Frequency spectrum transition-based pulse signal parameter identification method

Abstract

The invention discloses a pulse signal parameter identification method based on spectrum transition. In order to solve the problems encountered when existing digital waveform forming is adopted to obtain high-order complex nuclear pulse signal parameters, frequency spectrum movement is carried out on pulse signals, and a matched filter bank is designed for filtering; tracking the central frequency point in real time to overcome the inconsistency of subsequent parameter identification caused by circuit parameter fluctuation; the high sensitivity of the existing digital waveform forming method to the order and complexity of the pulse is overcome; the non-delay characteristic of analog signal processing and the flexibility of digital signal processing can be effectively combined; long-distance transmission of analog signals is facilitated for further analysis and processing; and finally, guarantee is provided for accurate measurement of the energy spectrum.

Description

Technical Field

[0001] The invention relates to a pulse signal parameter recognition method based on spectrum transition. Background Art

[0002] In radioactivity measurement, the front-end analog system of a nuclear radiation detector is composed of a detector, a preamplifier, a CR / RC network, an amplifier circuit, and a conditioning circuit designed to adapt to specific radiation scenarios. When these circuit links are numerous and the composition is complex and diverse, the pulse signal output by the system has the characteristics of diversity and complex waveform, that is, it is complex and high-order. In fact, the complexity and diversity of the pulse output by the front-end analog system are manifested as follows: the mathematical model of the pulse signal is of a high order (possibly infinitely high); when the pulse signal is subsequently digitized and waveform-shaped (for example, standard Gaussian, quasi-Gaussian SK, trapezoidal, bullet-shaped, and other 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, the digital waveform shaping algorithm is difficult to design or difficult to ensure the standardization of the pulse after shaping, which in turn leads to reduced accuracy or even failure of energy spectrum measurement. For example, when the order of the pulse signal is too high, the shaping method based on the mathematical model is difficult to perform recursion or has poor consistency after shaping due to too many coefficients, too large coefficient differences, pulse tail breakage, and too short pulses; and the incomplete collection of the "high-order information" of the signal during sampling leads to reduced recognition accuracy or even failure. In the measurement of energy spectrum, it is necessary to develop a new and effective method to solve the above difficulties in obtaining the amplitude of high-order complex nuclear pulse signals by using the existing digital waveform shaping. The present invention adopts a pulse signal parameter identification method based on spectrum transition to solve the above problems and ultimately provide guarantee for the accurate measurement of energy spectrum. Summary of the invention

[0003] The purpose of the present invention is to disclose a pulse signal parameter identification method based on spectrum transition, to perform spectrum shift on the high-order complex pulse signal output by the front-end analog system of the nuclear radiation detector, to filter the pulse signal in a higher frequency band and to estimate and identify the final amplitude, thereby overcoming the specific difficulties of the existing digital waveform shaping method when dealing with high-order complex, short-time and tail-breaking pulse signals, and providing a guarantee for the accurate measurement of the energy spectrum.

[0004] The present invention relates to a pulse signal parameter identification method based on spectrum transition, which is realized by the following steps ① to ⑥.

[0005] Step ① Combine the nuclear pulse signal f(t) and the oscillation signal g(t; ω 0 ) are multiplied together to obtain the expression for the noisy oscillatory signal x(t).

[0006] Step ② obtain the performance function p[x(t)|ω] for the high-frequency signal x(t) containing noise 0 ], follow the steps (1) to (2) below: (1) Design an orthogonal function set φ M,k (t), and find the signal x(t) in this function set φ M,k Orthogonal projection in (t); (2) Based on angular frequency ω 0 and phase θ, find the probability density function of x(t) p[x(t)|ω 0 ,θ]: First, find the orthogonal projection vector The joint probability density function of Then, we can find the signal x(t) based on ω 0 The probability density function of θ is p[x(t)|ω 0 ,θ]; Finally, find the signal x(t) based on ω 0 The probability density function of the performance function p[x(t)|ω 0 ].

[0007] Step ③ Based on the performance function, search for the angular frequency ω 0 The optimal value of is achieved by following steps (1) to (2): (1) Determine the performance function p[x(t)|ω 0 ] about the monotonically increasing property of ρ; (2) Searching for angular frequency ω 0 The optimal value of is achieved by following steps A to D: Step A, designing a filter bank; Step B: Find the filter bank h m Output y of (t) m (t); Step C: Find the output y of the filter bank m (t) The value at time T Step D: From the numerical value Select the largest one and take its corresponding filter angular frequency as the optimal angular frequency ω opt .

[0008] Step ④ uses the optimal angular frequency ω obtained in step ③ opt Based on this, further refine the search for the angular frequency, as follows 4S 1 ~4S 5 accomplish: Step 4S 1, design the filter bank as follows; Step 4S 2 , find the output of the filter bank Step 4S 3 , find the output of the filter bank Included The value at time T; Step 4S 4 , from step 4S 3 The values ​​obtained in Select the largest one and take its corresponding filter angular frequency as the optimal angular frequency Step 4S 5 , calculate the angular frequency error E obtained between two adjacent iterations ω If E ω ≤E 0 or i ≥ I 0 , proceed to step ⑤; if E ω >E 0 , and i<I 0 , then return to step 4S 1 Continue searching; E 0 and I 0 They represent the allowed error and the maximum number of iterations respectively.

[0009] Step ⑤, search for the optimal phase of x(t) as follows: (1) Modify the value range of x(t); (2) Constructing the true phase value θ and the phase estimate Error (3) The phase search process of x(t) is carried out according to the following steps A, B, and C: A. Settings Initialize the number of iterations and calculate the mean phase error B. Yes Make corrections and recalculate the phase error mean C. If the error or the number of iterations meets the conditions, obtain the optimal phase of x(t) and then proceed to step ⑥; otherwise, return to step B.

[0010] Step ⑥, calculate the optimal amplitude of x(t) according to the optimization algorithm.

[0011] In summary, through steps ① to ⑥, the spectrum shifting method is used to achieve parameter identification of high-order complex nuclear pulse signals.

[0012] The beneficial effects of the present invention are: In radioactive measurement, the front-end analog system of nuclear radiation detectors is composed of detectors, preamplifiers, CR / RC networks, amplifier circuits, and conditioning circuits designed to adapt to specific radiation scenarios. When these circuit links are numerous and the configuration methods are complex and diverse, the pulse signals output by the system have the characteristics of diversity and complex waveforms, that is, they are complex and high-order. This high-order complexity is manifested in: the mathematical model of the pulse signal is of high order (possibly infinitely high); when the pulse signal is subsequently digitized and waveform-shaped 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, the digital waveform shaping algorithm is difficult to design, run, or ensure the standardization of the pulse after shaping, which in turn leads to reduced accuracy or even failure of energy spectrum measurement. For example, when the order of the pulse signal is too high, the shaping method based on the mathematical model is difficult to perform recursion or has poor consistency after shaping due to too many coefficients, too large coefficient differences, pulse tail breakage, and too short pulses; and the incomplete collection of the "high-order information" of the signal during sampling leads to reduced recognition accuracy or even failure. In view of the difficulties in obtaining the parameters of high-order complex nuclear pulse signals by using the existing digital waveform shaping, the present invention adopts a pulse signal parameter identification method based on spectrum transition to solve the above problems. The beneficial effects of this method are: (1) the spectrum of the high-order complex pulse signal is moved, and a filter group matching the signal is designed in a suitable higher frequency band to filter out noise; (2) the center frequency point of the spectrum after movement is tracked in real time to overcome the inconsistency of subsequent parameter identification caused by the frequency change caused by the fluctuation of the parameters of the front-end oscillation circuit; (3) the recognition of the signal amplitude by this method is almost unaffected by the order and complexity of the pulse signal, and overcomes the high sensitivity of the existing digital waveform shaping method to the order and complexity of the pulse; (4) it is convenient to effectively combine the delay-free characteristics of analog signal processing with the flexibility of digital signal processing; (5) for the case where the pulse complexity is too high and it is not convenient to process it on site, it is convenient to transmit the analog signal over a long distance for further analysis and processing. Finally, it provides guarantee for the accurate measurement of the energy spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0014] The following is a detailed description of an embodiment of the present invention in conjunction with the accompanying drawings. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and process are given, but the protection scope of the present invention is not limited to the following embodiment.

[0015] The present invention relates to a pulse signal parameter identification method based on spectrum transition, which is realized by the following steps ① to ⑥.

[0016] Step ① Combine the nuclear pulse signal f(t) and the oscillation signal g(t; ω 0 ) to obtain the expression of the noisy oscillatory 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; Oscillating signal g(t;ω 0 )for: g(t;ω 0 )=cos(ω 0 t+θ) (2) Among them, θ is uniformly distributed in the interval (-π,π); Define the signal s(t; ω 0 )for: The signal s(t; ω 0 ) and the oscillation signal g(t;ω 0 ) after multiplication, the signal containing noise n(t) is x(t), which is expressed as follows: Where n(t) is Gaussian white noise with zero mean and power spectral density N 0 / 2; Special note: The nuclear pulse signal f(t) is not limited to the exponential signal form shown in formula (1), but can also be in other forms; 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.

[0017] Step ② obtain the performance function p[x(t)|ω] for the high-frequency signal x(t) containing noise 0 ], follow the steps (1) to (2) below:

[0018] (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); Wherein M and K are positive integers. x(t) in the function set φ Mk Orthogonal projection x in (t) k As shown in formula (6):

[0019] (2) Based on angular frequency ω0 and phase θ, find the probability density function of x(t) p[x(t)|ω 0 ,θ]; 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 |ω 0 ,θ)=s k (8) variance: Among them, the orthogonal projection vector Then, we can find the signal x(t) based on ω 0 The probability density function of θ is p[x(t)|ω 0 ,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 signal x(t) is based on the angular frequency ω 0 The probability density function of the phase θ is p[x(t)|ω 0 ,θ] is: Finally, find the signal x(t) based on ω 0 The probability density function of the performance function p[x(t)|ω 0 ]: In formula (14),

[0020] Step ③ Based on the performance function, search for the angular frequency ω 0 The optimal value of is achieved by following steps (1) to (2):

[0021] (1) Determine the performance function p[x(t)|ω 0 ] About the monotonically increasing property of 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)|ω 0 ] is also a monotonically increasing function of ρ; it also shows that: the performance function p[x(t)|ω 0 ] corresponds to the maximum value of ω 0 Equivalent to ω corresponding to the maximum value of ρ 0 .

[0022] (2) Searching for angular frequency ω 0 The optimal value of is achieved by following steps A to D: Step A: Design the filter bank as follows: set up but where S′(ω) is s′(t; ω 0 )’s frequency domain expression; 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 from the oscillation of the waveform 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 the 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. This step searches for the angular frequency ω 0 The necessity is to generate an oscillation signal g(t; ω 0 ) changes in circuit parameters lead to fluctuations in angular frequency.

[0023] Step ④ uses the optimal angular frequency ω obtained in step ③ opt Based on this, further refine the search for the angular frequency, as follows 4S 1 ~4S 5 accomplish: Step 4S 1 , design the filter bank as follows: Where λ is a constant greater than 1. Step 4S 2 , find the output of the filter bank Follow these steps: Wherein, j=1,...,(2M+1), and “*” represents a convolution operation. Step 4S 3 , 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 4S 4 , from step 4S 3 The values ​​obtained in Select the largest one and take its corresponding filter angular frequency as the optimal angular frequency The expression is as follows: Step 4S 5 ,calculate and The error E ω : If E ω ≤E 0 or i ≥ I 0 , proceed to step ⑤; if E ω >E 0 , and i<I 0 , then set i=i+1 and return to step 4S 1 Continue searching; E 0 and I 0 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 expressed by ω OPTx Indicates that the expression of x(t) becomes:

[0024] 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; therefore, the phase error is calculated by the integral operation of (41). structure. 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 ≥ L 0 , 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, L 0 Indicates the allowed error and the maximum number of iterations.

[0025] 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).

[0026] In summary, through steps ① to ⑥, the spectrum shifting method is used to achieve parameter identification of high-order complex nuclear pulse signals.

[0027] As described above, the method for parameter identification of high-order complex nuclear pulse signals based on spectrum shifting uses a signal-matched filter group to filter out noise in a suitable higher frequency band; the center frequency point of the spectrum after the shift is tracked in real time to overcome the inconsistency of subsequent parameter identification caused by frequency changes caused by parameter fluctuations of the front-end oscillation circuit; the recognition of signal amplitude is almost unaffected by the order and complexity of the pulse signal, overcoming the high sensitivity of existing digital waveform shaping methods to the order and complexity of the pulse; it is convenient to effectively combine the delay-free characteristics of analog signal processing with the flexibility of digital signal processing; for situations where the pulse complexity is too high and it is not convenient to process it on site in real time, it is convenient to transmit the analog signal over long distances for further analysis and processing; and ultimately, it provides a guarantee for the accurate measurement of the energy spectrum.

[0028] In the above-mentioned embodiment of the present invention, a pulse signal parameter identification method based on spectrum transition is described in detail, but it should be noted that the above is only one embodiment of the present invention. When other forms of signals are involved in utilizing the method mentioned in this article, the present invention is still effective. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in 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) as an example, 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 s(t; ω0) 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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