(t; ω0), and the resulting signal with noise n(t) is x(t), and the expression is as follows:

[0052]

[0053] where n(t) is Gaussian white noise with a mean of zero and a power spectral density of N0 / 2; Special note: The nuclear pulse signal f(t) is not limited to the exponential signal form shown in formula (1), and can also be other forms; This step ① realizes the spectral shift of the nuclear pulse signal f(t), and x(t) is called a high-frequency signal with noise.

[0054] Step ② Obtain the performance function p[x(t)|ω0] for the high-frequency signal x(t) with noise, which is realized according to the following steps (1) to (2):

[0055] (1) Design the orthogonal function set φ M,k (t), as shown in formula (5); and find the orthogonal projection of the signal x(t) in this function set φ M,k (t), as shown in formula (6);

[0056]

[0057] where M and K are positive integers.

[0058] The orthogonal projection of x(t) in the function set φ MkOrthogonal projection \(x\) in \((t)\) k As shown in Equation (6):

[0059]

[0060] (2) Based on the angular frequency \(\omega_0\) and phase \(\theta\), obtain the probability density function \(p[x(t)|\omega_0,\theta]\) of \(x(t)\);

[0061] First, obtain the orthogonal projection vector of the joint probability density function According to the following Equations (7) - (9);

[0062] Joint probability density function:

[0063] Mean: \(E(x k |\omega_0,\theta)=s k (8) Variance: where the orthogonal projection vector

[0064] Then, obtain the probability density function \(p[x(t)|\omega_0,\theta]\) of the signal \(x(t)\) based on \(\omega_0\) and \(\theta\):

[0065]

[0066] where, The conversion between \(M\) and \(K\) is shown in Equation (5).

[0067] Further transform the integral in Equation (10):

[0068]

[0069] The parameter expressions in Equation (11) are as follows:

[0070]

[0071] Then the probability density function \(p[x(t)|\omega_0,\theta]\) of the signal \(x(t)\) based on the angular frequency \(\omega_0\) and phase \(\theta\) is:

[0072]

[0073] Finally, obtain the probability density function of the signal \(x(t)\) based on \(\omega_0\), that is, the performance function \(p[x(t)|\omega_0]\):

[0074]

[0075] In Equation (14),

[0076]

[0077] Step ③ Based on the performance function, search for the optimal value of the angular frequency ω0, which is implemented according to the following steps (1) to (2):

[0078] (1) Judge the monotonic increasing property of the performance function p[x(t)|ω0] with respect to ρ

[0079] Let And transform f(ρ) according to the following method:

[0080]

[0081] Since Then f(ρ) > 0;

[0082] Take the derivative of f(ρ):

[0083]

[0084] It can be obtained from formula (17): Therefore, f(ρ) is a monotonically increasing function with respect to ρ, and the performance function p[x(t)|ω0] is also a monotonically increasing function with respect to ρ; at the same time, it also shows that: the ω0 corresponding to the maximum value of the performance function p[x(t)|ω0] is equivalent to the ω0 corresponding to the maximum value of ρ.

[0085] (2) Search for the optimal value of the angular frequency ω0, which is implemented according to the following steps A to D:

[0086] Step A: Design a filter bank according to the following method:

[0087] Let

[0088] Then where S′(ω) is the frequency-domain expression of s′(t; ω0);

[0089] Let H(ω) = S′ * (ω)e -jωT (20)

[0090]

[0091] h(t) is the time-domain expression of H(ω);

[0092] The expression of the filter bank h m (t) is as follows:

[0093]

[0094] That is: where, ω00 is the rough angular frequency observed from the waveform oscillation of x(t), and Δω is the angular frequency interval between the filters.

[0095] Step B. Obtain the output y m (t) of the filter bank h m (t) in the following way:

[0096]

[0097] That is: where "*" represents the convolution operation, and m = 0,..., M.

[0098] Step C. Obtain the envelope of the output y m (t) of the filter bank at time T and let

[0099]

[0100] That is,

[0101]

[0102] where is the envelope of y m (t), m = 0,..., M; ρ m has the same meaning as ρ in formula (15).

[0103] Step D. Select the maximum value from the values shown in formula (27), and use the corresponding filter angular frequency as the optimal angular frequency ω opt , in the following way:

[0104]

[0105] and let Set the iteration number i = 1.

[0106] The necessity of searching for the angular frequency ω0 in this step is that the change in the circuit parameters generating the oscillating signal g(t; ω0) leads to the fluctuation of the angular frequency.

[0107] Step ④ Based on the optimal angular frequency ω opt obtained in step ③, perform a further fine search for the angular frequency, which is implemented according to the following steps 4S1 to 4S5:

[0108] Step 4S1. Design the filter bank in the following way:

[0109]

[0110] where λ is a constant greater than 1.

[0111] Step 4S2, obtain the output of the filter bank In the following way:

[0112]

[0113] where j = 1,...,(2M + 1), and "*" represents the convolution operation.

[0114] Step 4S3, obtain the output of the filter bank the inclusion of at time T

[0115] and let

[0116]

[0117] where is the inclusion of, j = 1,...,(2M + 1); has the same meaning as ρ in formula (15).

[0118] Step 4S4, select the maximum value from the values obtained in Step 4S3 and use the corresponding filter angular frequency as the optimal angular frequency The expression is as follows:

[0119]

[0120] Step 4S5, calculate and the error E of ω :

[0121]

[0122] If E ω ≤ E0 or i ≥ I0, proceed to Step ⑤; if E ω > E0 and i < I0, then let i = i + 1 and return to Step 4S1 to continue the search; E0 and I0 respectively represent the allowed error and the maximum number of iterations; when the iteration ends, is the optimal angular frequency of x(t), and is represented by ω OPTx and the expression of x(t) becomes:

[0123]

[0124] Step ⑤ Search for the optimal phase of x(t) and implement it according to the following methods (1) - (3):

[0125] Let the true value of the phase of \(x(t)\) be \(\theta\), and the estimated value of the phase be

[0126] (1) Modify the value range of \(x(t)\) to \(0\sim T'\), where \(T'\) is as follows:

[0127]

[0128] where denotes rounding down, and the expression of \(x(t)\) is modified again to:

[0129]

[0130] (2) Construct the phase error in the following way:

[0131]

[0132] From formulas (36) - (39), the proportional relationship shown in formula (40) is obtained;

[0133]

[0134] When is relatively small, it is further obtained that:

[0135]

[0136] where \(\gamma\) is a positive constant, and is called the mean value of the phase error; therefore, the integral operation in (41) is used to construct the phase error .

[0137] In addition, when , from it is obtained that:

[0138] (3) The phase search process of \(x(t)\) is carried out according to the following steps A, B, and C:

[0139] A. Set the iteration number \(l = 1\), calculate the mean value of the phase error according to formulas (38) and (39) and let

[0140] B. First, correct according to the following formula (42):

[0141]

[0142] where \(\alpha\) and \(\beta\) are negative constants, and let

[0143] Then, recalculate the mean value of the phase error according to formulas (38) and (39).

[0144] C. If formula (43) holds, or l ≥ L0, then the optimal phase of x(t) is and is denoted as θ OPTx , then go to step ⑥; otherwise, let l = l + 1 and return to step B;

[0145]

[0146] E in formula (43) θ is the allowable error, and L0 represents the allowable error and the maximum number of iterations.

[0147] Step ⑥ The optimal amplitude a of x(t) opt is obtained according to the following algorithm:

[0148] From the optimization algorithm of formula (44), the optimal amplitude A of x(t) is obtained opt , as shown in formula (45).

[0149]

[0150] In summary, through steps ① - ⑥, by using the method of spectrum shift, the parameter identification of high - order complex nuclear pulse signals is realized.

[0151] As described above, the method for parameter identification of high - order complex nuclear pulse signals based on spectrum shift uses a filter bank for signal matching in a suitable higher frequency band to filter out noise; it tracks the center frequency point of the shifted spectrum in real - time to overcome the inconsistency of subsequent parameter identification caused by frequency changes due to fluctuations in the parameters of the front - end oscillation circuit; the identification of the signal amplitude is hardly affected by the order and complexity of the pulse signal, overcoming the high sensitivity of the existing digital waveform shaping methods to the order and complexity of the pulse; it is convenient to effectively combine the non - delay characteristic of analog signal processing with the flexibility of digital signal processing; for the situation where the pulse complexity is too high and not convenient for on - site immediate processing, it is convenient to transmit the analog signal over a long distance for further analysis and processing; ultimately, it provides a guarantee for the accurate measurement of the energy spectrum.

[0152] In the above - mentioned embodiments of the present invention, a method for parameter identification of pulse signals based on spectrum transition is described in detail. However, it should be noted that the above is only one embodiment of the present invention. When other forms of signals involve using the method proposed herein, the present invention is still valid. Any modifications, equivalent replacements, improvements, etc., made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A pulse signal parameter identification method based on spectrum transition, characterized in that: Parameter identification of pulse signals is achieved through the following steps ① to ⑥: Step ① Multiply the nuclear pulse signal f(t) by the oscillation signal g(t; ω0) to obtain the expression of the noisy oscillation signal x(t): The present invention takes the nuclear pulse signal f(t) as a high-order exponential signal as shown in the following formula (1), that is, where τ i is the time constant, A is the amplitude, and N is the order; The oscillation signal g(t;ω0) is: g(t;ω0)=cos(ω0t+θ) (2) Among them, θ is uniformly distributed in the interval (-π,π); Define the signal s(t;ω0) as: After multiplying the signal f(t) with the oscillation signal g(t; ω0), the signal x(t) containing noise n(t) is obtained, which is expressed as follows: Where n(t) is a Gaussian white noise with a mean of zero and a power spectrum density of N0 / 2; this step ① realizes the spectrum shift of the nuclear pulse signal f(t), and x(t) is called a high-frequency signal containing noise; Step ② obtains the performance function p[x(t)|ω0] for the high-frequency signal x(t) containing noise, and is implemented according to the following steps (1) to (2): (1) Design an orthogonal function set φ M,k (t), see formula (5); and find the signal x(t) in the function set φ M,k Orthogonal projection in (t), see formula (6); Where M and K are positive integers; x(t) in the function set φ M,k Orthogonal projection x in (t) k As shown in formula (6): (2) Based on the angular frequency ω0 and phase θ, the probability density function p[x(t)|ω0,θ] of x(t) is obtained: First, find the orthogonal projection vector The joint probability density function of According to the following formulas (7) to (9); Joint probability density function: Mean: E(x k |ω0,θ)=s k (8) variance: Among them, the orthogonal projection vector Then, we obtain the probability density function p[x(t)|ω0,θ] of the signal x(t) based on ω0 and θ: in, The conversion between M and K is shown in formula (5); Further transform the integral in formula (10): The parameter expressions in formula (11) are as follows: Then the probability density function p[x(t)|ω0,θ] of the signal x(t) based on the angular frequency ω0 and phase θ is: Finally, find the probability density function of the signal x(t) based on ω0, that is, the performance function p[x(t)|ω0]: In formula (14), Step ③ Based on the performance function, search for the optimal value of the angular frequency ω0, which can be achieved by following steps (1) to (2): (1) Determine whether the performance function p[x(t)|ω0] is monotonically increasing with respect to ρ. make And transform f(ρ) as follows: because Then f(ρ)>0; Derivative of f(ρ): From formula (17), we can get: Therefore, f(ρ) is a monotonically increasing function of ρ, and the performance function p[x(t)|ω0] is also a monotonically increasing function of ρ. It also shows that the ω0 corresponding to the maximum value of the performance function p[x(t)|ω0] is equivalent to the ω0 corresponding to the maximum value of ρ. (2) Search for the optimal value of the angular frequency ω0, which can be achieved by following steps A to D: Step A: Design the filter bank as follows: set up but Where S′(ω) is the frequency domain expression of s′(t;ω0); Let H(ω) = S′ * (ω)e -jωT (20) h(t) is the time domain expression of H(ω); Filter Bank h m The expression of (t) is as follows: Right now: Among them, ω 00 is the rough angular frequency observed based on the waveform oscillation of x(t), and Δω is the angular frequency interval between filters; Step B: Find the filter bank h m Output y of (t) m (t), as follows: Right now: Where "*" represents convolution operation, m = 0, ..., M; Step C: Find the output y of the filter bank m (t) The value at time T And order Right now, in Yes m (t) includes, m = 0, ..., M; ρ m It has the same meaning as ρ in formula (15); Step D: From the value shown in formula (27) Select the largest one and take its corresponding filter angular frequency as the optimal angular frequency ω opt , the method is as follows: And order Set the number of iterations i = 1; Step ④ uses the optimal angular frequency ω obtained in step ③ opt Based on , further fine search of the angular frequency can be performed according to the following steps 4S1 to 4S5: Step 4S1, design the filter bank as follows: Where λ is a constant greater than 1; Step 4S2, find the output of the filter bank Follow these steps: Wherein, j=1,...,(2M+1), "*" represents convolution operation; Step 4S3, find the output of the filter bank Included The value at time T And order in yes The inclusion of , j = 1, ..., (2M + 1); It has the same meaning as ρ in formula (15); Step 4S4: The value obtained from step 4S3 Select the largest one and take its corresponding filter angular frequency as the optimal angular frequency The expression is as follows: Step 4S5, calculation and The error E ω : If E ω ≤E0 or i≥I0, proceed to step ⑤; if E ω > E0, and i < I0, then set i = i + 1 and return to step 4S1 to continue searching; E0 and I0 represent the allowable error and the maximum number of iterations respectively; when the iteration is completed, is the optimal angular frequency of x(t), and is expressed by ω OPTx Indicates that the expression of x(t) becomes: Step ⑤ searches for the optimal phase of x(t), which can be achieved by the following methods (1) to (3): Assume that the true phase value of x(t) is θ and the estimated phase value is (1) The value range of the modified x(t) is 0 to T′, where T′ is as follows: in Indicates rounding down, the expression of x(t) is corrected again as follows: (2) Structural phase error Follow these steps: From formulas (36) to (39), we can obtain the proportional relationship shown in formula (40); when When smaller, Further conclusion: Where γ is a positive constant, called is the mean phase error; the phase error is calculated by integrating (41) The structure of In addition, when When It turns out that: (3) The phase search process of x(t) is carried out according to the following steps A, B, and C: A. Settings The number of iterations is l = 1, and the mean phase error is calculated according to formulas (38) and (39): And order B. First of all, Correct according to the following formula (42): Among them, α and β are negative constants, and let Then, the phase error mean is recalculated according to formulas (38) and (39): C. If formula (43) holds, or l ≥ L0, then the optimal phase of x(t) is And denoted as θ OPTx , then go to step ⑥; otherwise, set l = l + 1 and return to step B; E in formula (43) θ is the allowable error, L0 represents the allowable error and the maximum number of iterations; Step ⑥ The optimal amplitude a of x(t) opt Obtained by the following algorithm: According to the optimization algorithm of formula (44), the optimal amplitude A of x(t) is obtained: opt , as shown in formula (45):

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