A Pulse Waveform Conditioning and Shaping Method Based on Component Suppression
Patent Information
- Authority / Receiving Office
- NL · NL
- Patent Type
- Patents
- Current Assignee / Owner
- CHENGDU UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2025-05-30
- Publication Date
- 2026-07-21
Abstract
Description
TECHNICAL FIELD The invention relates to . BACKGROUND In some nuclear radiation detection processes, due to the complexity and diversity of front-end analog channels composed of detectors and conditioning circuits, and the variability of electronic device parameters in pulse waveform conditioning circuits with time or external environment, the output pulse waveform may contain rich components; The types of components in the s-domain are proportional, inertial, integral, differential (rst or higher order), oscillation and other links, and the mathematical model composed of these components is high-order and complex. The types of components are exponential signal, step signal, ramp signal, oscillation signal and other waveforms in time domain, and the pulse signal composed of these components is characterized by the complexity and even singularity of the waveform. In nuclear energy spectrum measurement, it is necessary to shape these high-order, complex and strange pulses and extract their amplitudes. If simple typical signals (such as exponential signals and jump signals) are used to t or approximate the measured pulse signals, and the digital waveform is shaped by the mathematical models corresponding to these typical signals, the shaped pulse waveform will be distorted or even invalid. For example, the top of the shaped trapezoidal pulse is no longer a horizontal straight line (it may be an undulating twisted curve), which may lead to inaccurate or even invalid acquisition of amplitude. In addition, even if the waveform shaping algorithm is accurate in a certain measurement, due to the change of system parameters with time, the waveform shaping algorithm adopted may lead to the inconsistency between the formed pulse and the early one in the next measurement. Therefore, it is necessary to fully understand and deal with the components of highorder complex and singular pulses before forming, so as to realize the accurate forming of pulses and finally obtain highprecision nuclear energy spectrum. The purpose of this method is to fully identify the components of high-order, complex and singular pulses with rich components, and to suppress the key components (components that have a great inuence on waveform shaping), so that the processed pulses become relatively low-order, simple and standardized signals, so that the subsequent digital shaping becomes relatively simple and accurate, which guarantees the accurate measurement of energy spectrum. Mindset: Because of the existence of oscillation component, the whole pulse waveform uctuates, which brings great difculties for signal acquisition, standardized shaping of subsequent pulses and accurate extraction of amplitude. Therefore, for high- order, complex and singular pulses with rich components, the invention gives a set of related recursive algorithms by taking the identication, suppression processing and waveform shaping of oscillation components as examples. SUMMARY The purpose of the present invention is to disclose , which is used to fully identify each component of the high-order, complex and singular pulse with rich components output by the front-end simulation system of a nuclear radiation detector, and to suppress the key components (which have great inuence on waveform shaping, the invention takes the oscillation component as an example) and nally shape the waveform, so as to provide guarantee for the accurate measurement of the subsequent energy spectrum. In this method, the time domain, frequency domain, s-domain and zdomain of the pulse signal are effectively connected, and a set of algorithms for component identication, key component suppression and accurate shaping of highorder, complex and singular pulse signals with rich components are given, which overcomes the limitations of the current methods for signal identication and shaping based on typical pulse signal models (such as single (double) exponential signals and step signals). The invention fully identies each component of the highorder, complex and singular pulses output by the nuclear radiation detection channel, and suppresses the key components and accurately shapes them. This method takes the complex pulses containing oscillation components, inertial components and differential components as an example, and its component identication, oscillation component suppression and nal shaping recursive algorithm are realized through the following steps 1-10. Step 1: Give the sdomain function expression G(s) of the pulse containing oscillation component, inertial component and differential component. Step 2: Randomly extract a single pulse h(t) from the measured pulse, draw the trend line of the frequency characteristic of Mt), and nd the slope of the trend line and the intersection coordinates of the trend lines. Step 3: Construct the slope matrix and link matrix of the trend line, and gives the corresponding relationship between the slope matrix, link matrix and the intersection coordinates in step 2. Step 4: Adopt the slope of the trend line of the pulse h(t) and the coordinates of the intersection point in step 3 to nd the initial parameters of the function G(s). Step 5: Bring the parameter values obtained in step 5 into G(s), decomposes G(s) into the superposition of oscillation link, inertia link and differential link, and obtains the parameters of each link after G(s) decomposition. Step 6: Iteratively update the decomposed parameters of each link of G(S) to search for the optimal parameters. Step 7: The parameters before G(s) decomposition are updated by the optimal parameters obtained in Step 6, and then the time domain expression (7 (t) after h(t) has eliminated the oscillation component is obtained. Step 8: Find the waveform shaping algorithm after eliminating the oscillation component. The above steps 1 - 8 optimize the identication of the oscillation components contained in the pulse, and give the Z-domain shaping algorithm after deducting the oscillation components. The following steps 9 and 10 will give a timedomain recursive algorithm for conditioning and shaping the measured pulse x(t) containing oscillation components in specic applications; Taking the quadratic edge attopped pulse forming as an example, it means that x(t) is shaped into a quadratic edge attopped pulse. Step 9: For the actually measured pulse x(t) with oscillation link, a timedomain recursive algorithm for eliminating oscillation component is given. Step 10: For the actually measured pulse x(t) with oscillation link, a timedomain recursive algorithm is given to remove the oscillation component and shape it into a template pulse; The template pulse takes the quadratic edge at-topped pulse as an example. Through steps 1-10, the parameters of each link of pulse x( t) containing oscillation components are optimally obtained, and the time-domain recursive algorithm for suppressing (i.e. eliminating) oscillation components and waveform shaping is given. The invention has the benecial effects that: In the process of nuclear radiation detection, due to the complexity and diversity of the front-end analog channel composed of detector and conditioning circuit, and the variability of electronic device parameters in pulse waveform conditioning circuit with time or external environment, the output pulse waveform may contain rich components; The types of components in the S-domain are proportional, inertial, integral, differential (rst or higher order), oscillation and other links, and the mathematical model composed of these components is high-order and complex. The types of components are exponential signal, step signal, ramp signal, oscillation signal and other waveforms in time domain, and the pulse signal composed of these components is characterized by the complexity and even singularity of the waveform. In nuclear energy spectrum measurement, it is necessary to shape these high-order, complex and singular pulses and extract their amplitudes. If simple typical signals (such as exponential signals and jump signals) are used to t and approximate the measured pulse signals, and the digital waveforms are shaped by the mathematical models corresponding to these typical signals, the shaped pulse waveforms will be distorted or even invalid, so that effective energy spectrum cannot be obtained. Therefore, it is necessary to fully understand and deal With the components of high-order complex and singular pulses before forming. The advantages of this method are as follows: (1) The highorder, complex and singular pulses with rich components output by the frontend simulation system of nuclear radiation detector are optimally identied; (2) The key components (the components that have great inuence on waveform shaping, the invention takes the oscillation component as an example) are suppressed, which reduces the order, uctuation and complexity of the pulse, and provides a guarantee for the nal waveform shaping and accurate measurement of the energy spectrum; (3) The time domain, frequency domain, sdomain and zdomain of the pulse signal are effectively connected; (4) A complete algorithm and recursive process are given for component identication, key component suppression and accurate shaping of high-order, complex and singular pulse signals with rich components, which overcomes the limitations of current methods for signal identication and shaping based on typical pulse signal models. BRIEF DESCRIPTION OF DRAWINGS Fig. 1 is a frequency domain trend line diagram of a pulse signal; Fig. 2 is a ow chart of the method of the present invention. DETAILED DESCRIPTION OF EMBODIMENTS The embodiment of the present invention will be described in detail with the attached drawings. This embodiment is implemented on the premise of the technical scheme of the present invention, and the detailed implementation and process are given, but the protection scope of the present invention is not limited to the following embodiments. The invention relates to , which fully identies the components of high-order, complex and singular pulses, and suppresses and accurately shapes the key components. This method takes complex pulses containing oscillation components, inertial components and differential components as an example, and its component identication, oscillation component suppression and nal shaping recursive algorithm are realized through the following steps l-lO. Step 1: Give the s-domain function expression G(s) of the pulse containing oscillation component, inertial component and differential component: $$$? (1) (xls + 1)(T23 + Tls + 1) The denominator contains the following links: l inertial link: L , and the link serial number is l; Äs + 1 1 oscillation link: + , and the link serial number is "2; Tzs + Ts +1 1 differential link: TS +1 , and the link serial number is "3"; The above inertial link, oscillation link and differential link are also called inertial component, oscillation component and differential component respectively. Step 2: Randomly extract a single pulse h(t) from the measured pulse, draw the trend line of the frequency characteristic of h(t), and calculate the slope of the trend line and the coordinates of the intersection points between the trend lines, as follows: Find the frequency domain expression of h(t), as shown in formula (2): H(ja)) : [juneW: (2) Let u = H0 ln|H(]a))| 7 = Ina), H0 be anormal number; Draw a 7 _u curve with 7 as the abscissa and u as the ordinate, and draw a trend line on the 7 - u curve with a slope of "HO (n integer), and the trend line is a straight line; This embodiment is a pulse waveform described by formula (1), and there are four trend lines. The coordinate ofthe intersection of trend line 1 and the ordinate is ( 70 #0) , the serial number of the intersection is "0", and the slope is 0; The coordinate of the intersection of trend line 1 and trend line 2 is (71 #1), and the intersection number is "l"; The coordinate of the intersection of trend line 2 and trend line 3 is (72 #2), and the intersection number is 2; The coordinate of the intersection of trend line 3 and trend line 4 is ( 73 #3), and the intersection number is "3"; The trend line is shown in Figure l of the specication; Step 3: Construct the slope matrix and link matrix of the trend line, and give the corresponding relationship between the slope matrix, link matrix and the intersection coordinates in step 2, as follows: The possible slopes of trend line 2, trend line 3 and trend line 4 form a slope matrix U as follows: UL1 U1,2 Um H0 3H0 2H0 Um Um U2,3 _Ho 0 _2H0 U Um U32 Um 2H0 3H0 2H0 _ U4,1 U4,2 U4,3 _ _ZHo _Ho _2H0 (3) U5,1 U5,2 U53 Ho O _2H0 U6,1 U6,2 U63 Ho _Ho _2H0 From left to right, three elements in the same row in the matrix U correspond to the slopes of trend line 2, trend line 3 and trend line 4 respectively; Combining the slope characteristics of three link trend lines, the corresponding link matrix Wis obtained from the slope matrix U, W W W 1 2 3 W W W 1 3 2 W W11W11W11 213 _ W1 W W _ 2 3 1 <4) W,] Wm W53 3 1 2 W Wm WM 3 2 1 The element of Wis composed of the serial number of the link; Description of the correspondence between U, Wand the intersection point: Taking the rst row of U as an example, _HO, _3H0 and _ZHO respectively correspond to the slopes of trend line 2, trend line 3 and trend line 4, and correspond to the link numbers 1, 2 and 3 (i.e. inertial link, oscillation link and differential link) in the rst row of W, and also correspond to the intersection points (7' u), (72 #2) and (73 #3) respectively; This correspondence is summarized as shown in formula (5); Um <=> WEJ <=> ?mamm (71 ui) (5) Step 4: Using the slope of the trend line of the pulse h(t) and the coordinates of the intersection point in step 3, the initial value of the parameter of the function G(s) is obtained as follows (1)-(3): Firstly, let the slopes of trend line 2, trend line 3 and trend line 4 of h(t) correspond U1 U . 2 U . 3 . . . . to elements , and in the zth row of the slope matrix U respectively. According to the correspondence between U and W, there is also a onetoone . W 1 W2 W3 . . . . correspondence With the elements , and in the tth row of the link matrix W; (l) Inertial link parameters K and Ä are solved as follows: 1  = 6 e,, < ) In the formula, "j" represents the column number of the element with a value of " l " among the three elements W , Wil and Wi; From HolnK = uo: K = ello / Ho (7) (2) The solution of the rst-order differential link parameter T is as follows: 1 3 :; (8) In the formula, "l" represents the column number of the element with the value of "3" among the three elements W, Wil and Wi; (3) The solution of oscillation link parameters T2 and Tl is as follows: 1 1 T3=<+,>2 T1=Jî=T3=+q (9) e e In the formula, "q" represents the column number of the element with the value of "2" among the three elements W, Wii and Wi; Step 5: Take the parameter values K T, / 1,7", and Tl obtained in step 4 into the following formula G(s), decompose the oscillation link into conjugate complex roots, and further decompose G(s) to obtain parameters Ki, C , D, a and 6, and proceed as follows (1) and (2). (1) Firstly, the oscillation link is decomposed into conjugate complex roots: l l 2 = . . (10) Tzs +T1s+l T2(S+ajß)(s+a+jß) Wherein, the real part a and imaginary part ß of the conjugate complex root are obtained according to formula (10). (2) Further decompose the function G(s) with oscillation link according to formula (11): K 1 K 'D D G(s) zëzèJrcjLÀJFCTÀ (11) (x15+1)(T2s +T,s+1) (%) (s113) (Hmm) Parameters K1, C , D, are obtained according to the following formulas (12) (14); K (rs + 1) K = s+ 1 G s = 12 1 ( A) ( )is% Ä,(î-'2S2 + Tis +1) _ y ( ) S a C+jD=(s+aj)G(s)|_ _ =L) (13) " / ß T2(ÄS + 1)(S + a + jß) PGH / _ _ K (rs +1) C D = s + a + G s _ = _ J ( ]ß) ( NP T, + l)(s + a jß)ls__a_jß (14) After calculating K,CD,cx, BJ according to the above steps 4 and 5, take them as the initial values of the subsequent formula derivation, and make: Step 6: Searching the optimal parameters of the function G(s); Let the number of iterations be p and the initial value p=0; Kl ( p), C( p), D( p), a( p), B( p), / 1(p) represents the latest value of each parameter of G(s) after the completion of the p-th iteration, and Gp(s) represents the expression of G(s) after the completion of the p-th iteration; Perform iterative update according to the following steps 6Sl-6S2: Step 6S 1: The iterative updating algorithm corresponding to parameter K1(p)C(P)7D(p)>(Pmp)MP) is shown in formula (16) _ (21); 1 K1(p + 1) = K1(p)+ AEK, (P)K1(P) vp (16) 1 C(p +1) = C2(1)) + AECUW)C(W) vp (17) 1 DUW + 1) = D(r?) + AED(W)D(W) vp (18) 1 0660 +1) = 0609) + AEa(p)a(p) vp (19) 1 +1 = +AE ß(p ) b(p) 169mm) (20) 1 MP +1) = M1?) + AE) (19) / 1(1)) vp (21) AE in formulas (16) (21) is shown in formulas (22) (27): AEK, (p) = Eloi / MTL) gp<n71)]2 Zf=,[h(n11> g mon)? (22) AE?) = Zîzownîz) g,(nT.>]2 Zj=orh(nT.) g GW,)? (23) AE» = Zf=,[h(nT.) ggf / JS)? 210W?” g3_ <nT3)]2 (24) AE» = Z:,wnT.) g.,wr Z:,[hmm g (nur (25) AE, = 2:,[h(n71)gp <n1;)r 2:,[hmm g,,1 (nmr (26) AE» = Z:,wnîg) g(nmr 210%qu g, 3 <nr3>r (27) gp(WT3)3gp_3K,(WT,)gp_íCOWT.)3g3_+D(n7;)3g,_(WT3)3 gp__(WT3) and gp__,(nTs) in formulas (22) (27) are discrete expressions of gp(t), gp} K1 (t), gp_[c(t)agp_íD(Ï) g(ï) agp+uß(t) and (gang / 1(1) as Shown in formulas (28) ' (34) respectively, and hm]; ) is discrete expression of h(t); _] KM) C(p)+J'D(p) C(p)-J'D(p) g p (t)=L {_++_} 1 _ . . Áo») [s+a<p) moon [s+a(p)+J(p)] (28) = K1 (meT") + 25 {C (p) 008% (p)t] D(p) sinl (p)t1} g" (+) + Elfi? (S ©) ++ + [s fifi) P if??? J P >] + [s fg? I? limßli) J p >]} (29) = [K1(p) +ÛK116Î + 25 {C(p) c08[(p)t] D(p)sin[(p)t]} 83330) = La { K11(p) + [C(p) +DC1+ J'D(p) + [C(p)+ÜC]_jD(p)} (s+ / 1( p)) [S+a(p)-J(p)1 [S+a(p)+J / 3(p)] (30) = KlumÎ") + 25 {[C(p) +Ü C]COS[(p)t] D(p) sin[(p)t]} gpü) =L_1{ +K11(p) + C[(S+Î;(j+l)(+îî+(+++î+ + (lîlîoî(j+)+î(+)+(+Ûî+} (s ANP)) I? J p 19 J p (31) = KaneW) + Zee {C(p)005[ß(p)t1 [D(p) +DD]sin[ß(p)t]} ngaU) = 51+ K1109) + C(p)+jD(iW) + C(p)jD(p_)} (s+ Á) [s+a(p)+DaJ(p)] [S+a(p)+Da+J(p)] (32) = 1<1(p)eÈ + M {C(p)cos[ß(p)t] D(p)sin[ß(p)t]} _ l K1(p) C(p)+jD(p) C(p)jD(p) g (+) + + {(s +& + {S+a(p)j[ß(p)+Dß]} + {s www) mm} (33) = K1 (meW + 23+ (ap) cos[(ß(p) + Amt] D(p)sin[(ß(p) + Am} g "(t) + wcs + VKM) + [sîîgpäíïäln + [s 5335132125 [MP) +DM] (34) = Kwam + 2e {C(p)cos[ß(p)11 D(p)sin[ß(p)t]} In the above formula, Ïs represents the sampling period, v is a constant greater than 1, and AK12K1(0) / 270, AK1 = K(0) / 770 AC = C(0) / 770, AD = D(0) / 770, Aa = 02(0) / 270 , Aß = ß(O) / 770 A / l= / l(O) / 770,770D 1; Step 682: If the error J ( p) £ J0 or the number of iterations p 2 pmax , the search process for the G(s) parameter ends; At the end of the search process, if e( p) 5 E0 , then Kl ( p),C( p),D( p),a( p), ß( p), / l( p) is the optimal parameter of G(s); Otherwise, set p = p + 1, and return to step 6S1 to continue; J 0 , pmax are the end conditions of iterative process set according to needs; J0 is calculated according to the following formula (35); J(p) = Z:,wnn) g.<n2;>r (35) Step 7: Update the parameter Kl (p), C(p), D(p), a(p),,B(p), / 1(p) of G(s) from the optimal parameter K, 2', T2 obtained in step 6, and then nd the time domain expression Ë (t) after h(t) eliminating oscillation, as follows: First, K, 2', T2 is updated by the following formulas (36) and (37): K (2's +1) T21Ä(P)S + 1][S + a(P) - jß(p)][s + a(P) + j(P)l = Km + C(p) + J'D(p) + C(p) J'D(p) (36) [s + %1(p)] [s + 0269) mm] [s + 0101) + Jam] %)}? = K1 <p)[s + ann) moans a(p) jß(p)] + mm + JD(p)][s + % + an)) + wrm] (37) + [C(p) J'D(p)][s + %(ppis + a(p) mm)] For convenience, the updated specic expressions of each parameter of K, 2', T2 are not listed. Then, from the updated K , 2',T2 , nd the time domain expression (7 (t) after h(t) eliminating oscillation: l?(t)L1[ K(ps+1) ]L*1[ Kr(s+%) ] _ _ _ _1 T2(W(p)s+1) Mp)(s+ / )(p)) K + 1 + 1 1 = L- { "[" / 2(p) Á / 2(p)1} T À + 1 3 (p)(s / )(p)) (38) 1 _ 1 = E1 + Kr +  an] , 1 Mp) Mp)(s + / Ä(p)) K l _ l _, = K+ 5(1) + _+(Á Á) eW TM(P) TMG?) Step 8: The waveform shaping algorithm of Ä (t) after eliminating the oscillation component is carried out according to the following steps (1) and (2): (l) First solve the z-transform Ü(z) of Ë (t) : 1 _ 1 _ Kr (Á / 1( p)) z H(z)=+T (39) Mp) Mp) , _ 6% (2) Then solve the shaping algorithm F (z) for shaping Ë (t) into y(t): _ 1 <p(1 1 ) F(z) = Y(Z) / H(z) = Z) / {£ Jràéï} (40) Mp) Mp) , % Y(z) is the zdomain expression of the formed waveform y(t); Waveform y(t) depends on the need, such as trapezoidal, Gaussian or quadratic edge attopped pulse; The above steps 1 8 optimize the identication of the oscillation components contained in the pulse, and give the zdomain shaping algorithm after deducting the oscillation components; The following steps 9 and 10 will give a timedomain recursive algorithm for conditioning and shaping the measured pulse x(t) containing oscillation components in specic applications; Taking secondary edge forming as an example, that is to say, x(t) is shaped into a quadratic edge attopped pulse; Step 9: For the actually measured pulse x(t) with oscillation link, the oscillation component is eliminated according to the following time-domain recursive algorithm: Let x(t) be expressed as X(s) in sdomain, and its discrete form is x(nTs ); Let the pulse of x(t) after eliminating the oscillation component be ïc (t) and the s-domain of ïc (t) be expressed as )? (s) , and X(s) is obtained by the following formula (41): Î (S) = X (S)[S + OKI?) - j(P))(S + Ot(P) + j(P)l (41) = X (S)[S2 + 20!(P)S + 0!(P)2 + (P)2l ïc (t) is obtained from formula (42): f(t) = %+2(P)%+[0£(P)2 +(P)ZlX(î) (42) The discrete form x(nTs ) of x(t) is as follows: x(nT.) x[(n 1)I;] _ x[(n 1)T.] xan 2)T.] mahTs + Ts (43) + we» + [a(pf + p(p)2]x(pT,) Step 10: For the actually measured pulse x(t) with oscillation link, a time-domain recursive algorithm is given to remove the oscillation component and shape it into a template pulse, which is carried out according to the following steps (1) - (3): (1) First, nd the ztransform X(z) of the pulse )?(nTS) after eliminating the oscillation component: )Î(z) = [X(Z) X(z)z_' X(z)z_l + X(Z)Z+2] / TS2 + 206(119)[X(Z)- X(Z)Z1] / T1 + [06(10)2 + (p)2]X(Z) (44) = X(z) {1 221 + z2 + 2a(p)Ts 202(p)7sz1 + [06(P)2 + ß (P)21TÏ} / T3 (2) Secondly, the zdomain algorithm for nding that x(nTg ) is shaped into a quadratic edge attopped pulse 37(nTS) : _ _ _ Kr<1 1 ) Y(z) = X(z)F(z) = X(z)Y(z) / {£ +M+} Mp) Mp) , _ 6% +1 +2 +1 2 2 2 2 =X(Z) Y(Z){1 22 + Z + 206(P)Ts1 206(Î9)TSZ + [a(P) + MI?) E} / T3 (45) K2" + K+(Á _ / l(p)) Z Mp) Mp) Z _ 6% 1 2 = X(z) Y(z)(m + alz Z+ aZZ ) b1 + b2 _ Z@ In formula (45), 17(2) is the zdomain expression of ÿ(nT,) , and the expressions of parameters ai, az, m, bi, bg and b3 involved are as follows: a1 = {2 mwn / Tí a, = 1 / 1;2 m = {1+ 206(P)T3 + [06(P)2 +(P)ZlT32} / T32 ,, = L T2400) (46) K l _ l , = "( Â) 2 TZÀÜ?) b3 = 6%(12) (3) Then, the recursive process of x(nTS) forming into quadratic edge at-topped pulse ÿ(nTS) is given: For convenience, 37027;) is replaced by ÿ(n) , x(nTs) is replaced by x(n); The template y(n) that gives the quadratic edge attopped pulse is shown in formula (47); n(n+1) / 2 0Sn <na y(n) = na (na + 1) / 2 na S n < nb (47) (na n+nb)(na n+nb +l) / 2 nb Sn Snc Where nb +na znc; Parameters na nl? nc are integers, which are obtained by conversion according to the nuclear pulse counting rate; n is also an integer; The zdomain expression of y(n) is shown in formula (48); 2 n +2 n +2 n +2 n +1 n +2 Z Z Z Z n Z n Z WZ) =33+33z2 (48) (zl) (Zl) (Zl) (Zl) (Zl) (Zl) The zdomain expression (Z) of ÿ(n) is shown in formula (49): _ m + a 21 + Cl ZZ ZZ _ Z+n+2 + Z=nh+2 _ Z=n,,+2 Il Z=nu+1 + " Z+nb+2 Y(Z)=X(Z)w[3_%] bi (z1) (z1) 1 22-11, (49) _ l 2 2 _ =nu+2 =nb+2 _ =nc+2 =na+l =nb+2 =X(Z)(Z b3)(m+alz +a2Z )[z Z +Z 3 Z _naz +nuZZ ] (b1+b,)zb1b3 (z 1) (z 1) Further solvrng is shown 1n formula (50). X (Z) @ _ (1 173Z+l )(m + alz++ + aziz) Z+l (1 + na )z++l + (1 + na)z++| [ ++ nüz+ + naz+""+2 X(z) + (5, + b,) -5,5,z-) 132" + 32-2 _z-3 _ [m + (a, b,m)z+l + (a2 173a])z+2 b3azz3] z1 = (1 + a )z'"'I + (1 + na)z'" = z'" " + naz'w + ",Z"Z (50) + (5, + b,) b,b,z") 132'1 + 32'2 _; Let A = (a1 b3m) , B = (a2 b3a1) , and V = [9,012 , and nally get the recurrence formula that x(n) (x(nTs ) ) is shaped into a quadratic edge at-topped pulse y(n) (y(nTS)) as follows: The numerator of formula (50) is simplied as: Numeratm :mz + + AZ + + BZ 3 Vz + m(l + m).-{+4 [A + (A 1111)]z"'n'2 [B + 5, (B A)] f + [V + (B + V)]z'«" V.z"*u'S n1naz" + [m + na(m A)]zl + [A + na(A B)]í"rl + [B + na(B + V)]z+""+'+ V(l + "« )z+++ mz " 1Az "2+Bz " ++Vz"4 (51) The denominator of formula (50) is simplied as: peu = (51 + b,) (35, + 35, + 5,15,)2" + (35, + 35, + 316115,).2'2 (5, + 52 + 31';,1b,)z'3 + (1)1155I (52) Finally, it is concluded that the recurrence formula of x(n) (x(nTs) ) forming into quadratic edge attopped pulse y(n) ( y(nTS)) is as follows: Y(n) = 3b1 _; 13:21): 5,53 y (" _ 1) _ 3b1 +51:i I: 3b1b3 y (n _ 2) + b1 +bb12++bjblb3 y (n _ 3) %y(n4)+b]:1bzx(n1)+x(n2)+x(n3)Q:b2x(n4) _ m(l+na)x(n_na _1)_ [A+nZ(Am)]x(n_na _2)_ [B+n,(BA)]x(n_na _3) bl +192 [91 +b2 bl +b2 (53) JFWXM +n, 4)b,+íb,x(n +n, +5) äx(n nb)+Wx(n +n, l)+Wx(n +n, +2) +Wxm nh 3)%x(n nh 4) m A B V x(n n, l)x(n n, 2)+x(n n, 3)+x(n n6 4) Through steps 1 - 10, the parameters of each link of pulse x(t) containing oscillation component are optimally obtained, and the time-domain recursive algorithm for suppressing (i.e. eliminating) oscillation component and waveform shaping is given. In the above-mentioned embodiments of the present invention, the component suppression and shaping methods of high-order, complex and singular pulse signals output by the detection system are described in detail, but it should be noted that the above is only one embodiment of the present invention. When other similar component suppression processing and shaping methods involve the use of the methods proposed in this paper, the present invention is still effective, and any modication, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included.< / na>
Claims
1. A method for conditioning and shaping pulse waveforms based on of component suppression, characterized by the component identification, component suppression and formation of higher-order, complex and singular pulses are realized by the following steps 1-10: step 1: as an example the pulse taking an oscillation component, inertial component and differential component contains, the function expression G(s) in the s-domain is given: G(S) = _ KJr 1) 1 ; the denominator contains the vo 1 and the verb b' 1n d' 1n and: (xls +1)(T2s2 +Tls + 1) ( ) gg 1 inertia connection: m, and the serial number of the connection is 1; 1 S 030111at1everb1nd1ng:2, and the serial number of the connection is 2; 1 Tzs + Ts +1 differential connection: TS+1, and the serial number of the connection is "3"; the above inertial connection, oscillation connection and differential connection are also called inertial component, oscillation component and differential component respectively component called; step 2: extract randomly a single pulse h(t) from the measured pulse, draw the trend line of the frequency response of Mr) and calculate the slope of the trend line and the coordinates of the intersections between the trend lines as follows: find the frequency domain expression of ha), as shown in formula (2): oo _ = H 1 H ' _ .. H ( ja)) = jo h(t)e_"'dt (2); let u ° nl (Ml, 7 _ Ina), H0 be a normal number; draw a 7 J! curve with 7 as the abscissa and as the ordinate, and draw a trendline on the 7 il curve with a slope of "HO (n integer), and the trendline is a straight line; this embodiment is a pulse waveform described by formula (1), and there are four trend lines; the coordinate of the intersection of trend line l and the ordinate is ( 70 #0 ), the intersection point serial number is "0" and the slope is 0; the coordinate of the intersection of trendline l and trendline 2 is (71'u), and the intersection number is "1"; the coordinate of the intersection of trendline 2 and trendline 3 is (72'al), and the intersection number is "2; the coordinate of the intersection of trendline 3 and trendline 4 is (73 #3), and the intersection number is "3"; the trendline is shown in Figure 1 of the description; step 3: construct the slope matrix and the connection matrix of the trend line and give the corresponding relationship between the slope matrix, connection matrix and the intersection coordinates in step 2, as follows: the possible slopes of trendline 2, Trendline 3 and trendline 4 form a slope matrix U as follows: Ui1 U1,2 U13 _Ho _3Ho 2HO UZ,1 U2,2 U273 H0 O 2H0 U U3,1 U32 U33 _ZHO _3Ho _2H 0 = = 3 _ U4,1 U4,2 U4,3 _2Ho _Ho 2H0 ( ) U51 U5,2 U5,3 H o 0 _2H 0 U6,1 U6,2 U63 H0 _H0 _2H0 from left to right, three elements in the same row in the matrix U correspond with the slopes of trendline 2, trendline 3 and trendline 4 respectively; by the By combining slope characteristics of three connecting trend lines, the corresponding connection matrix errkregen from the slope matrix U, W Wu W 1 2 3 W,, W WM 1 3 2 W W11W1,1W1,1z13 _ W1W1 W 2 3 1 (4); W11W1W113 1 2 W1 W2 W13 2 1 the element of W is composed of the serial number of the compound; description of the correspondence between U, W and the intersection: if we consider the first Taking row U as an example, _HO , _3H0 and 2H0 correspond respectively with the slopes of trendline 2, trendline 3, and trendline 4, and correspond to the connection numbers 1, 2 and 3 (i.e. inertial connection, oscillation connection and differential connection) in the first row of W, and also correspond to the intersections respectively(7 'u), ( 72 #2) and(7 / 3 #3); this correspondence intersection is summarized as shown in formula (5); UU <=> Wi © " (7 / 1' ai) (5); step 4: using the slope of the pulse trend line h( t) and the coordinates of the intersection point in step 3 become the initial value of the parameter of the function G(s) obtained as follows (l)(3): first let the slopes of trendline 2, trendline 3 and trend line 4 of h(t) correspond to the elements U , U and respectively U in the i-th row of the slope matrix U; according to the correspondence between U and . , , , , . . W1 W , W3 . W 1s there is also a one-to-one correspondence with the elements , '» and " 1n the i-th row of the connection matrix W; (1) the inertial connection parameters K and xl 1 are solved as follows: À = 7 (6): In the formula, "j" represents the e / column number of the element with a value of "1" among the three elements W , W 2 W 3 _ ) . . " and " ; from H0 lnK u0 : K = e° ° (7); (2) The solution of the differential . . 1 . The first order coupling parameter T is as follows: T = 7 (8); 1n the formula el "I" represents the column number of the element with the value "3" between the three elements, W, W and W; (3) the solution of the 1 ] oscillation connection parameters T2 and T1 are as follows: T2 = (Ty T1 = E = T2 = 7 e , e " (9); in the formula, "q" represents the column number of the element containing the value "2" between the three elements W , W and W ; K TÄ TZ and T obtained in this step is used as the initial values of the parameters of the function G(s); Step 6: Update the probability matrix component H in the function- HL information matrix W as follows: hxq(t+1) = (l 77)hxq (t) + ZAhíq (19); l=] where hxq(t) represents the value of information hxq after the tth iteration, l ] C ll ° 0<77<1; if h =q, then Ahq =1;if h =q,then Ah =O; Ciseconstant; xx J x xq Jl is the value of the objective function of Gl(z) ; step 5: take the parameter values K, TJ, T2, and T1 obtained in step 4 in the following formula G(s), decompose the oscillation link in conjugated complex roots and further decomposes G(s) to obtain the parameters K 1, C, D, 01 and ß to be obtained, and proceed as follows (1) and (2): (1) Ten first, the oscillation link is decomposed into conjugate complex roots: _ 1 = _ 1 10 ; where ' h et row 1 ed ee 1 01 and h et Tzs2 +T1s+l T2(s+ajß)(s+a+jß)( ) imaginary part [3 of the conjugated complex root are obtained according to formula (10); (2) further decomposes the function G(s) with oscillation link according to formula (11): G(s) = & : L+C+_«ÏD_+C__]P (Às+l)(T,s +T,s+1) (%) (cm) (Hmm) (11); parameters K1, C, D, are obtained according to the following formulas (12) - (14); K rs + 1 K, = (s + %)ij = % 81% W(T25 + TIS +1) _ 1 W (12); . . K TS + 1 GHD = (S + WW-ww = ml 2 HW (13); . . K TS + 1 C _ = 11 + + WWM-131.11 = i 2 ] PCm (14); after K CD aßJ, calculated according to steps 4 and 5 above, these if the initial values of the subsequent derivation of the formula are taken and make: K1(0) = Kl, C(O) = C, D(0) = D, a(0) = a, ß(0) = ß, MO) = Ä (15); Step 6: Find the optimal parameters of the function G(s); let the number iterations p are and the initial value p=0; K1(p), C(p),D(p),a(p),(p), )t(p) represents the last value of each parameter of G(s) after completion of the pth iteration, and Gp(s) represents the expression of G(s) after completion of the p- the iteration; perform an iterative update according to the following steps 6S 1 6S2: step 6S 1: the iterative update algorithm corresponding to the parameter K1(p),C(p),D(p),a(p),(p), Ä(p) is expressed in formula (16) (21): 1 1 KKP + 1) = K109) + AEK, (P)K1(P) 1 _ C(P +1) = C200) + AEc(1D)C(p) VP ( 6): Vp (17); 1 D(p +1) = DU?) + AED(119)D(19) _ vp (18), 1 a(p +1) = 0109) + 4E2(p)a(p) E (19); 1 309 + 1) = 23(19) + AE(p)(p)(20)g 1 Mp + 1) = Mp) + AEApwm ( AE in formulas (16) - (21) is represented in formulas (22) - (27): AEK,(1D) = 2101110171) _ g,1(T_1)l2 _ ZZOWWTS) - gp_íK, (WR)]2 (22); AECU?) = ZZOUIOWTS) _ g,1(WT1)l2 _ Zíolhm) _ g1__c(WT1)l2 (23); AED(19)= ZÎîûlhTs) _ g,(nT1)l2 _ ZÎZOMMTJ _ g,2;D(WT2)]2 (24); AE11(19)= ZÎZÛWWTS) _ g,,(ïlTJl2 _ Zíolhm) _ g1__11(WT_1)l2 (25); A15100): ZZOUIOWTS) _ g,("T.1)l2 _ Ei[hmm _ gpjßülTJ]2 (26); MM) = 22011111111) g,(nr1)r 2101111112.) g1_11(nT1)r (27); g(WT1)1g,_11(WT1)1g1_1C(WT1)gp_1D(Wî"1)1gp_(Wîl) gp_m11(WT1) and gp(WTJ in formulas (22) - (27) are discrete expressions of gp(t) , g pj K. (t) , g LMU) , gp_íDû) gh 2 (t) gp_íû) and gp_Mû) as shown in formulas (28) - (34), and h(t) is a discrete expression of _1 K1(p) C (p) + jD(p) C (p) jD(p) g,1(t)=L {+.+.} (s + %) [S + 06(1)) - Jß(p)1 [S + 01019) + Jß(p)] (28) = K1 (meÎ + 25 {C (P) COSLÛ (mt ] _ DU?) sin[ß(p)t]} _1 K1(p)+UK1 C(p)+jD(p) C(p)jD(p) DK t = L _ _. _. g ( ) {(s + %) + [s + am 1.5(P)l+[s + 01119) + mm} (2 = [K1(10)+UK116É + 25 {C (p) COS[ß(p)f ] _ DU?) sin[ß(p)t]} 9) 1 1 + _ D (s AU?) p J pp J p (30) = K1(p)eÎ + % {[C(p) +DC]cos[(p)t] D(p) sin[ß(p)r]} 1 1 . _ . D (S AU») PJP p J p (3 = K209)? + zé {C(p)cos[(p)t] [D(p) +E1D1sin[ß(p)t]} 1) g (1): . { K2102) + C(p)+J'D(JW) + C(p)jD(p_) , ( / 1(p)) [s+a(p)+DaJ <p)1 [s+a(p)+Da+J(p)1 (3 = ImmeÎ + MW {C(p)cos[(p)1] D(p)s1n[ß(p>r]} 2) _1 Km C(p)+JD(p) cm)woa) _ = L _ _ _ g (+) {(s + %) + {s + au») j[ß(p) +DM} + {s + 0:02) + J'[(p) mm} (3 = km? + MW {C(p)cos[(ß(p) + Amt] D(p)sin[((p) + Amri} 3) _1 K1(p) C(19) + J'D(p) C (p) - jD(p) g 2(t)=L {l_+f+_.} (s+ Â) [s+a <p) moa) [Naam+ / m)] = K100)?w + 2e {C(p)cos[ß(p)t] D(p)s1n[ß(p)1]} (34); in de bovenstaande formulae stelt Ts de bemonsteringsperiode voor, v is een constant groter dan 1, AKl = K1(O) / 770 en AK, = K, (O) / 770, AC = C(0) / 770 AD = D(0) / 770 Aa = 0((0) / 770 , A = (0) / 770 A / l = / 1(0) / 770, 770 D 1; step 6S2: if the error J(p) £ JO or the number of iterations p is Z p max, it ends search process for the parameter G(s); at the end of the search process, if e( p) £ E0 , then K, (p), C(p),D(p),a(p),(p), Mp) is the optimal parameter of G(s); otherwise, set p = p +1 and return to step 681 to continue; JO , pmax are the end conditions of the iterative process, determined based on the needs; JO is calculated according to the following formula (35); J(p) = Zioihm'.) g,,(nmr (35); Step 7: Update the parameter K, (p), C(p), D(p), a(p), (p), Mp) of G(s) from the optimal parameter G(s) obtained in step 6, and then find the time domain expression 17(t) after h(t) , where oscillation is eliminated as follows: first K r, T2 is updated by the following formulas (36) and (37): K (z's +1) 13140108 + 1][S + (p) jß_(}?)][S + 06(1?) + jß(n)] (36)- = K1(p) + C(p) + JD(p) + C(p) _ JD(p) [s + yam] [s + a(p) Jam] [s + ann) + moan %)}? = K1(p)[s + a(p) Jmpms + 0103) + mom +[C(p)+JD(p)1[s+y,(p)1[s+a(p)+J(p)1 (37); + [C(p) JD(p)1[s + yup) + a mom] For convenience, the updated specific expressions of each parameter of K + T2 not mentioned; then from the updated KT T2 , Find the time-domain expression ++ after h(t) by eliminating oscillation: M) _ [;[ K(TS+l) , _ [+ Kf(s+%) ] _ _ _ 1 T2(W(p)s+1) 122 <p)<s+ ,(,)) K + 1 + 1 1 Á Ááp} T+S / Â(p) : L*1{_ T & + y 2 (PXS Â(p)) (3 8); 1 _ 1 =L=l{ KT + [(+-[A APPEES} 1 Mp) Mp) <s + ,(p)) KT ( 1 y ) l = KT 501) + Á Ä(p) eMp) EMP) T1Ä(p) Step 8: The algorithm for forming the waveform of Ê(t) is, after elimination of the oscillation component, performed according to the following steps (1) and (2): (1) first solve the z-transform Fl(z) of Z(t): 1 _ 1 _ KT K+(Á AU)) Z . H(Z)=+r (39), Mp) Mp) , _ 6% (2) Then solve the shaping algorithm F(z) to transform A to y(t): _ Kr<1 1 ) F(z) = Y(z) / H(z) = Hz) / {ï + @+} (40); Mp) Mp) , _ 6% Y(z) is the z-domain expression of the formed waveform y(t); waveform y(t) is depending on the need, such as trapezoidal, Gaussian or quadratic EdgeFlat pulse; the above steps 18 optimize the identification of the oscillation components in the pulse and give the z-domainShaping algorithm after subtraction of the oscillation components; the following steps 9 and 10 give a recursive time-domain algorithm for conditioning and shaping the measured pulse x(t) which contains oscillation components in specific applications; where secondary edge formation is taken as an example, that is, x(t) is formed into a squared edge-plane pulse; step 9: for the actually measured pulse x(t) with oscillation connection, the oscillation component is eliminated according to the following recursive algorithm in time domain: let x(t) be expressed as X(s) in the s-domain, and the discrete form is x(nîl) ; let the pulse of x(t) after elimination of the oscillation component be x(t), and the s- domain of ;?(t) is expressed as )?(t), and X(s) is obtained by the next formula (41): Î(S) = X(S)[S + (p) _ jß(p))(S + (p) + jß(l9)] (41)_ = X(S)[S2 + 206(19)S + 05(P)2 + ß(p)2] )? (t) is obtained from formula (42): Î(S) = X(S)[S + 05(10) jß(P))(S + OK!?) + jß(p)] (41)' = X (S)[S2 + 206(P)S + (p)2 + ß(P)+] )? (t) is obtained from formula (42): _ d2x t dx t x(t) = # + mooj +1a <p)2 + (p)2]x(t) <42); dt dt the discrete form )?(nTS ) of X(t) is as follows: X(WT1) _ X[(W _ 1)T.1] _ XK" _ 1)T_1] _ mm:TS TS T1 (43); x nT x n1 T + zom( ,) T ) ,] + [)2 + (p)21x(nT,) step 10: for the actually measured pulse x(t) with oscillation connection, a recursive algorithm in the time domain is given to determine the oscillation component remove and convert it into a single-wave pulse, which is performed according to the following steps (1) (3): (1) first find the ztransform )?(z) of the pulse )?(nTS) after eliminating the oscillation component: K(z) = [X(Z) X(z)z+1 X(z)z+l + X(z)z+2] / T+2 + 206(10)[X(Z) _ = X(z){1 22*1 + 52 + 2a(p)T+ 2a(p)T_îz+1 + 101019)2 + ß(iv)2]T12} / T12 (3) Second, the z-domain algorithm for finding that )?(nTS) has the form of a quadratic edge with a flat top, 37(nTS) : my 1 ) KT T Ä Z Y(z) = X(z)F(z) = X(z)Y(z) / { + Jn} T2Ä(p) TZÄ'Ü?) z_e+Á(p) Y(Z) {1 _ 2271+ Z+2 + 206(1'7)T1 _ 206(1D)T1Z+1 + WU?)2 + 3(1D)2]T12} / T12 = X (Z) [(l1 KT + T(ÁÁUÙ) Z Mp) Mp) , _ ,,,% 1 2 = X(z) Y(z)(m + alz + azz ) b, + b, L zQ (45) In formula (45), 17(2) is the z-domain expression of y(nTs ), and the involved expressions of parameters a], 512, m, bl, [)2 and [)3 are as follows: a, =12 mmm / Tí a, = 1 / 1;2 m = {1+ 20!(119)T1 + [05(19)2 + 23(19)2]7}2} / T22 ,, = £ T240?) (46); K l _ l ,, = Á ßen) 2 TMP) b3 = 5% (4) Next, the recursive process of x(nTs) which forms into a square-wave, flat-topped pulse 37017;) given: For convenience, y(nTS) is replaced by 3701) , x(nTs) is replaced by x(n) ; the template y(n) containing the flat-topped quadratic edge yields, is shown in formula (47); n(n+l) / 2 0£n <na y(n) = na(na + l) / 2 na £ n < n,, (47); (na n+nb)(n n+n +1) / 2 nb S n Snc where n,, +na = nc ; parameters are integers na nb, obtained are converted according to the core pulse count rate; n is also an integer; the z-domain expression of y(n) is shown in formula (48); Z2 Zna+2 Znb+2 Znc+2 n Zn,,+1 n Znb+2 Y z =__+____ 48; () (Zl)3 (Zl)3 (Zl)3 (Zl)3 (Zl)2 (Z_1)2( ) the z-domain expression 17(2) of ÿ(n) is shown in formula (49): _ m + (ZZ=1 + a Z=2 ZZ _ Zn+2 + Zn+2 _ Zn+2 Zn+1 + n Zn,,+2 Y(2)=X(2)( 1 ; )[_,, a +, 1 [914.1327 (2) (Z_) Z b3 Z bm + a [1 + a 2+2 22 z+""+2 + z+"+2 z+"+2 n Z+"+1 + n z+""+2 :X(Z)( 3)( 1 2 ) [ 3 _ a a2 ] (b, + b,)zb,!)3 (z 1) (z 1) (49); further solving for % is shown in formula (50): Z Æ _ (l b3z++ )(m + 51.24 + aziz) z+l (1 + " )z+"+1 + (1 + na)z+"+1 [""+ naz+"" + Haz""'2 X(z) + (b, +b,)b,b,z_) 1-35] +35Z z+3 _ [m + (a, b3m)z+l + (a2 b,a,)z+2 b3azz+3] zl (l + na )z'"'l + (1 + na)z+"+l z+"+ln,,z+" + HHz"2 + (b, +b2) b,b,z'1) 132-1 + 3z-2 _ 2-3 (50; let A = (a, b3m), B = (a2 b3a,) , and V = 193g, , using the stress slot of The recursive formula die x(n) (x(nTS) ) of a given quadratic function is then set to The borrower y(n) ( y(nTs) also says: _ 3b1 + 3b2 + b,b3 3b1 + 3b2 + 3b,b3 b, + b, + 3b,b3 =_ 1_ 2 +_ 3 Y(n) bl + b, y( ) b) + b, y(n ) b, + b, y(n ) %y(n4)+Lx(n1)+LanznixmaLWo b, +b2 b, +b2 b, +b2 b, +b2 b, +b2 FATHER m(++n")x(nna1)[ +n( m)+x(nna2)[ +n( )]x(nna3) b, +b2 b, +b2 b, +b2 VBV b1 + b2 b, + b2 AAAB _%x(_nb)+x(_nb_1)+x(_nb_2) b, +b2 bl +b2 bl +b2 BBV +x(n_nh _3)_Mx(n_nh _4) à+æ @+æ äx(n nc l)Éx(n _"1 2)+b1+3b2x(n nc 3)+Éx(n nc 4) (51) The parameters of each connection of pulse x(t) are determined via steps 1 to 10 which contains an oscillation component, is optimally obtained and the recursive time-domain algorithm for suppressing (i.e., eliminating) the oscillation component and the waveform shaping are given. 1 / 2 FIG.1< / na> < / s>