Device for determining characteristics of a random process

FIELD: computer science.

SUBSTANCE: device has buffer memory register, pulse generator, switches, register, commutators, pulse counter, inversions number counter, comparison circuit, AND elements group, subtraction elements group, scale amplifiers group, adders group, delay elements groups, delay elements, cycles counter, OR elements group, reverse value computation blocks group, square-ware generators group.

EFFECT: higher precision.

1 dwg

The invention relates to specialized tools of computer technology and may find application in the determination of the statistical characteristics of random variables in the case when the original one-dimensional distribution is unknown.

A device for determining the characteristics of a random process, containing the pulse counter, count number of inversions, the pulse generator, the group of items, the case of the buffer memory, a comparison circuit, a radio group, case, two switches, a group of adders, large-scale amplifiers, blocks and subtraction counter cycles [1].

The device has a relatively narrow functionality, because it determines the assessment only sample quantiles, not providing a definition of their dispersions and density values at the points of quantiles.

The closest in purpose and technical nature of the claimed is a device for determining the characteristics of a random process, containing the pulse counter, count number of inversions, the pulse generator, the group of items, the first inputs of which are integrated, the register of the buffer memory, a comparison circuit, a radio group, case, two switches, a group of delay elements, a group of adders, large-scale amplifiers, loop counter, the reset input in the initial state of which is connected to vyhoda the count of the number of inversions and the counting input combined with the respective control inputs of the first and second switches and is connected to the output of the pulse generator, an additional input connected to the output of the loop counter, the two groups of blocks subtraction, the group of blocks calculate the reciprocal and the group of the squares, and the input register of the buffer memory is an input device that controls the output register of the buffer memory is connected to the input of the start pulse generator, and an information output register buffer memory connected to the information input of the register, a clock input connected to the first output of the pulse generator, a second output of which is connected to the input of the pulse counter and control inputs of the first and second switches the outputs of the bits of the register are connected to the corresponding inputs of the first switch and the second input element group And the output of the first digit of the register connected to the first input of the first switch group, the yield of the i-th digitN is the sample size of the random process) is connected with the second input of the (i-1)th switch and the first input of the i-th switch group output the last N-th digit of the register is connected to the second input of the (N-1)-th switch group, the first and second outputs of the i-th switchconnected with the responsibly to the inputs of the i-th and (i+1)-th bits of the register, both outputs of the first switch are connected to the corresponding inputs of the comparison circuit, the output of which is connected to the information input of the second switch and with the information input counter number of inversions, set input connected to the output of the pulse counter and the output counter of the number of inversions is connected to the stop input of the pulse generator and to the first inputs of elements And groups, the i-th outputa second switch connected with the control input of the i-th switch, the outputs of the elements And groups are a first group of outputs, the first and second inputs of the i-th block subtraction groupconnected to the outputs of the i-th and (i+1)-th elements And groups, respectively, and the output of the (i)th element And the group is connected also to the input of the i-th delay element group, the output of each block subtraction through proper scaling amplifier is connected to one input of the corresponding adder group, the outputs of which are the second group of outputs of the device, the other input of the i-th adder groupconnected to the output of the i-th delay element group, and the entrance wichitaeagle unit subtracting the second group, which provides estimates of the variance and density for the (i+N)-th quintile, connected to the output of the i-th element And the group W - whole part of N; N is an even sample size), and reducing input - output (i+2W)-th element And the group, the output of the specified block subtraction of the second group connected to the input of the same unit for computing the reciprocal of the group whose output is the output probability density function estimation device, and connected to the inlet of the same name Quad band whose output is the output of the estimated variance of quantiles of the device [2].

The disadvantage of the prototype is the low precision of the estimate of the variance of quantiles, because of the permanent structure parameter of the device that do not depend on the probabilities provided by quantiles, while this dependence is very significant.

The required technical result is a more accurate characterization of the random process.

This technical result is achieved in that in a device containing a pulse counter, count number of inversions, the pulse generator, the group of items, the first inputs of which are integrated, the register of the buffer memory, the input of which is the input device for determining the characteristics of a random process, a comparison circuit, a group of switches, the register, the first and second switches, the first group of delay elements, the first group of adders, the first group of large-scale amplifiers, loop counter, the reset input in the outcome of the first condition of which is connected to the output count of the number of inversions and the counting input combined with a counter input pulse counter and control inputs of the first and second switches and is connected to the output of the counting and control pulses of the pulse generator, the stop input of which is connected to the output of the counter overflow pulse, the first and second groups of blocks subtraction, the group of blocks calculate the reciprocal and the Quad, while the control output register buffer memory is connected to the input of the start pulse generator, and the information output is connected to the information input of the register, a clock input connected to the output of clock pulse generators, the installation log count of the number of inversions is connected to the output of the control discharge pulse counter, the outputs of the bits of the register are connected to the corresponding inputs of the first switch and the second inputs of elements And groups, the output of the first digit of the register connected to the first input of the first switch group, the yield of the i-th digitregister is connected with the second input of the (i-1)th switch and the first input of the i-th switch group, the output of the N-th digit of the register is connected to a second input of the N-th switch group, the first and second outputs of the i-th switchconnected respectively to the inputs of the i-th and (i+1)-th bits of the register p is pout and second outputs of the first switch are connected respectively with the first and second inputs of the comparison circuit, the output of which is connected to the information input of the second switch and with the information input counter number of inversions, the output of which is connected with the first inputs of elements And groups of the 1st exita second switch connected with the control input of the i-th switch group, the outputs of the elements And groups are a first group of outputs of the device for determining the characteristics of a random process, the first and second outputs of the i-thunit subtracting the first group of blocks subtraction are connected to the outputs of the i-ro and (i+1)-th elements And groups, respectively, and the output of the (i)th element And thegroup of elements And is connected to the input of the i-th delay element of the first group of delay elements, the output of which is connected to the first input of the i-ro adderthe first group of adders, a second input connected to the output of the i-th scale amplifierthe first group of large-scale amplifiers whose inputs are connected to outputs of the respective blocks subtraction of the first group of blocks subtracting the outputs of the first group of adders are the second group of outputs of the device for determining the characteristics of a random process, reducing input of the i-th block subtractionthe second group of blocks of visit the deposits connected with the output ([P _jN]+W₁)-th element And group elements, And the output wichitaeagle - output ([P_jN]-W₁)-th element And group elements And (W₁=[NN]; of 0.15<P_j<0,85; j=1-[0,7N]+1, [] - taking a part), the outputs of the i-th computing unit reciprocal group blocks calculate the reciprocal and the i-th Quad band Quad are respectively the outputs of the probability density and outputs the estimated variance of quantiles device for determining the characteristics of a random process, introduced the third and fourth groups of blocks subtraction, the first and second delay elements, the second, third and fourth groups of large-scale amplifiers, group of items, OR, second, and third group of delay elements, the second group of adders, moreover, the input of the first delay element is connected with the first inputs of elements And groups of elements, And an output connected to the input of the second delay element and the input resolution on the withdrawal of the second group of adders and the output of the second delay element is connected to the reset input of the adders of the second group of adders, reducing input of the j-th block of the subtraction of the third group of blocks subtraction is connected to the output ([P_jN]+W₂)-th element And group members, and the entrance wichitaeagle - output ([P_jN]-W₂)-th element And group items And reducing input of the j-th unit subtracting the fourth group which locks the subtractor is connected to the output ([P _jN]+W₃)-th element And group members, and the entrance wichitaeagle - output [P_jN]-W₃-th element And element group And (where K=2,3; W_k=[NN]+(K-1)[(0,17N+24)P-6.42 PER 0,001N-5,57]; P=Pj when RJ<0,5; otherwise, P=1-P_j; [.] - taking a part), the outputs of blocks subtracting the second, third and fourth groups of blocks of the subtraction are connected with the inputs of the same large-scale amplifiers, second, third and fourth groups of large-scale amplifiers, respectively, the outputs of large-scale amplifiers of the second and fourth groups are connected to respective inputs of the delay elements of the second and third groups of delay elements, respectively, and the outputs of large-scale amplifiers of the third group of large-scale amplifiers connected to respective inputs of the first group of inputs of a group of items OR, to the corresponding inputs of the second and third group of inputs which are connected respectively to the outputs of the delay elements of the second and third groups of delay elements, and outputs elements OR groups of elements OR connected to respective inputs of the components of the second group of adders, the output of which is connected to the corresponding inputs of the computing unit reciprocal and groups of adders.

The drawing shows an electrical block diagram of the device for determining the characteristics of a random process.

A device for determining characteristics the tick of a random process contains register 1 buffer memory, which input is the input of the generator 2 pulse, the switches 3, register 4, the first switch 5, a counter 6 pulses, the counter 7 number of inversions, figure 8 comparison, the second switch 9, a group of items And 10, the first inputs are combined, the first group of blocks 11 subtraction, the first group of large-scale amplifiers 12, a group of adders 13, a counter 14 cycles, the second group of blocks 15 subtraction, the group of blocks 16 calculate the reciprocal, Quad band 17, the first group of elements 18 delay, the fourth group of blocks 19 subtraction, the fourth group of large-scale amplifiers 20, the third group of elements 21 delay, the third group of blocks 22 subtraction, the third group is a large-scale amplifier 23, a group of items OR 24, the second group of adders 25, a second group of large-scale amplifiers 26, the second group of elements 27 delay, the first element 28 delay, the second element 29 delay.

A device for determining the characteristics of a random process input reset state of the counter 14 cycles coupled to the output of the counter 7 number of inversions, and the counting input combined with a counter input counter 6 pulses and to control inputs of the first 5 and 9 second switches and is connected to the output of the counting and control pulse generator 2 pulse, the stop input of which is connected to the output of the counter overflow 6 impulse is, control output register 1 buffer memory is connected to the input of the start pulse generator 2, and the information output is connected to the information input of the register 4, a clock input connected to the output of the clock pulse generator 2 pulse setting input of the counter 7 number of inversions is connected to the output of the control digit counter 2 pulse outputs bits of the register 4 is connected to the corresponding inputs of the first switch 5 and the second inputs of elements And 10 groups, the output of the first digit of the register 4 is connected to the first input of the first switch group 3, the output of the i-th digitN is the sample size of the random process) register 4 is connected with the second input of the (i-1)th switch and to the first input of the i-th switch group 3, the output of the N-th digit of the register 4 is connected to a second input of the N-th switch group 3, the first and second outputs of the i-th switchconnected respectively to the inputs of the i-th and (i+1)-th bits of the register 4, the first and second outputs of the first switch 5 are connected respectively with the first and second inputs of the comparison circuit 8, the output of which is connected to the information input of the second switch 9 and with the information input of the counter 7 number of inversions, the output of which is connected with the first inputs of elements And group 10.

In addition, the i-th you is od the second switch 9 is connected with the control input of the i-th switch group 3, the outputs of elements And group 10 are the first group of outputs of the device for determining the characteristics of a random process, the first and second outputsunit subtracting the first group of 11 blocks subtraction are connected to the outputs of the i-th and (i+1)-th elements And group 10 elements, And accordingly, the output of the i-th element And group 10 elements And is connected to the output of the i-th delay element of the first group 18 of the delay elements, the output of which is connected to the first input of the first adderthe first group 13 adders, a second input connected to the output of the i-th scale amplifierthe first group of 12 large-scale amplifiers whose inputs are connected to outputs of the respective blocks subtraction of the first group of 11 blocks subtracting the outputs of the first group 13 adders are the second group of outputs of the device for determining the characteristics of a random process, reducing input of the i-th block subtractionthe second group of 15 blocks subtraction is connected to the output ([P_jN]+W₁)-th element And 10 groups of elements, And the output wichitaeagle - output ([P_jN]-W₁)-th element And group 10 element, And (W₁=[NN]; of 0.15<P_j<0,85; j=1-[0,7N]+1; [.] - take a cha is less) the outputs of the i-ro unit for computing the reciprocal group 16 blocks calculate the reciprocal and the i-th Quad band 17 Quad are respectively the outputs of the probability density and outputs the estimated variance of quantiles device for determining the characteristics of a random process.

Additionally, the output of the first delay element 28 is connected with the first inputs of elements And group 10 elements, And the output connected to the input of the second delay element 29 and the entrance permit the withdrawal of the second group 25 adders, the output of the second delay element 29 is connected to the reset input of the adders of the second group 25 adders, reducing input of the j-th block, subtracting the third group 22 blocks subtraction is connected to the output ([P_jN]+W₃)-th element And group 10 element, And the input wichitaeagle - output ([P_jN]-W₃)-th element And group 10 element, And (K=2,3; W_k=[NN]+(K-1)[(0,17N+24)P-6.42 per·0,001N-5,57]; P=P_jP_j<0,5; otherwise, P=1-P_j; [.] - taking a part), the outputs of blocks subtracting the second 15, the third 22 and fourth 19 groups of blocks of the subtraction are connected with the inputs of the same large-scale amplifiers, second 26, third 23 and fourth groups of 20 large-scale amplifiers, respectively, the outputs of large-scale second amplifiers 15 and 19 fourth groups of large-scale amplifiers are connected with the inputs of the corresponding element of the RC delay of the second 27 and third 21 groups of delay elements, respectively, and the scale outputs of the amplifiers of the third group 23 large-scale amplifiers connected to respective inputs of the first group of inputs of a group of 24 items OR, to the corresponding inputs of the second and third group of inputs which are connected respectively to the outputs of the delay elements of the second 27 and third 21 groups of delay elements, and outputs elements OR groups of 24 elements OR connected to respective inputs of the components of the second group of adders 25, the output of which is connected to the corresponding inputs of the block 16 calculation of the inverse of the magnitude and group 17 of the Quad.

A device for determining the characteristics of a random process as follows.

First, let us describe the generalized algorithm of its work.

1. The device periodically samples the independent values of the displacement of N (even) members and ranks it according to

where (i) is the number of the member of the sample ranked in a row.

2. Each member of the ranked list x_(j)is the sample quantile X_pwith the level of probability P_jthat satisfies the relation

If for a given P_jfrom (2) results in a fractional number

the value of x_pproviding this level of RJ, is using interpolate is from the expression

where [.] the symbol takes the integer part of

F_j=(i)j-[(i)j] - share interpolation;

x_([(i)j]+1)x_[(i)j])accordingly the next larger and the next smaller to intermediate between the value of x_(i); members of the ranked sample with the specified integer numbers.

Sample quantiles obtained using (2) and (4)are removed from device to use.

3. For j sample quantiles (j=1-[0,7 N]+1; of 0.15<R<0,85 [.] - take the integer part), obtained without interpolation are determined by evaluation of the dispersions D(x_pthese quantiles and evaluation of the source probability density at the point of quantiles f(x_p). To do this:

in advance for given N and Pj are defined W_kin accordance with

where K=1-3; P=P_jP_j<0,5 otherwise, P=1-P_j; [.] - the symbol of the taking a part, and are defined rooms triple pairs of elements in 10 groups ([P_jN]+W_k), ([P_jN]-W_k)_cinvolved in the connections specified in the claims;

- for each of the specified in clause 3 of the algorithm quantile estimation of variance and estimation of the density at the point of quantiles is performed using expressions, respectively

where C_j=P_j(I-P_jN/36

where Z=6/N; [.]- taking the integer part of the number;

x(.) - ranked member of the sample with the specified number.

Grade D (x_p) and f(x_p) derived from device to use.

The presented algorithm is implemented in the device as follows.

Register buffer memory after filling out the issues with his control output signal generator 2 pulse. The signal generator 2 generates pulses at the clock input of register 4 pack of N pulses. Under the influence of clock pulses of the sequence value from the register buffer memory sequentially received via the data input to the register 4 by volume of N bits, thus mainly the case 4 is formed of a disordered sample of values (x₁x₂,..., x_i,..., x_N).

Generator 2 pulse, after the issuance of a stack of N clock pulses, starts to produce a continuous sequence of sync pulses on singlemode first switch 5, the second switch 9 and to the input of counter 6 pulses.

Under the influence of the sequence of clock pulses and in tact with them begins the procedure of ordering (ranking) of the sample.

The ranking procedure is based on the algorithm pairwise permutations. When you first view each sampled value x_jcompared with neighboring value of x_j+1. A pair of sample values, for the Kotor is x true inequality x _i>x_i+1are swapped.

The fact of the inequality x_i>x_i+1when pairwise viewing the sample is the inverse, and the function of the sum of inversions is determined by the expression

where

Value τ calculated at each cycle pairwise comparison and permutations of the sample, the sign of the end of the ranking of the sample is the value of the τ≤1, sochetannoe per scan cycle.

The ranking of the sample is as follows.

Information from outputs ([P_jN]+W_kand ([P_jN]-W_kelements And 10 groups (where K=1-3, and W_kis determined by (5)) is supplied respectively to the input and reducing input wichitaeagle j-x blocks 15, 22, 19 subtracting the second, third and fourth groups. For blocks 15, 22, 19, the value is assumed to be equal To respectively 1, 2 and 3. Outputs of the i-x blocks 15, 22, 19 subtracting formed in them the difference between x([p_jN]+W_k)-x([p_jN]-W_kgo to the corresponding large-scale amplifiers 26, 23, 20, which are multiplied by the corresponding coefficients 1/W_kforming first, second and third components. One component directly, and the other two through the elements 27, 21 delays the second and third groups received the item OR 24 group, where consistently fall for summation at the input of slag the units of the j-th adder of the second group of 25.

The delayed output signal of the first element 28 delay arrives at the inputs of permit issuance amount of the adders of the second group of 25, and after a delay in the second delay element 29 to the reset input of these adders. The sum of the j-th adder of the second group 25 enters the j-th squarer 17 group, which is being built to a square. The result in the Quad representing the estimate D(x_pwith accuracy up to a constant known factor, is supplied to the corresponding output device.

To estimate the density function at the point quintile sum of the j-th adder of the second group 25 enters the j-th block 16 calculate the reciprocal group, which is accurate to a known constant factor Z is formed evaluating f(x_pj)coming to the appropriate output device.

Thus, thanks to the introduction of new units and relationships, achieved the required technical result increased accuracy, since the device enhances the accuracy of the estimate of the variance of quantiles due to the possibility of adjusting the device settings depending on the type of random process.

Sources of information

1. USSR author's certificate No. 1043665, CL 06 F 15/36.

2. USSR author's certificate No. 1479939, CL 06 F 15/36.

Device for determining the characteristics of a random process, containing the pulse counter, Chechik number of inversions, the pulse generator, the group of items, the first inputs of which are integrated, the register of the buffer memory, the input of which is the input device for determining the characteristics of a random process, a comparison circuit, a group of switches, the register, the first and second switches, the first group of delay elements, the first group of adders, the first group of large-scale amplifiers, loop counter, the reset input in the initial state of which is connected to the output count of the number of inversions, and the counting input combined with a counter input pulse counter and to control inputs of the first and second switches and is connected to the output of the counting and control pulses of the pulse generator, the stop input which is connected to the output of the counter overflow pulse, the first and second groups of blocks subtraction, the group of blocks calculate the reciprocal and the Quad, while the control input of the last register of the buffer memory is connected to the input of the start pulse generator, and the information output is connected to the information input of the register, a clock input connected to the output of the clock generator pulses, the installation log count of the number of inversions is connected to the output of the control discharge pulse counter, the outputs of the bits of the register are connected to the corresponding inputs of the first switch and the second is mi inputs of elements And groups, the output of the first digit of the register connected to the first input of the first switch group, the yield of the i-th digitN is the sample size of the random process), the register is connected to the second input of the (i-1)-th switch group and to the first input of the i-th switch group output the last N-th digit of the register is connected to a second input of the N-th switch group, the first and second outputs of the i-th switchconnected respectively to the inputs of the i-th and (i+1)-th bits of the register, the first and second outputs of the first switch are connected respectively with the first and second inputs of the comparison circuit, the output of which is connected to the information input of the second switch and with the information input counter number of inversions, the output of which is connected with the first inputs of elements And groups, the i-th outputa second switch connected with the control input of the i-th switch group, the outputs of the elements And groups are a first group of outputs of the device for determining the characteristics of a random process, the first and second inputs of the i-th block subtractionthe first group of blocks subtraction are connected to the outputs of the i-th and (i+1)-th elements and groups, And, accordingly, the output of the i-th element And thegroup of elements And is connected to vhoda-th delay element of the first group of delay elements, the output of which is connected to the first input of the first adderthe first group of adders, a second input connected to the output of the i-th scale amplifierthe first group of large-scale amplifiers whose inputs are connected to outputs of the respective blocks subtraction of the first group of blocks subtracting the outputs of the first group of adders are the second group of outputs of the device for determining the characteristics of a random process, reducing input of the i-th block subtractionthe second group of blocks subtraction is connected to the output ([P_j·N]+W₁)-th element And group elements, And the output wichitaeagle to exit ([P_j·N]-W₁)-th element And group elements And (W₁=[N· N]; of 0.15<R_j<0,85; j=1-[0,7· N]+1; [· ] - taking a part), the outputs of the i-th blockcalculate the reciprocal of the group of blocks calculate the reciprocal of the group and of the i-th Quadgroup Quad are respectively the outputs of the probability density and outputs the estimated variance of quantiles device for determining the characteristics of a random process, characterized in that it introduced the third and fourth groups of blocks subtraction, the first and second delay elements, the second, the third, the fourth group of large-scale amplifiers, group of elements OR, second, and third group of delay elements and the second group of adders, with the input of the first delay element is connected with the first inputs of elements And groups of elements, And an output connected to the input of the second delay element and the input resolution on the withdrawal of the second group of adders, the output of the second delay element is connected to the reset input of the adders of the second group of adders, reducing input of the j-th block of the subtraction of the third group of blocks subtraction is connected to the output ([P_j·N]+W₂)-th element And group members, and the entrance wichitaeagle - output ([P_j·N]-W₂)-th element And the group elements And the input reducing the j-th block of the subtraction of the fourth group of blocks subtraction is connected to the output ([P_j·N]+W₃)-th element And group members, and the entrance wichitaeagle - output ([P_j·N]-W₃)-th element And group elements And (W_k=[N· N]+(K-1)· [(0,17N-24)· P-6.42 per· 0,001· N-5,57]; where K=2,3; P=P_jP_j<0,5 otherwise P=1-P_j;), the outputs of blocks subtracting the second, third and fourth groups of blocks of the subtraction are connected with the inputs of the same large-scale amplifiers, second, third and fourth groups of large-scale amplifiers, respectively, the outputs of large-scale amplifiers of the second and fourth groups of large-scale amplifiers connect the s inputs of the respective delay elements of the second and third groups of delay elements, respectively, and the scale outputs of the amplifiers of the third group of large-scale amplifiers connected to respective inputs of the first group of inputs of a group of items OR, to the corresponding inputs of the second and third group of inputs which are connected respectively to the outputs of the delay elements of the second and third group of delay elements, and outputs elements OR group of elements OR connected to respective inputs of the components of the second group of adders, the output of which is connected to the corresponding inputs of the computing unit reciprocal and groups of the Quad.