JP5122348B2 - Random error evaluation method and evaluation apparatus - Google Patents

Description

  The present invention relates to a random error evaluation method and evaluation apparatus for a digital signal having a predetermined error rate and including errors at random, and in particular, an adjacent error between adjacent errors of each error included in the digital signal. The present invention relates to a random error evaluation method and a random error evaluation device for quantitatively evaluating the degree of approximation (compatibility) of the occurrence interval distribution with respect to the geometric distribution.

  In a test apparatus that performs various tests on various communication devices incorporated in a digital communication network using a general electric signal cable or an optical communication network using an optical fiber cable, this communication is performed on the communication device to be tested. A test signal that matches the actual usage status of the device is input to evaluate the response operation of the communication device. As one type of evaluation test for such a communication device, a test signal that intentionally includes an error is employed as a test signal that matches the actual usage situation transmitted to the communication device to be measured. Then, the communication device evaluates to what extent the error rate (error rate) p included in the test signal operates normally.

For some reason including external noise etc. in various digital signals transmitted / received in a communication network connecting between stations, not between general user terminals and base stations or between subscriber terminals and telephone stations, The occurrence rate (error rate) p of normally included errors (error bits) is on the order of p = 10 ⁻² to 10 ⁻⁸ . Moreover, errors occur randomly.

  Here, in other words, when random is unpredictable, the number of errors that occur within a given time is unpredictable, and the time interval between the occurrence of one error and the next error is also unpredictable. It is. The former property relating to the number of errors is referred to as count property unpredictability, and the latter property relating to the error occurrence interval is referred to as interval property unpredictability.

  Therefore, in addition to the test signal generation circuit that generates the original digital test signal, the test apparatus also receives a random error signal that causes an error of a bit “1”, for example, at a specified error rate p and randomly. A random error signal generating circuit for generating is incorporated. Then, the specified error rate is obtained by performing an exclusive theoretical sum operation of the digital test signal output from the test signal generation circuit and the random error signal output from the random error signal generation circuit, and inverting the operation result. Create a test signal containing p errors.

Here, the statistical properties of errors occurring in the random error signal are verified using probability theory. That is, in the random error signal, it is not determined whether or not an error occurs in one clock cycle T _C , but the error occurrence probability is fixed to a fixed value p. In terms of probability theory, such a random error generation circuit can be said to be a device that repeats Bernoulli Trials with a constant (occurrence rate) p at a certain cycle.

  A Bernoulli trial with a parameter p is a trial with a probability of success of p (0 <p <1) and a probability of failure of q = (1-p). Is output. “Independent” means that the result of each trial does not affect the results of other trials.

  The probability distribution obtained by repeating the Bernoulli trial with the parameter p can be expressed as a geometric distribution. That is, the geometric distribution is a probability distribution obtained by repeating Bernoulli's trial of the parameter (probability) p (0 <p <1), and the probability P that the number of trials until success (“1”) is j. (J, p) is expressed by the following equation.

P (j, p) = q ^j · p j = 0, 1, 2, 3,.
However, q = 1-p 0 <q <1
Thus, the distribution of error intervals (intervals from the occurrence of one error to the next error) of each error included in the random error signal theoretically follows a geometric distribution.

  Therefore, whether or not each error included in the random error signal can actually be regarded as random is evaluated from the following two viewpoints.

  (A) The number of error occurrences within a predetermined counting time follows a binomial distribution (asymptotic to a Poisson distribution in the limit where the calculation time is sufficiently long and the error rate p is sufficiently small). Evaluating a random error signal from this viewpoint is referred to as examining the count property of the error as described above.

  (B) The interval between the occurrence time of an error and the occurrence time of another error (hereinafter, for the sake of simplicity, this amount is referred to as an error occurrence interval) follows a predetermined distribution. In particular, the adjacent error occurrence interval should follow the geometric distribution described above. From this point of view, evaluating the randomness of the random error signal is referred to as examining the interval property of the error as described above.

With respect to the aspect (a), an example of an error signal generation circuit that generates a Poisson distribution error signal having an error distribution according to a Poisson distribution with an asymptotic binomial distribution when the error rate p is sufficiently small is disclosed in Patent Literature 1 is proposed. Non-Patent Document 1 presents a basic theory of a chi-square goodness-of-fit determination method that quantitatively determines whether or not a statistically obtained event occurrence distribution conforms to a theoretical distribution. ing.
JP 2002-330192 A “Statistics Summary” for Engineers Gutman / S. C. Published by virus Ishii and Hori Co-translated Baifukan 1968

  However, at the present time, the technique for evaluating the interval property of the error, which is the extent to which the distribution of the adjacent error occurrence intervals of the random error signal (b) described above follows the geometric distribution, is incomplete. Note that accurate evaluation of the error occurrence rate p included in the random error signal can be realized relatively easily using a counter and a comparator.

  Actually, it is a time series data composed of the symbols “0” and “1”, and the random error signal that satisfies the above-described numerical property of (a) but does not satisfy the above-mentioned characteristic property of (b) can be easily obtained. Can be created. Therefore, in order to guarantee the randomness of the error of the random error signal, it is indispensable to evaluate the interval property of (b) in addition to the evaluation of the count property of (a).

  The present invention has been made in view of such circumstances, and the distribution of adjacent error occurrence intervals between adjacent errors of each error included in a digital signal having a predetermined error rate output from a signal generation circuit is as follows. The purpose is to provide a random error evaluation method and a random error evaluation apparatus that can quantitatively grasp how much the geometric distribution matches and can improve the test accuracy of a test apparatus incorporating the signal generation circuit. And

  In order to solve the above problem, in the random error evaluation method of the present invention, an error for calculating an adjacent error occurrence interval between adjacent errors of each error in a digital signal having a predetermined error rate and randomly including errors. An interval calculation step, a storage holding step for taking in and storing a predetermined number of samples as the measurement value of the adjacent error occurrence interval calculated in the error interval calculation step, and a measurement stored and held in the storage holding step A maximum value extracting step for extracting the maximum value, a section dividing step for dividing the maximum value extracted in the maximum value extracting step into a plurality of sections, and a section dividing step from the measured values of the number of stored samples. A measurement frequency counting step for counting each measurement frequency that is the number of each measurement value belonging to each section divided by Using an average value calculating step for calculating an average value of the measured values stored and held in the holding step, a realization probability of an adjacent error occurrence interval determined by a geometric distribution in which a probability function is determined using the average value, and the number of samples A theoretical power calculating step for calculating a theoretical power for each section divided in the section dividing step, and a chi-square value obtained by integrating the deviation between the measured power and the theoretical power in each section over all the sections. A chi-square value calculating step, a target chi-square value calculating step for calculating a target chi-square value corresponding to a designated significance level in a chi-square distribution function determined by the degree of freedom determined from the number of sections; A conformity determination step of determining that the distribution of adjacent error occurrence intervals of the digital signal is suitable for the geometric distribution when the calculated chi-square value is smaller than the target chi-square value; It is provided.

  In the random error evaluation method configured as described above, first, an adjacent error occurrence interval between adjacent errors of each error of the digital signal to be measured is calculated, and the adjacent error occurrence interval is calculated as a distribution evaluation target. A predetermined number of samples are taken in and stored as measurement values.

  The maximum value of each adjacent error occurrence interval (maximum interval) calculated for comparison with the distribution of error occurrence intervals and the statistical distribution (probability density function) indicating the probability (frequency) of occurrence for each measured value. Is divided into a plurality of simple divisions with a predetermined number of divisions, and each measurement frequency that is the number of measurement values belonging to each division is calculated. Next, the theoretical frequency of each section on the geometric distribution is calculated.

  Then, a chi-square value indicating the area deviation between the geometric distribution and the measured distribution is calculated, and when the chi-square value is smaller than the target chi-square value corresponding to the designated significance level, It is determined that the distribution of error occurrence intervals of the digital signal matches the geometric distribution.

  According to another aspect of the present invention, a random error evaluation is performed to evaluate a conformity of a distribution of adjacent error occurrence intervals between adjacent errors in a digital signal having a predetermined error rate and randomly including errors. Device.

  The random error evaluation device is configured to input input measurement conditions including the number of measurement values of the adjacent error occurrence interval of the digital signal, the number of divisions when the measurement value is divided into a plurality of sections, and the significance level of conformity evaluation. An error interval calculation unit that calculates an adjacent error occurrence interval between the measurement condition memory to be stored and the adjacent error of each error in the digital signal, and the adjacent error occurrence interval calculated by the error interval calculation unit is sampled as a measurement value A measurement value memory that captures and stores the number, a maximum value extraction unit that extracts the maximum value of the measurement values stored in the measurement value memory, and a section division unit that divides the extracted maximum value into sections of the number of divisions A measurement frequency counting unit that counts each measurement frequency that is the number of each measurement value belonging to each divided section from the measurement value of the number of samples stored in the measurement value memory; A measurement value table that stores the measurement frequency counted for each section, an average value calculation unit that calculates an average value of the measurement values stored in the measurement value memory, and a geometric distribution in which a probability function is determined using the average value The theoretical frequency calculation unit that calculates the theoretical frequency for each section divided by the section dividing unit using the realization probability of the adjacent error occurrence interval determined by the above and the number of samples, and writes the theoretical frequency to the measurement value table, and each section A chi-square value calculation unit for calculating a chi-square value obtained by integrating the deviation between the measured frequency and the theoretical frequency over all intervals, and a chi-square distribution function determined by the degree of freedom obtained from the number of intervals. A target chi-square value calculation unit for calculating a target chi-square value corresponding to the significance level, and a distribution of adjacent error occurrence intervals of a digital signal when the calculated chi-square value is smaller than the target chi-square value But Includes what distribution compatible and determining acceptability determining unit, and a display unit for displaying the determination result of the matching determination unit.

  The random error evaluation apparatus configured as described above can achieve substantially the same operational effects as the random error evaluation method described above.

  In the present invention, it is quantitatively determined whether or not the distribution of the measured adjacent error occurrence intervals of the digital signal to be measured conforms to the geometric distribution using the chi-square conformity determination method. Therefore, it is possible to improve the test accuracy for the test object of the test apparatus in which the digital signal generation circuit is incorporated.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

  FIG. 1 is a block diagram showing a schematic configuration of a random error evaluation apparatus employing a random error evaluation method according to an embodiment of the present invention.

  For example, in a random error evaluation apparatus configured by an information processing apparatus such as a computer, an operation unit 1 including a mouse, a keyboard, and the like for a measurement operator to input various measurement conditions and initial setting conditions of a significant level. For example, an interface (IF) circuit 3, for example, an operation unit 1, which is inputted with a digital signal a having a predetermined error rate p to be measured and outputted from the signal generation circuit 2 and containing an error at random is inputted. There are provided hardware components of a display unit 4 for displaying and outputting measurement conditions and determination results, and a storage device 5 comprising, for example, an HDD (hard disk drive) for storing and holding various data. In addition, in the random error evaluation apparatus, in addition to the hardware components described above, there are many software components configured on an application program.

  In the storage device 5, a measurement condition memory 6, a measurement value memory 7, and a measurement value table 8 are formed. Hereinafter, the configuration and operation of each unit will be described in order.

  In the measurement condition memory 6, the number of samples of the measurement value t as an adjacent error occurrence interval in which information related to the digital signal a to be measured input from the operation unit 1 by the measurement operator is processed by the measurement condition setting unit 9. N, the division number M set to determine the interval width ΔT (time width), and the significance level α (%) used as the determination criterion for chi-square conformity determination are stored.

  The error interval calculation unit 10 calculates an adjacent error occurrence interval t between adjacent errors of each error in the digital signal a input via the interface (IF) circuit 3, and uses the storage device 5 as a measured value t. The measured value memory 7 is written.

A specific calculation operation of the adjacent error occurrence interval t in the error interval calculation unit 10 will be described with reference to FIG. The digital signal a output from the signal generating circuit 2 is composed of “0” bits indicating normality synchronized with the clock and “1” bits indicating error b. When the error rate p of the digital signal a is, for example, 10 ⁻³ , the digital signal includes “1” bits at a rate of 1 out of 1000 “0” bits.

Each error occurrence time i ₁ , i ₂ , i ₃ , b _{n + 1} of each error b ₁ , b ₂ , b ₃ , b ₄ , b ₅ ,..., B _n ,. i ₄ , i ₅ ,..., i _n ,..., i _{N + 1} are represented by integer multiples of the clock cycle T _C. Then, n-th error b _n adjacent error generation interval (measured value) t _n, using the error occurrence time i _n self, and error occurrence time i _{n + 1} of the following error b _{n + 1,} It is shown by the following formula. The unit is an integer multiple of the clock period T _C.

Adjacent error occurrence interval (measured value) t _n = (i _{n + 1} −i _n ) −1
When the error b occurs at the next clock, the adjacent error occurrence interval t is zero (t = 0), so “1” is subtracted.

Here, n is a number that specifies the error b and the adjacent error occurrence interval (measured value) t,
n = 1, 2, 3, 4, 5,..., N
N is the number of samples of this measurement value (adjacent error occurrence interval) stored in the measurement condition memory 7. Thus each error b ₁ which is _{calculated, b 2, b 3, b} 4, b 5, ..., b n, ..., b N + 1 of the (N + 1) each adjacent error generation interval t ₁ of, t _2, t ₃ , t ₄ , t ₅ ,..., t _n ,..., t _N are written as measured values in the measured value memory 7 shown in FIG.

The maximum value extraction unit 11 includes the maximum value Tmax of the adjacent error occurrence interval (measurement value) among the measurement values t _{1 to} t _N of the _N adjacent error occurrence intervals written in the measurement value memory 7. That is, the longest time indicated by an integer multiple of the clock cycle T _C from the occurrence of one error b to the occurrence of the next error b is extracted and sent to the section dividing unit 12.

The section dividing unit 12 divides the section having the maximum value Tmax on the right end and 0 on the left end by the number of divisions M (positive integer) stored in the measurement condition memory 6 to obtain M sections I ₁ , I ₂ , I ₃ ,..., I _j ,..., I _M are created, and the measurement value table 8 having the _M sections I _{1 to} I _M is formed in the storage device 5. A specific operation for forming _M sections I _{1 to} I _M will be described with reference to FIG.

Sorting the measured value t ₁ ~t _N of the written sample number N adjacent error generation interval in ascending order of for example, a value (distance) t to the measured value memory 7, as shown, adjacent error generation interval t There are N measured values t from zero (t = 0) to the maximum value (t = Tmax). Then, M sections I ₁ , I ₂ , I ₃ ,..., I _j ,... Obtained by dividing the range that can be taken by the measured values t ₁ to t _N from t = 0 to t = Tmax. The section width ΔT expressed in units of the clock cycle T _C of I _M is
Section width ΔT = T _max / M
Thus, the range of the j-th interval I _j is [(j−1) ΔT, jΔT 1) that can be taken by the measurement value t. The expression of this range means (j−1) ΔT or more and less than jΔT.

The number of samples N and the number of divisions M are selected so that the number of measurement values (measurement frequency f) belonging to each of the divided sections I _{1 to} I _M is at least 5 or more. Specifically, the error rate p in the digital signals a, since the clock period T _C is given, the number of samples N is corresponding to the matching determination accuracy and data processing time of the computer, for example, 10 ⁴ to 10 about ⁵ The division number M is set to about several tens.

FIG. 5 is a diagram showing a measurement value table 8 formed in the storage device 5. In the measurement value table 8, for each of the M sections I ₁ , I ₂ , I ₃ ,..., I _j , ..., I _M , the corresponding measurement frequencies f ₁ , f ₂ , f ₃ , _{..., f j, ..., f} M, and the corresponding respective theories power _{e 1, e 2, e 3} , ..., e j, ..., each region 8a for writing e _M, 8b are respectively formed .

The measurement frequency counting unit 13 measures the measured values t ₁ , t ₂ , t ₃ , t ₄ , t ₅ ,..., T _n ,. from _N, each interval I _1, which is divided into _{M, I 2, I 3, ...} , I j, ..., each measurement frequency is the number of the measurement values belonging to _{I M f 1, f 2,} f 3, ... , F _j ,..., F _M are counted. Then, the counted measurement frequencies f ₁ , f ₂ , f ₃ ,..., F _j , f _M are used as the intervals I ₁ , I ₂ , I _{3 ,.} .., I _M is written in the corresponding area 8a.

Average value calculating section 14 calculates the average value T _m of a measured value t ₁ ~t _N measurement sample number written in the memory 7 N number of adjacent error generation interval, sends to the theoretical number calculating section 15 To do.

T _m = (t ₁ + t ₂ + t ₃ + t ₄ + t ₅ +, ..., + t _n +, ... + t _N ) / N
The theoretical frequency calculation unit 15 uses the number of samples N and the average value Tm stored in the measurement condition memory 6 to measure each interval I ₁ , I ₂ , I ₃ ,..., I _j,. each theoretical frequency of _{I M e 1, e 2,} e 3, ..., e j, ..., each section I ₁ measured value table 8 by calculating the _{e M, I 2, I 3} , ..., I j, ... , I _M is written into the corresponding area 8b. However, the probability function of the geometric distribution is determined using the average value T _m .

Next, a procedure for calculating the theoretical frequency e in the geometric distribution will be described. The probability function of the geometric distribution described above,
P (j, p) = q ^j · p j = 0, 1, 2, 3,.
p: Error rate 0 <p <1
However, q = 1-p 0 <q <1
In using the average value T _m of a error interval calculated above to calculate the maximum likelihood estimation error rate p _a error rate p of the digital signal a measure by the following formula.

p _a = 1 / (1 + T _m )
Then, in the same manner as described above, when the qa = 1-p _a, equation expressing the probability function P (j, p) = q a j · p a j = 0,1,2,3, ...
It becomes. The probability of realizing the adjacent error occurrence interval included in the j-th interval I _j is the position of each unit of the clock cycle T _{C in} the interval [(j−1) ΔT, jΔT) with the interval width ΔT = N / M. When x, the probability function P (x, p _a) a = q _a ^x · p _a in q _a exponential x, plus while moving sequentially from x = (j-1) ΔT to x = jΔT-1 Is. Then, the number of samples N is multiplied in order to convert to frequency. Therefore, _the theoretical frequency ej _in the j-th interval _Ij is expressed by the following equation.

It becomes. That is, FIG. 6, the theoretical frequency e _j intervals I _j characterizing geometric distribution 22 shown in FIG. 8 is determined by the average value Tm, and the number of samples N and the section width ΔT and the section number j.

Each region 8a of the measurement value table 8 shown in FIG. 5, the measurement frequency f ₁ ~f _M against 8b, and in a state in which the writing has been completed the theoretical power e ₁ to e _M, 6, each measurement frequency f which is determined _{1, f 2, f 3,} ..., f j, ..., a measurement profile 21 shown by a broken line obtained from f _M, the theoretical frequency computed _{e 1, e 2, e 3} , ..., e j, ... shows a comparison of the theoretical distribution of the geometric distribution 22 indicated by the solid line obtained from e _M. A chi-square determination for quantitatively determining how close the measured distribution 21 of the input digital signal a indicated by the broken line is to the theoretical distribution of the geometric distribution 22 indicated by the solid line will be described.

The measurement table 8 of FIG. 5, the above-mentioned measurement frequency f, in addition to the theoretical power e, the interval _{I 1, I 2, I 3} , ..., I j, ..., the theoretical frequency of measurement frequencies f for each I _M amount of deviation ^{_{e (f j -e j) 2}} , normalized deviation amount ^{_{(f j -e j) 2 /}} e j is written are areas 8c, 8d are formed.

Naturally, when the measurement power f and the theoretical power e are integrated over all the intervals I _{1 to} I _M , the number of samples N is obtained. Further, a value obtained by integrating the normalized deviation amount (f _j −e _j ) ² / e _j over all the sections I _{1 to} I _M is a value generally called “chi-square value”. This chi-square value is written as “χ ² ” using Greek letters for convenience.

When the writing of the measured frequencies f _{1 to} f _M and the theoretical frequencies e _{1 to} e _M is completed in each of the regions 8a and 8b of the measured value table 8 shown in FIG. 5, the section integration unit 16 is activated and the chi-square value is activated. The calculation unit 17 executes a preparation process for performing the chi-square calculation.

  For example, if a section I having a theoretical frequency e of 5 or less exists at the right end portion of the exponential waveform of the geometric distribution 22, the section integration unit 16 merges with an adjacent section to form one section. As a result, the number of sections is changed from M to (M−1). This is necessary in order to improve the calculation accuracy of the chi-square value. Of course, if there is no section I with a theoretical frequency e of 5 or less, the sections are not merged, and the section number M remains the same.

Chi-square value calculator 17, the arrow "↓" in the geometric distribution 22 of Figure 6, as indicated by the "↑", each section _{I 1, I 2, I 3} , ..., I j, ..., in I _M measured measured frequency _{f 1, f 2, f 3} , ..., f j, ..., the theoretical frequency e ₁ of _{f M, e 2, e 3} , ..., e j, ..., 2 square value of the difference with respect to e _M shift amount indicated in (f-e) ^2, and each shift amount normalized ^{_{(f 1 -e 1) 2 /}} e 1, (f 2 -e 2) 2 / e 2, (f 3 -e 3) ² / ^e ₃ ,..., (F _j −e _j ) ² / ^e _j ,..., (F _M −e _M ) ² / ^e _M are calculated and written in the areas 8 c and 8 d of the measurement value table 8.

Then, each normalized deviation amount (f _j −e _i ) ² / ^e _j is integrated over all the sections I _{1 to} I _M to calculate “chi-square value χ ² ”.

χ ² = [(f ₁ −e ₁ ) ² / ^e ₁ ] + [(f ₂ −e ₂ ) ² / ^e ₂ ] +,.
+ [(F _j −e _j ) ² / ^e _j ] +,..., + [(F _M −e _M ) ² / ^e _M ]
The chi-square value calculation unit 17 sends the calculated chi-square value χ ² to the conformity determination unit 18.

Next, the degree-of-freedom calculating unit 19 sets the degree of freedom φ for calculating the chi-square function (probability density function) F (χ ² , φ) shown in FIG. 7 in the measured value table 8 shown in FIG. A value obtained by subtracting 2 from the number M of the integrated adjusted sections I.

φ = M-2
Here, the degree of freedom φ is
φ = number of items in table (number of sections I) -1-k
It is expressed. k is the number of parameters estimated in parameter estimation. In this case, since the average value T _m is estimated, the above value is obtained.

The chi-square function F (χ ² , φ) is

Indicated by

Γ (φ / 2) is a gamma function. For example, when the degree of freedom is φ = 5,
Γ (φ / 2) = Γ (5/2) = (3π ^1/2 ) ≒ 1.392
It becomes.

As shown in FIG. 7, the chi-square function F (χ ² , φ) is a [chi-square value χ ² for quantitatively determining how well the measured distribution fits the target distribution. ] Is a distribution probability density function having a variable, and if the degree of freedom φ of the interval I _j is determined, the function value F (χ ² , φ) in each [chi-square value χ ² ] is uniquely determined. is there.

The smaller the [chi-square value χ ² ] corresponding to the sum of the deviations from the geometric distribution calculated by the chi-square value calculation unit 17, the greater the fitness, that is, the fitness is the chi-square shown in FIG. It can be evaluated by the ratio (%) of the right tail area S on the right side of the [chi-square value χ ² ] indicated by the diagonal line of the distribution to the total area S _A (= 1).

  The measurement person designates a significance level α (%) determined that the measured distribution is suitable for the target distribution by the operation unit 1 and is set in the measurement condition memory 6 in advance. This significance level α (%) is empirically α = 5%, and it can be considered that a well-measured distribution fits the target distribution.

Therefore, the target chi-square value calculation unit 20 determines that the ratio (%) of the right foot area S to the total area S _A (= 1) in the chi-square function F (χ ² , φ) shown in FIG. A target chi-square value (χ ² ) _α that is (%) is calculated and sent to the conformity determination unit 18.

The conformity determination unit 18 determines that the [chi-square value χ ² ] calculated by the chi-square value calculation unit 17 is the [target chi-square value (χ ² ) _α calculated by the target chi-square value calculation unit 20. ], The distribution of the adjacent error occurrence intervals of the digital signal a to be measured is determined to match the geometric distribution, and the determination result is displayed and output to the display unit 4.

As shown in FIG. 8, the display unit 4 includes a measured distribution 21, a geometric distribution 22, an error rate p, a sample number N, a maximum value T _max , an average of the adjacent error occurrence intervals of the digital signal a to be measured. A value T _m , a degree of freedom φ, a chi-square value χ ² , a significance level α (%), a target chi-square value (χ ² ) _α , a determination result, and the like are displayed.

FIG. 9 is a flowchart showing the overall evaluation operation of the random error evaluation apparatus configured as described above. When measurement conditions such as the number N of samples, the number M of divisions, the significance level α, and the error rate p are input from the operation unit 1 (step S1), the measurement conditions are set in the measurement condition memory 6 (S2). Then, the adjacent error occurrence interval of the digital signal a to be measured is measured (calculated) by the number of samples N (S3). Next, the maximum value T _max of the measured value t of the measured adjacent error occurrence interval is calculated (S4). Then, the measurement frequency f for each section I is calculated (S5).

Further, an average value T _m of the measured values t of the measured adjacent error occurrence intervals is calculated (S6). The theoretical frequency e of each section I _j in the geometric distribution 22 is calculated using the sample number N and the average value T _m (S7). Next, [target chi-square value (χ ² ) _α ] corresponding to the designated significance level α is calculated (S8). Also, the [chi-square value χ ² ] corresponding to the sum of the deviation amounts of the measured power f measured earlier and the theoretical power e is calculated (S9).

Then, the magnitudes of both are compared (S10), and when the [chi-square value χ ² ] of the digital signal a to be measured is smaller than the [target chi-square value (χ ² ) _α ] (S10), the measurement object It is determined that the adjacent error occurrence interval of the digital signal a conforms to the geometric distribution 22 (S11), and the conformity determination result is displayed and output on the display unit 4 (S13).

On the other hand, when the [chi-square value χ ² ] of the digital signal a to be measured is larger than the [target chi-square value (χ ² ) _α ] (S10), the adjacent error occurrence interval of the digital signal a to be measured is determined. It is determined that the distribution does not match the geometric distribution (S12), and the non-conformity determination result is displayed and output on the display unit 4 (S13).

Using the random error evaluation device of the embodiment configured as described above, it was evaluated whether or not the distribution of the adjacent error occurrence intervals of the two digital signals a ₁ and a ₂ shown in FIG. In the digital signal a ₁ , as shown in FIG. 11, the measurement distribution 21 of the adjacent error occurrence interval approximates (adapts) to a distribution that matches the geometric distribution 22. On the other hand, in the digital signal a ₂ , as shown in FIG. 12, the measurement distribution 21 of the adjacent error occurrence interval has a distribution far away from the geometric distribution 22.

As shown in FIG. 10, the measurement conditions are that both the digital signals a _{1 and} a ₂ have the same error rate p = 10 ⁻² , the number of samples N = 16383, and the significance level α = 5%. In the digital signals a _{1 and} a ₂ , M = 32 and M = 57 are set, respectively. However, as a result of the action of the section integration unit 16, the degrees of freedom φ = 25 and φ = 26 are substantially equal. Further, the target chi-square value (χ ² ) _α = 37.7 and the target chi-square value (χ ² ) _α = 38.8 of both digital signals a _{1 and} a ₂ are substantially equal.

However, the digital signal a ₂ is because the distribution of adjacent error generation interval is concentrated in one, the chi-square value (chi ²⁾ is 14341.6, digital signal a ₁ of the chi-square value of (chi ²⁾ Very large compared to 11.5. Therefore, in the digital signal a ₂ , the chi-square value (χ ² ) (= 14341.6) is much larger than the target chi-square value (χ ² ) _α (= 38.8). As a result, a non-conformance determination in which the distribution of the adjacent error occurrence intervals of the digital signal a ₂ does not conform to the geometric distribution is output.

On the other hand, the chi-square value (χ ² ) (= 11.5) of the digital signal a ₁ is less than or equal to the target chi-square value (χ ² ) _α (= 37.7). As a result, a conformity determination that matches the distribution of the adjacent error occurrence intervals of the digital signal a _{1 to} the geometric distribution is output.

  As described above, in the random error evaluation method and the random error evaluation apparatus according to the embodiment, whether the distribution of the adjacent error generation intervals of the digital signal a output from the signal generation circuit 2 matches the ideal geometric distribution existing in nature. Can be determined quantitatively.

  In addition, this invention is not limited to embodiment mentioned above. For example, by setting the significance level α to, for example, 10% exceeding 5%, it is possible to set the test conformity determination criteria more strictly.

1 is a block diagram showing a schematic configuration of a random error evaluation device to which a random error evaluation method according to an embodiment of the present invention is applied. The figure which shows the calculation method of the adjacent error generation interval of the digital signal of the measuring object in the random error evaluation apparatus of the embodiment The figure which shows the method of dividing | segmenting the adjacent error generation interval into a several area in the random error evaluation apparatus The figure which shows the memory content of the measured value memory formed in the memory | storage device of the random error evaluation apparatus The figure which shows the memory content of the measured value table formed in the memory | storage device of the random error evaluation apparatus Diagram showing the relationship between the measured frequency and the calculated theoretical frequency The figure which shows the chi-square value function employ | adopted with the random error evaluation apparatus The figure which shows the display content in the display part of the random error evaluation apparatus Flow chart showing overall evaluation operation of the random error evaluation device Shows the measurement conditions and the measurement and evaluation results of the digital signal a _1, a ₂ in the random error evaluation device Graph showing measured data of the digital signal a ₁ in the random error evaluation device Figure also showing another actually measured data of the digital signal a ₂ in the random error evaluation device

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Operation part, 2 ... Signal generation circuit, 3 ... IF circuit, 4 ... Display part, 5 ... Memory | storage device, 6 ... Measurement condition memory, 7 ... Measurement value memory, 8 ... Measurement value table, 9 ... Measurement condition setting part DESCRIPTION OF SYMBOLS 10 ... Error interval calculation part, 11 ... Maximum value extraction part, 12 ... Section division part, 13 ... Measurement frequency counting part, 14 ... Average value calculation part, 15 ... Theoretical power calculation part, 16 ... Section integration part, 17 ... Chi-square value calculation unit, 18 ... conformity determination unit, 19 ... freedom degree calculation unit, 20 ... target chi-square value calculation unit, 21 ... measurement distribution, 23 ... geometric distribution

Claims (2)

An error interval calculating step of calculating an adjacent error occurrence interval between adjacent errors of each error in a digital signal having a predetermined error rate and randomly including errors;
A storage holding step for capturing and storing a predetermined number of samples as a measurement value for the adjacent error occurrence interval calculated in the error interval calculation step;
A maximum value extraction step for extracting the maximum value of the measurement values stored and held in this memory holding step;
A section dividing step for dividing the maximum value extracted in the maximum value extracting step into a plurality of sections;
A measurement frequency counting step of counting each measurement frequency that is the number of each measurement value belonging to each section divided in the section division step from the stored measurement value of the number of samples;
An average value calculating step for calculating an average value of the measurement values stored and held in the memory holding step;
Theoretical frequency calculation for calculating the theoretical frequency for each section divided in the section division step using the realization probability of the adjacent error occurrence interval determined by the geometric distribution in which the probability function is determined using the average value and the number of samples. Steps,
A chi-square value calculating step for calculating a chi-square value obtained by integrating the deviation between the measured power and the theoretical power in each section over all the sections;
A target chi-square value calculating step for calculating a target chi-square value corresponding to the designated significance level in the chi-square distribution function determined by the degree of freedom determined from the number of sections;
And a conformity determination step for determining that the distribution of adjacent error occurrence intervals of the digital signal matches the geometric distribution when the calculated chi-square value is smaller than the target chi-square value. Random error evaluation method. A random error evaluation device that evaluates a conformity of a distribution of adjacent error occurrence intervals between adjacent errors of each error in a digital signal having a predetermined error rate and randomly including errors,
A measurement condition memory (6) for storing input measurement conditions including the number of measurement values of the adjacent error occurrence interval of the digital signal, the number of divisions when dividing the measurement values into a plurality of sections, and the significance level of conformity evaluation When,
An error interval calculation unit (10) for calculating an adjacent error occurrence interval between adjacent errors of each error in the digital signal;
A measurement value memory (7) that captures and stores the adjacent error occurrence interval calculated by the error interval calculation unit as the measurement value by the number of samples;
A maximum value extraction unit (11) for extracting the maximum value of the measurement values stored in the measurement value memory;
A section dividing unit (12) that divides the extracted maximum value into sections of the number of divisions;
A measurement frequency counting unit (13) for counting each measurement frequency that is the number of each measurement value belonging to each divided section from the measurement value of the number of samples stored in the measurement value memory;
A measurement value table (8) for storing the counted measurement frequency for each section;
An average value calculation unit (14) for calculating an average value of the measurement values stored in the measurement value memory;
The measurement is performed by calculating the theoretical frequency for each section divided by the section dividing unit using the probability of adjacent error occurrence interval determined by the geometric distribution in which the probability function is determined using the average value and the number of samples. A theoretical frequency calculator (15) to be written in the value table;
A chi-square value calculation unit (17) for calculating a chi-square value obtained by integrating the deviation between the measured power and the theoretical power in each section over all the sections;
A target chi-square value calculation unit (20) for calculating a target chi-square value corresponding to the significance level in the chi-square distribution function determined by the degree of freedom determined from the number of sections;
A conformity determination unit (18) that determines that the distribution of adjacent error occurrence intervals of the digital signal matches the geometric distribution when the calculated chi-square value is smaller than the target chi-square value;
A random error evaluation device comprising: a display unit (4) for displaying a determination result of the conformity determination unit.

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