RU2050585C1 - Random process generator - Google Patents

Abstract

FIELD: computer engineering. SUBSTANCE: device has generator of random numbers with uniform distribution, unit of NOT gates, functional converter, multiplexer, adder and multiplier. Device provides possibility to control value and sign of forth-order cumulant of uniform probability distribution of generated random process. EFFECT: increased functional capabilities. 1 dwg

Description

 The invention relates to computer technology and can be used to generate random processes with predetermined values of cumulants of the first, second and third orders and an adjustable value of a cumulant of fourth order for an arbitrarily set form of the autocorrelation function of the generated process in devices for simulating and processing signals in radio paths, in identifying linear and nonlinear systems.

 A known random process generator containing a reversible counter, the direct outputs of the discharges of which are connected to a group of information inputs of a digital-analog converter and the inputs of the first and second decoders, respectively, the outputs of which are connected respectively to the first and second inputs of the OR element, the output of which is connected to the counting input of the trigger, a pulse generator whose output is connected to the first inputs of the first and second elements AND, the outputs of which are connected respectively to the subtracting and summing inputs a reversible counter, the output of the digital-to-analog converter is the generator output, a Poisson pulse stream generator and a random pulse stream intensity code generator comprising a pulse generator, a trigger, first and second AND elements, a delay element, a gated decoder, first and second AND-OR elements, the outputs of which connected respectively to the unit and zero inputs of the trigger, the direct and inverse outputs of which are connected to the second inputs, respectively, of the first and second elements And, the output The generator of the Poisson pulse stream is connected to the first inputs of the first and second elements AND of the converter; the code is the intensity of a random pulse stream, the second inputs of which are connected respectively to the direct and inverse outputs of the trigger, the counting input of which is connected to the output of the pulse generator of the converter; code is the intensity of the random pulse stream; the output of the first element And is connected to the counter input of the counter, the output of the second element And converter code the intensity of the random pulse flow directly It is connected directly to the gating gate of the gated decoder and through the delay element to the “Reset” input of the counter, the discharge outputs of which are connected to the inputs of the corresponding bits of the gated decoder, the outputs of which are connected to the first groups of inputs of the first and second AND-OR elements, respectively, the direct outputs of the bits of the reversible counter connected to the second group of inputs of the first AND-OR element, respectively, the inverse outputs of the bits of the reversible counter are connected to the second group of inputs of the second element and AND-OR, respectively.

 The generator generates a discrete diffusion random process with a normal probability density of instantaneous values due to the negative feedback feedback adjustable between the current process values and the value of random increments generated by converting the initial Poisson stream of pulses. The degree of approximation to the normal law of the process being formed depends on the magnitude of the intensity of the Poisson stream, the value of the clock frequency and the capacity of the used reverse counter. The disadvantage of the generator is the lack of operational control over the value of the fourth-order cumulant of the one-dimensional probability distribution of the process being formed, which does not allow expanding the generator’s functionality and using it to generate random processes with an adjustable degree of deviation of the one-dimensional distribution function from the Gaussian due to a change in the value and sign of the fourth-order cumulant at constant values of all lower order cumulants.

 In addition, it is impossible to generate a random process with an arbitrary type of autocorrelation function in the generator.

 The closest in technical essence to the present invention is a random process generator containing a clock pulse generator, a reversible counter, subtracting and summing the inputs of which are connected respectively to the outputs of the first and second elements And, and the discharge output is the output of the generator, a sensor of independent uniformly distributed random numbers, a delay element, a comparison circuit, the first input of which is connected to the first output of the random number sensor, the second input of the comparison circuit is connected to the output a reverse counter, the output “Less” of the comparison circuit is connected to the first input of the first And element, and the output is “greater” to the first input of the second And element, the second inputs of which are connected to the delay element, the input of which is connected to the output of the clock generator connected to the trigger input of the random number sensor, a register, an additional comparison circuit, the first input of which is connected to the second output of the sensor of independent uniformly distributed random numbers, the second input with the information output of the register, whose input is the input of the job correlation interval, the output is "Less" additional comparison circuit is connected to the third inputs of the first and second elements I.

 The generator uses a one-step method for generating a normal random process with a given value of the correlation interval, in which each next count is obtained after comparing two random uniformly distributed numbers with the previous process value and with a constant that determines the value of the correlation interval.

Lack generator ^_ inability to quickly adjust the degree of deviation of the one-dimensional distribution of the generated Gaussian process by controlling the value of the fourth order cumulant at constant values of all lower-order cumulants.

 This narrows the generator’s functionality, not allowing expanding the class of generated processes, which is necessary, in particular, when testing radio systems for non-Gaussian signals, as well as simulating the evolution of a process type from harmonic to pulsed or its non-stationarity in the fourth-order cumulant.

 In addition, the generator forms a process with a limited class of autocorrelation functions: only of an exponential type, although with an operatively changing value of the correlation interval.

The purpose of the invention ^_ expansion of functional capabilities of the generator by controlling the value of the fourth-order cumulant of the probability distribution and a view of the autocorrelation function of a random process generated at constant values of the cumulants of the lowest order.

 This is achieved by the fact that in a random process generator containing a sensor of uniformly distributed random numbers, a first and second comparison circuit, a register, a clock pulse generator, the output of which is connected to a triggering input of a uniformly distributed random number sensor, the output of which is connected to the first input of the first comparison circuit , a block of elements NOT, a functional converter, a multiplexer, an adder, a multiplier are introduced, and the output of the sensor of uniformly distributed random numbers is connected to the first input of the second the second comparison circuit, the second input of which is connected to the output of the block of elements NOT, the input of which is combined with the input of the functional converter, the second input of the first comparison circuit and is the input of setting the cumulant value of the fourth order of the generator, the outputs of the first and second comparison circuits are connected respectively to the first and second control the inputs of the multiplexer, the first, second and third information inputs of which are inputs of the job modes of the generator, the output of the multiplexer is connected to the information input register a, the outputs of which are connected to the corresponding control inputs of the type of operation of the adder components, the synchronization input of which is connected to the synchronization inputs of the register and the multiplier and connected to the output of the clock generator, the adder output is connected to the input of the first multiplier of the multiplier, the information inputs of the adder components are respectively the values generator weights, the output of the functional converter is connected to the input of the second multiplier of the multiplier, the output of which I I wish to set up the output of the generator.

The introduction of new elements and the corresponding functional relationships allows us to expand the generator’s functionality due to the operational control of the fourth-order cumulant size and sign of the one-dimensional probability distribution of the generated random process. At the same time, constant values of a lower order cumulant are ensured in the entire range of variation of the fourth-order cumulant value:
zero value of the cumulant of the third order;
the unit value of the variance for an arbitrary form of the formed autocorrelation function of the process specified by the array of weight coefficients of the impulse response of the filter;
zero expectation;
In addition, the accuracy of the generation of a Gaussian random process is improved by providing, with an appropriate control signal, a fourth-order cumulant value, zero excess coefficient and fourth-order cumulative functions for any digit capacity of the generated discrete samples of the process. The low accuracy of the formation of a Gaussian random process in the known generator is due to the fact that the generated process has a one-dimensional distribution law, which only asymptotically approaches the Gaussian one with increasing bit depth of the reverse counter. Although the distribution law of the process being formed has symmetry, as a result of which the asymmetry coefficient and third-order cumulant functions are equal to zero, but with any increase in the capacity of the reversible counter, the excess coefficient and fourth-order cumulant functions are nonzero and only tend to it asymptotically. This limits the scope of use of the generator, not allowing, for example, to be used to identify systems with quadratic nonlinearity, as well as as a model noise generator.

 To form a random process, a nonlinear transformation controlled by an external signal is used to convert a stationary sequence of independent random numbers evenly distributed in the range from -1 to +1 to a sequence of independent ternary numbers (+1.0, -1) with zero asymmetry coefficient, mathematical expectation and a variable cumulant value fourth order and filtering the resulting ternary sequence with a filter with a finite impulse response (FIR filter).

 Filtering is carried out by controlling, in the process of summing all the weights of the impulse response of the filter, the sign of each weights using the corresponding members of a moving sample of finite sizes formed from the ternary sequence.

 The number of discrete levels of an intermediate random sequence formed in the generator equal to three is the minimum necessary so that a random sequence with an adjustable value of the fourth-order cumulant can be obtained while maintaining the symmetry of the probability distribution and zero mathematical expectation. Due to this, the generator has a simple structure. When filtering, there is no need to store, shift and multiply multi-digit numbers, which also increases the speed of the generator.

 The probabilities of each of the three discrete levels of the generated ternary sequence are varied when the fourth-order cumulant value is controlled by coordinated changes in the thresholds of the comparison circuits performing nonlinear transformation of the initial stationary sequence of independent uniformly distributed random numbers from one control signal of the signal for setting the fourth-order cumulant value of the generator.

 The resulting stationary sequence of independent identically distributed random ternary numbers is a non-Gaussian discrete digital noise. Filtering this sequence will lead to the normalization of this sequence and a decrease in the coefficient of excess of the process at the output of the digital filter.

b $\genfrac{}{}{0ex}{}{\text{4}}{\text{j}}$ * X

; F₄=

* F

где: j

размер массива весовых коэффициентов КИХ-фильтра;
b_j весовые коэффициенты массива импульсной характеристики фильтра, заданные из условия получения требуемой автокорреляционной функции процесса на выходе фильтра генератора;
Х₄, F₄ кумулянт четвертого порядка и коэффициент эксцесса троичной последовательности на входе фильтра.Using the known relations, one can obtain the following dependences of the fourth-order cumulant X ₄ and the excess coefficient F _{4 of a} random sequence at the output of the FIR filter on the filter characteristics and parameters of the random ternary sequence at its input:
X ₄ =

b $\genfrac{}{}{0ex}{}{\text{4}}{\text{j}}$ * X

; F ₄ =

* F

where: j

size of the array of FIR filter weighting coefficients;
b _j weight coefficients of the array of impulse response of the filter, specified from the conditions for obtaining the required autocorrelation function of the process at the output of the generator filter;
X ₄ , F _{4 is a} fourth-order cumulant and the kurtosis coefficient of the ternary sequence at the input of the filter.

b $\genfrac{}{}{0ex}{}{\text{2}}{\text{j}}$ 1 дисперсия процесса на выходе фильтра не зависит от характеристик фильтра и определяется только дисперсией процесса на входе. Для стабилизации дисперсии на единичном уровне (D 1) необходимо использовать корректирующую функцию дисперсии
f(V) (1 V)^-1/2 где V величина сигнала управления значением кумулянта четвертого порядка генератора (0 ≅ V ≅ 1), на значение которой необходимо умножать выходные отсчеты фильтра. Зависимость значения кумулянта четвертого порядка Х₄ на выходе генератора от величины сигнала управления значением кумулянта четвертого порядка определяется из выражения:
X₄= F₄=

b $\genfrac{}{}{0ex}{}{\text{4}}{\text{j}}$ *

Фильтрация с помощью КИХ-фильтра случайной троичной последовательности является линейной операцией, не вносящей никаких дополнительных статистических связей в выходной процесс. Так как числа формируемой троичной последовательности являются независимыми и между ними отсутствуют статистические связи любого порядка, то при нулевых значениях кумулянтов третьего и четвертого порядков троичной последовательности на входе фильтра будут равны нулю и кумулянты, и кумулянтные функции третьего и четвертого порядков на выходе фильтра. Это позволяет получить лучшее приближение к гауссовскому случайному процессу по сравнению с известным генератором, у которого кумулянт четвертого порядка не равен нулю.When the relation

b $\genfrac{}{}{0ex}{}{\text{2}}{\text{<figure-callout id="1" label="j" filenames="00000016.png" state="{{state}}">j</figure-callout>}}$ 1, the dispersion of the process at the filter output does not depend on the characteristics of the filter and is determined only by the dispersion of the process at the input. To stabilize the dispersion at a unit level (D 1), it is necessary to use the correction function of the dispersion
f (V) (1 V) ^-1/2 where V is the magnitude of the control signal for the fourth-order cumulant value of the generator (0 ≅ V ≅ 1), by the value of which it is necessary to multiply the filter output samples. The dependence of the value of the fourth-order cumulant X ₄ at the output of the generator on the value of the control signal of the value of the fourth-order cumulant is determined from the expression:
X ₄ = F ₄ =

b $\genfrac{}{}{0ex}{}{\text{4}}{\text{j}}$ *

Filtering with the FIR filter of a random ternary sequence is a linear operation that does not introduce any additional statistical relationships in the output process. Since the numbers of the generated ternary sequence are independent and there are no statistical relationships between them of any order, at zero values of the cumulants of the third and fourth orders of the ternary sequence at the input of the filter, both the cumulants and cumulant functions of the third and fourth orders at the filter output will be equal to zero. This makes it possible to obtain a better approximation to a Gaussian random process in comparison with the well-known generator, in which the fourth-order cumulant is not equal to zero.

 With an increase in the number of weight coefficients of the impulse response of the FIR filter, which is equivalent to an increase in the capacity of the reverse counter in the known generator, a greater degree of normalization of the random process will take place, which will allow to obtain lower values of cumulative coefficients and normalized cumulative functions of higher orders.

The drawing shows a structural diagram of a random process generator, where
1 sensor of evenly distributed random numbers;
2 block of elements NOT;
3 clock generator;
4,5 first and second comparison schemes;
6 multiplexer;
7 register;
8 functional converter;
9 adder;
10 multiplier;
A ^-1 , A ^o , A ¹ codes of control signals for the type of operations of the adder;
b ₁ -b _N weighting factors of the impulse response of the filter of the generator;
V control signal of the cumulant value of the fourth order generator;
f (V) is the correction function of the variance of the formed process.

 The generator contains a sensor of uniformly distributed random numbers 1, made, for example, on the basis of a digital generator of a pseudo-random sequence (M sequence). The trigger input of the sensor 1 is connected to the output of the clock generator 3, and the output of the random number generator 1 is connected to the first inputs of the first and second comparison circuits 4 and 5. The clock generator 3 is a standard digital clock generator, made, for example, on an integrated system clock generator type KM 1804 GG1. Comparison schemes 4 and 5 are made on typical integrated digital circuits for comparing multi-digit numbers. The outputs of the first and second comparison circuits 4 and 5 are connected respectively to the first and second control inputs of multiplexer 6, the first, second and third information inputs of which are inputs of setting values of control signals by the type of operation of the adder 9, and the output is connected to the information input of register 7. Multiplexer 6 is a switch of three two-digit digital highways into one two-digit digital highway. It can be performed on dual standard single-digit digital selectors multiplexers of the 155, 530, 531 series, commuting at least three one-bit lines into one, working in parallel and synchronously and having common control inputs.

 The outputs of the register 7 are connected to the corresponding control inputs of the type of operations of the adders 9, the synchronization input of which is combined with the synchronization inputs of the register 7, the multiplier 10 and connected to the output of the clock 3. Register 7 is a sequential shift register of two-digit numbers by N positions and has N parallel two-bit outputs. It can be performed on two standard single-bit universal shift registers by N positions with parallel outputs, common synchronization inputs and synchronizing with clock pulses from a clock generator 3, recording the bits of two-bit numbers in parallel code arriving at their serial inputs and shifting them along the registers.

 The output of the adder 9 is connected to the input of the first multiplier of the multiplier 10, and its information inputs of the terms are inputs for setting the values of the weight coefficients of the impulse response of the filter of the generator. The adder 9 can be performed in order to obtain maximum speed according to the pyramidal parallel adder using standard four-digit four-input, incremented by the digitizer sections of the adder (a subtractor type КР 1802 ИМ1, having inputs for controlling the type of operation of each of the terms coming to their information inputs using the corresponding control digital signals, which allows addition) subtraction or exclusion of the term from the summed.

 The scheme of the summation block of four multidigit numbers, performed on the KR 1802 IM1 microcircuits, is advisable to use as a more enlarged element when constructing a parallel adder for N multidigit numbers. The output of the functional converter 8 is connected to the input of the second factor multiplier 10, and the input is combined with the input of the block of elements NOT 2, with the second input of the first comparison circuit 4 and is the input for setting the value of the fourth-order cumulant of the generator. The output of the block of elements NOT 2 is connected to the second input of the second comparison circuit 5. The output of the multiplier 10 is the output of the generator. The multiplier 10 is a parallel multiplier of two multi-digit numbers and can be performed, for example, on standard parallel multipliers like KM 1802, BP4, KM 1802 BP5. The block of elements NOT 2 is a standard device for inverting the sign of a multi-bit binary number, presented in parallel code. Functional converter 8 can be made in the form of programmable read-only static storage device about arbitrary parallel selection of information based on standard electrically programmable read-only memory devices of series 556, 573.

 The generator operates as follows.

The signals from the clock generator 3, arriving at the triggering input of the sensor of randomly distributed numbers 1, generate another random number, evenly distributed in the range from -1 to 1, arriving at the first inputs of the first and second comparison circuits 4 and 5. Simultaneously with the start random number sensor 1 value of the two-digit code of the control signal of the type of operations A ^{1 of the} adder components (i -1,0,1) obtained in the previous clock of the generator, from the output of the multiplexer 6 is written in sequential inf the input to the first cell of register 7. In this case, a shift along the register of all signals A ¹ recorded in it in previous clock cycles occurs by one position. Also, simultaneously with the start of the random number sensor 1, the amount generated in the previous clock cycle of the generator is overwritten from the output of the adder 9 into the input information buffer register of the first multiplier of the multiplier 10, as well as the value of the correction function of the variance f (V) is recorded in the input register of the second multiplier of the multiplier 10 and issuing from the output of the multiplier 10 formed by the generator of the next sample of a discrete random process.

The second inputs of the comparison circuits 4 and 5 receive codes of numbers characterizing the thresholds V ₁ and V ₂ , respectively, which are linear functions of the control signal code V with the value of the fourth-order cumulant. In this case, the value of the operating threshold V ₂ -V of the comparison circuit 5 is formed by a block of elements NOT 2. Depending on the results of comparing the next random number with thresholds V ₁ and V _{2, the} signals from the outputs of the comparison circuits 4 and 5, controlling the operation of multiplexer 6, are connected to it the output is one of three control signals of the type of operation of the terms A ⁱ , (i -1,0,1) of the adder 9.

Записываемые в каждом такте работы с выхода мультиплексора 6 в регистр 7 числа Аⁱ образуют случайную стационарную последовательность независимых чисел, эквивалентную последовательности троичных чисел Y_к с вероятностями появления значений +1,0,-1, определяемыми регулируемыми порогами срабатывания V₁ и V₂ схем сравнения 4 и 5, и имеющую заданные значения кумулянтов до четвертого порядка включительно. Выбираемый из формируемой последовательности чисел А¹ с помощью скользящего окна длинной N позиций, реализуемого регистром 7, массив чиселAⁱ}_N управляет работой сумматора 9. После записи очередного числа А¹ в регистр 7 и сдвига предыдущих чисел на одну позицию по сигналу от генератора тактовых импульсов 3 происходит запись массива значений весовых коэффициентов импульсной характеристики фильтраb_j}_N (j 1,N) во входные информационные регистры слагаемых сумматора 9. Текущий массив чисел A¹} _N, поступающий с выходов регистра 7 на соответствующие входы управления видом операций слагаемых сумматора 9, задает знак операции каждого слагаемого b_j в образуемой общей сумме при значениях чисел А¹, соответствующих +1, -1, либо исключает слагаемое из общей суммы при A¹ соответствующем нулю. Преобразованный с помощью управляющего словаA¹}_N массив весовых коэффициентов b_j}_N суммируется и поступает в выходной регистр сумматора 9. Описываемая совместная работа регистра 7 и сумматора 9 эквивалентна работе линейного КИХ-фильтра, оператор преобразования которого можно записать в виде скользящего суммирования троичных чисел Y_k c весами, определяемыми массивом значений весовых коэффициентовb_j)_N импульсной характеристики фильтра:
W(n)

b_j * Y(n-j) при условии

b $\genfrac{}{}{0ex}{}{\text{2}}{\text{j}}$ 1
Одновременно с началом работы сумматора 9 в умножителе 10 происходит вычисление произведения ранее записанных в его входных регистрах сомножителей: значения суммы с выхода сумматора 9 и значения корректирующей функции дисперсии
f(V) (1 V)^-1/2,
выработанное функциональным преобразователем 8, и запись результата произведения в выходной регистр умножителя 10. В следующем такте работа генератора повторяется. Формирующаяся на выходе генератора последовательность чисел образует стационарный случайный процесс с нулевым математическим ожиданием, нулевым коэффициентом асимметрии, единичной дисперсией, значением кумулянта четвертого порядка Х_k, измеряемого внешним сигналом V в соответствии с выражением
X₄=

b $\genfrac{}{}{0ex}{}{\text{4}}{\text{j}}$ *

и автокорреляционной функцией, определяемой заданным массивом весовых коэффициентов импульсной характеристики фильтраb_j}_N.The information content of each code of the number А ¹ may correspond when this number subsequently arrives at any of the inputs of controlling the type of operations of the summands of the adder 9 or the addition command, or subtract, or to exclude the corresponding term coming to the input of the adder 9 in this clock cycle work of the generator from among the summed The nonlinear operation implemented by comparison schemes 4 and 5 by multiplexer 6 over a sequence of independent uniformly distributed numbers Z _k from the output of the random number sensor 1 is equivalent to the operation described by the relation
Y _k =

The work A recorded in each clock cycle from the output of multiplexer 6 to register 7 of the number A ⁱ forms a random stationary sequence of independent numbers equivalent to a sequence of ternary numbers Y _k with the probabilities of occurrence of values + 1.0, -1, determined by adjustable operation thresholds V ₁ and V ₂ circuits comparisons 4 and 5, and having preset values of cumulants up to fourth order inclusive. Selected from the generated sequence of numbers A ¹ using a sliding window of long N positions, implemented by register 7, the array of numbers A ⁱ } _N controls the operation of adder 9. After writing the next number A ¹ to register 7 and shifting the previous numbers by one position according to the signal from the clock of pulses 3, an array of values of the weight coefficients of the impulse response of the filter b _j } _N (j 1, N) is recorded in the input information registers of the terms of the adder 9. The current array of numbers A ¹ } _N coming from the outputs of register 7 to the corresponding the inputs for controlling the type of operations of the terms of the adder 9, sets the operation sign of each term b _j in the generated total for values of the numbers A ¹ corresponding to +1, -1, or excludes the term from the total for A ¹ corresponding to zero. The array of weight coefficients b _j } _N transformed using the control word A ¹ } _{N is} summed up and goes to the output register of adder 9. The described joint operation of register 7 and adder 9 is equivalent to the operation of a linear FIR filter, the conversion operator of which can be written as a moving summation of ternary numbers Y _k with weights determined by an array of values of weight coefficients b _j ) _N impulse response of the filter:
W (n)

b _j * Y (nj) provided

b $\genfrac{}{}{0ex}{}{\text{2}}{\text{<figure-callout id="1" label="j" filenames="00000016.png" state="{{state}}">j</figure-callout>}}$ 1
Simultaneously with the beginning of the operation of the adder 9 in the multiplier 10, the product of the factors previously recorded in its input registers is calculated: the values of the sum from the output of the adder 9 and the values of the dispersion correction function
f (V) (1 V) ^-1/2 ,
generated by the functional converter 8, and recording the result of the product in the output register of the multiplier 10. In the next clock cycle, the operation of the generator is repeated. The sequence of numbers formed at the output of the generator forms a stationary random process with zero mathematical expectation, zero asymmetry coefficient, unit dispersion, and a fourth-order cumulant value X _k measured by an external signal V in accordance with the expression
X ₄ =

b $\genfrac{}{}{0ex}{}{\text{4}}{\text{j}}$ *

and an autocorrelation function determined by a given array of weighting coefficients of the impulse response of the filter b _j } _N.

Claims (1)

 A random process generator, comprising a uniformly distributed random number sensor, a first and second comparison circuit, a register, a clock, the output of which is connected to a triggering input of a uniformly distributed random number sensor, the output of which is connected to the first input of the first comparison circuit, characterized in that it introduced a block of elements NOT, a functional converter, multiplexer, adder, multiplier, and the output of the sensor of uniformly distributed random numbers is connected to the first input of W the second comparison circuit, the second input of which is connected to the output of the block of elements NOT, the input of which is combined with the input of the functional converter, the second input of the first comparison circuit and is the input of setting the cumulant value of the fourth order of the generator, the outputs of the first and second comparison circuits are connected respectively to the first and second control the inputs of the multiplexer, the first, second and third information inputs of which are inputs of the generator modes, the output of the multiplexer is connected to the information input of the reg tra, whose outputs are connected to the corresponding control inputs of the operation type of the adder components, the synchronization input of which is connected to the synchronization inputs of the register and the multiplier and connected to the output of the clock pulse generator, the output of the adder is connected to the input of the first multiplier of the multiplier, the information inputs of the adder components are respectively the inputs of the set values generator weights, the output of the functional converter is connected to the input of the second multiplier of the multiplier, the output of which is the output of the generator.

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