JPH0682142B2 - Method and apparatus for estimating random error in transfer function estimation value - Google Patents

Description

The present invention relates to a method for determining the magnitude of a random error included in an estimated value in estimating a transfer function of a vibration transfer system of a mechanical structure, a control loop circuit, or the like. And a measuring device therefor.

[Prior Art] When estimating a transfer function of a signal transfer system driven by a random signal, a power spectrum of an input signal of the system and a cross spectrum between input and output are generally obtained by a fast Fourier transform, and transfer is performed from a ratio thereof. A method of computing the function is used. In this case, in order to reduce the influence of a random error caused by the irregularity of the input signal, it is necessary to obtain a large number of transfer errors and average them. improves. Furthermore, if the disturbance noise and the input signal are uncorrelated and the statistical properties of the disturbance noise do not change during the analysis period, the variance due to the disturbance noise included in the estimated value of the transfer function decreases as the number of averaging increases. .

However, when trying to estimate the transfer function of an actual target such as a vibration transfer system of a mechanical structure or a control loop circuit, the existence of disturbance noise, much less its magnitude and statistical properties, is unknown. . Therefore,
In such a case, it has been unclear how much random error is included in the estimated transfer function, and so to speak, the average number of times has been determined based on experience.

[Problems to be Solved by the Invention] For this reason, it is inevitable that the estimated transfer function will vary from person to person due to the difference in experience of the measurers, and there is a problem in its reliability. In order to solve this, it is sufficient to make the above average number extremely large and to make the error negligible, but it takes a lot of time and there is a problem in practical use.

[Means for Solving the Problem] As a result of various studies, the present invention has found that the magnitude of the above-mentioned accidental error can be evaluated based on the change in the transfer function estimated value with respect to the increase in the average number. It was originally created and will be explained first.

In FIG. 9 showing a signal transmission system, the impulse response of the system is h (t), the input signal of the system is x (t), the output signal is y (t), and the disturbance noise mixed in the output signal is u.
Letting (t) be, these relationships are expressed by the following equations. still,
The signals that can be observed here are y (t) and x (t).

y (t) = h (t) * x (t) + u (t) (1) where * represents the convolution integral. The above formula (1) is Fourier-transformed in the range of −∞ <t <+ ∞,
Expressed on the frequency axis, the following equation is obtained.

Y (f) = H (f) X (f) + U (f) (2) Alternatively, X ^* (f) Y (f) / X ^* (f) X (f) = H (f) + X ^* (f ) U (f) / X ^* (f) X (f)
(3) Here, the superscript * represents a conjugate complex number. Here, if the input signal x (t) and the disturbance noise u (t) are uncorrelated with each other, their cross spectrum X
^* (F) U (f) is 0, and the right side is transfer function H (f)
Will be the only item.

Next, when discretizing and sampling, p is a sample number, τ is a sampling interval, and time t = τp is expressed by the following equation.

y (p) = h (p) * x (p) + u (p) (4) If k is a discrete frequency and the above equation is subjected to discrete Fourier transform,
We obtain

Y (k) = H (k) X (k) + U (k) (5) Alternatively, X ^* (k) Y (k) / X ^* (k) X (k) = H (k) + X ^* (k ) U (k) / X ^* (k) X (k)
(6) Eqs. (4) to (6) are expressed by discretizing Eqs. (1) to (3). It is necessary to have a small sampling interval, infinitesimal resolution of amplitude and infinite observation time. However, in reality it is impossible to meet this condition,
A / D conversion with finite time resolution and amplitude resolution is performed, and discrete Fourier transform is performed via a finite length window function. Further, at this time, averaging for reducing the influence of the second term on the right side of the above equation (6) is executed, but this is also a finite number of times and eventually becomes a finite observation time.

Hereinafter, the relationship between the errors caused by these and the transfer function estimated value calculated by averaging will be examined.

In FIG. 10 which shows the sampling of input / output signals and the processing system as a model, the input signal x (t) and the output signal y (t) are shown.
Are A / D converted respectively, and then A / D of consecutive M points
For example, a window function indicated by a wavy line is multiplied for each conversion data. One time window data is obtained by multiplying the data at the M points (0 ≦ p ≦ M−1) by the window function, and i = 1 to Nth of the time window data are sequentially cut out. Now, it is calculated based on the i-th (i = 1 to N) M-point discrete Fourier transform value X _i (k), Y _i (k), which is repeated N times and averaged on the discrete frequency axis. The transfer function estimate (Here, <N> indicates an average value of N samples), and this is expressed as follows in correspondence with the above equation (6).

The second term on the right side of the above equation is an error due to the disturbance noise similar to the equation (6), and when there is no correlation between the disturbance noise and the input signal, it becomes an error by chance.

In addition, the first term on the right side of the above equation includes a systematic (bias) error and a random error that occur when the true transfer function H (k) does not satisfy the above three requirements. The terms can be expressed as:

However, here, the true transfer function H (k) is the discrete frequency k
It is defined that Δf (Δf = 1 / Mτ) coincides with H (f), and the second term on the right side is the systematic error caused by the finite discrete Fourier transform described above, and the third term is the stochastic method. Error that occurs when the transfer function is estimated using various input signals (when the input fluctuates randomly even if disturbance noise is not mixed in the output, the transfer function estimate is Error occurs).

By the way, the actual observable signal is Xi as described above.
(K) and Yi (k), and it is difficult to evaluate the magnitude of each error term in the above equation.

Therefore, when performing the averaging operation N times, the estimated value of the transfer function obtained by using only the samples of the odd-numbered windows (i = 1, 3, ... Considering the estimated value of the transfer function obtained using only the samples of the (i = 2, 4, ..., N) th window, the difference ε (k)
Consider the properties of ^<N> . The transfer function is obtained by averaging the above two estimated values, and this is used as the estimated value by averaging N times.

However, N is an even number, and <N / 2, odd> is the average value of only the odd-numbered windows of the averages up to N times. Similarly, <N / 2, even> is only the even-numbered windows. Represents the average value using.

First, to study the first term on the right side of equation (9), the bias error is the same even if the transfer function is obtained using either odd or even window, and this is zero. Becomes

Next, consider the third term as the second term on the right side is postponed.

If the input signal and the disturbance noise are uncorrelated with each other, ▲ X ^* _i
▼ (k) U _i (k) is randomly distributed about the origin on the complex plane for each sample, so its expected value is zero. The _{^{▲ X * i ▼ (k)}} U phase angle _i (k) that are random (i.e., (9) does not change the statistical be positively changed a negative sign of the third term) nature And the fact that the expected value of N / 2 averages by the odd-numbered windows of the input auto spectrum is equal to the expected value of N / 2 averages by the even-numbered windows, the third term on the right-hand side is H _d defined by
It has the same statistical properties as ^<N> .

That is, H _d ^<N> is the same as that obtained by doubling the random error due to the disturbance noise included in the N-time averaged transfer function estimated value. And this is 1 / ▲ √ as the average number N increases.
It has the property of decreasing in proportion to ▼.

Finally, considering the second term, if the input signal is random on a sample-by-sample basis, the above discussion holds for the second term as well.

As described above, the statistical property of ε (k) ^<N> is similar to the sum of the random errors of the second term on the right side of equation (7) and the third term on the right side of equation (8), and , U _i (k) is unknown, the error can be evaluated by chance by using this ε (k) ^<N> .

To express this accidental error by power, ε (k) ^<N> may be multiplied by its complex conjugate ε ^* (k) ^<N> . That is, Pε
(k) ^<N> = ε ^* (k) ^<N> ε (k) ^<N> (11) Also, the ratio of the random error to the estimated value of the transfer function is as follows. In addition, the power of the error may be normalized by the power of the estimated value of the transfer function. That is, Further, when displaying Pε (k) ^<N> as a function of the average number N, an overall obtained by integrating Pε (k) ^<N> along the discrete frequency may be used. That is, This invention was created based on the above findings,
The invention comprises the following method and apparatus.

A first invention relates to a method of estimating a random error included in a transfer function estimated value obtained by averaging a certain number of times, and sequentially determines the input and output signals of an estimated signal transfer system in a predetermined function form. Of the discrete Fourier transform data X _i (k) and Y _i (k) are obtained by cutting through the time window of [where k is a discrete frequency, i is the number of the time window], and it is used on the discrete frequency k When the average value of the transfer function of N times (where N is an even number) is calculated, the average transfer function of each N / 2 times based on the data of every odd number and even number of the above time window Is calculated for each [where the superscript * represents a complex conjugate], and the error is calculated based on the difference between the two calculated values.

The second invention uses the random error calculated based on the first invention, and obtains the average number of times that the random error is within the allowable value from the relationship with the average number of times. Each of the input and output signals is sequentially cut out through a time window of a predetermined functional form to obtain discrete Fourier transform data X _i (k), Y _i (k) thereof (where k is a discrete frequency, i time window , The discrete frequency k
When obtaining the above average transfer function within the specified tolerance, the average transfer function based on the cut-out data for each odd-numbered and even-numbered time window above Is calculated sequentially up to the appropriate time window number for each
L is the time window number at each time point, and the superscript * represents the complex conjugate]
The error is calculated based on the difference between the two calculated values, the relationship between the calculated error and each corresponding time window number is obtained, and the required average number of times is calculated from the corresponding time window number and the allowable error determined based on the relationship. It is characterized by making a prediction.

A third invention uses the random error calculated based on the first invention and compares it with an allowable error value to obtain an estimated transmission error when the error is within the allowable value. The input and output signals of the transfer system are sequentially cut out through a time window of a predetermined function form, and discrete Fourier transform data X _i (k) and Y _i (k) thereof are obtained [where k is a discrete frequency, i number of time window], and the discrete frequency k
When obtaining the above average transfer function within the specified tolerance, the average transfer function based on the cut-out data for each odd-numbered and even-numbered time window above Are sequentially calculated [where L is the time window number at that point, and the superscript * represents a complex conjugate]. An error is calculated based on the difference between the two calculated values, and the calculated error and the allowable error are calculated. The feature is that the average transfer function of the average number of times within the allowable error is obtained by comparison.

A fourth invention relates to a device for carrying out the above-mentioned first invention, including a sampling unit for A / D converting input / output signals of an estimated signal transmission system and storing the same in a memory, M of D conversion data
One time window data is obtained by multiplying each point by a predetermined window function, and a discrete Fourier transform is applied to data for each time window from i = 1 to N-th (where N is an even number selected appropriately). A first calculation unit that performs a transformation to obtain X _i (k) and Y _i (k) [where k is a discrete frequency], and an average transfer based on Fourier transform data for each of the odd-numbered and even-numbered time windows function Is separately calculated [where superscript * represents a complex conjugate], and a second calculation unit that calculates an error based on the difference between the two calculated values.

A fifth invention relates to a device for carrying out the above-mentioned second invention, which comprises a sampling unit for A / D converting the input and output signals of the estimated signal transmission system and storing the same in a memory, and One of the time window data is obtained by multiplying each of the D conversion data by M points sequentially by a predetermined window function, and the discrete Fourier transform is performed on the data for each time window to obtain X _i (k), Y _i (k ) [Where k is a discrete frequency, i is a time window number], and an average transfer function based on Fourier transform data for each of the odd-numbered and even-numbered time windows Is calculated sequentially for each up to a predetermined time window number [However,
L is the time window number at each time point, and the superscript * represents the complex conjugate]
The second arithmetic unit that calculates an error corresponding to each time window number based on the difference between the averaging unit and the two calculated values, and the relational expression between the calculation error and the time window number is obtained and set in advance based on the relational expression. And an average count predicting unit that determines a time window number within the allowable error.

A sixth invention relates to a device for carrying out the above-mentioned third invention, including a sampling unit for A / D converting input / output signals of an estimated signal transmission system and storing the same in a memory, One time window data is obtained by multiplying the D conversion data by a predetermined window function,
A first arithmetic unit for obtaining X _i (k) and Y _i (k) [where k is a discrete frequency] by performing a discrete Fourier transform on the data for each time window, and an odd number of the above time window, Average transfer function based on even-numbered Fourier transform data Is calculated sequentially for each [where L is the time window number at each time point,
A superscript * represents a complex conjugate], a second arithmetic unit that sequentially calculates an error based on the difference between the two calculated values, and an allowable error by comparing the calculated error with a preset allowable error. And a comparison unit for extracting the average transfer function in.

[Operation] When the method of the first aspect of the invention is performed using the apparatus of the fourth aspect of the invention, the difference between the average transfer functions of N / 2 times based on the data of the odd number and the even number is obtained. Based on this difference, the magnitude of the random error included in the transfer function estimated value calculated by averaging N times is found.

Further, when the method of the second invention is carried out by using the device of the fifth invention, the difference between the average transfer functions based on the odd-numbered data and the even-numbered data is thereby sequentially increased to appropriate time window numbers. Calculated separately, and then the relationship between the two is obtained from the calculated error and its corresponding time window number, based on the relationship, the time window number when the error falls within the allowable value,
That is, the required average number of times is predicted.

When the method of the third aspect of the invention is carried out using the device of the sixth aspect of the invention, the difference between the average transfer functions based on the odd-numbered and even-numbered data and the error tolerance are sequentially compared. , The estimated transmission error when the tolerance value is entered is obtained.

[Embodiment] First, the present invention will be described based on a computer simulation result.

FIG. 3 shows an estimated signal transfer system used in the simulation.

The FIR type digital filter 20 is a 256-point type digital filter 20 prepared inside the computer, and its transfer function is shown in FIG. For the input signal x (p), a signal obtained by sampling wideband Gaussian white noise is used as the disturbance noise u (p).
, A pseudo-normal random number sequence generated from a computer was used as a signal having no correlation with x (p).

The discrete Fourier transform in this simulation was executed with double precision, FFT was 1024 points, and Hanning's window was used for the window function. In addition, the time windows are set so that they do not overlap in order to perform averaging independently. DC is the discrete frequency k
From 401 to 400 (the value obtained by multiplying the value of k by 2π / 1024 is the normalized angular frequency) is used for display.

First, as a preliminary study, a deterministic signal as an input signal (a periodic signal whose spectrum has a magnitude of 1 at all frequencies and whose phase has a delay proportional to the square of the frequency and which is synchronized with each time window) Was used to calculate the power P ε (k) ^<N> of the random error in the absence of disturbance noise. The result is, of course, zero since the average number N = 2. Next, the above-mentioned input signal is changed to white noise, and similarly, the power P of the random error is
ε (k) ^<N> was calculated. This Pε (k) ^<N> is, as shown in FIG. 5, the form of the transfer function described in the above equation (8) (fourth
An error corresponding to the third term on the right-hand side of the equation (8), which is still affected by (see the figure), appears, and it was confirmed that the present invention can detect the error.

FIG. 6 shows the disturbance noise u (p) in the system of FIG.
Is the result when S is mixed into the output signal y (p) of the system at an S / N ratio of 37 dB. In the figure, the calculated ξ (k) ^<N> , that is, the value of the power of the random error normalized by the power of the estimated value of the transfer function is shown in the log on the vertical axis, and the discrete frequency is linear on the horizontal axis. ing.

In this normalization, the power P ε of the accidental error is
Since (k) ^<N> fluctuates due to the discrete frequency k, this P
The value of ε (k) ^<N> was subjected to a simple moving average of 41 points for k, and then divided by the power of the estimated value of the transfer function.

According to this, when the average number N = 256 and 1024, there is almost no difference in the error near the peak of the transfer function (see Fig. 4), but there is room for improvement due to the increase in the average number near the tail. It is shown that there is.

FIG. 8 shows how the random error contained in the estimated value of the transfer function changes depending on the average number of times under various disturbance noise mixing conditions. The vertical axis is the overall error power by chance and the horizontal axis is the average frequency.The dotted line in the figure shows the case where no disturbance noise is mixed, the solid line shows S / N of -2.8 dB, and the broken line shows S / N. In the case of 37 dB, the two-dot chain line shows the case where the S / N is 37 dB and the dispersion of the disturbance changes.

According to this, how to reduce the power of the random error with respect to the increase of the average number tends to be almost the same regardless of the condition, and this power is almost equal to the disturbance noise u (p) and the input signal x (p). It turns out that it depends on the S / N.

As described above, according to this, when the magnitude of the random error included in the transfer function estimated under a certain average number is known, and conversely, when it is desired to estimate the transfer function within the allowable value of the random error, the above As can be seen from FIG. 8, the minimum required number of averages is predicted and determined in the averaging process from the changing state of the random error, or the random error and the allowable value of the random error are compared sequentially in the averaging process. Then, the objective is achieved by extracting the transfer function when it is within the allowable value.

Next, an example in which a bandpass analog filter having a center frequency of 2.1 kHz with variable Q is measured will be described as an example of an actual measurement target.

In this system, wideband Gaussian white noise is used for the input signal x (t), and Gaussian white noise of the white noise generator having no correlation with x (t) is used for the disturbance noise u (t).

FIGS. 1 and 2 show a processing system for obtaining a transfer function estimated value and a random error included in the estimated transfer function value based on the input and output of the above system. An input memory 2 to be stored, and a first arithmetic unit 3 for executing a discrete Fourier transform using the stored data for each window.
2 channel FFT analyzer, and the first and second averaging units 4 and 5 for respectively performing the averaging process by individually introducing the Fourier transform data for the data of the odd-numbered and even-numbered windows, and the respective averaged data thereof. The second arithmetic unit 6 which executes the operation of the odd-numbered and even-numbered extraordinary transfer functions based on the above, and introduces the odd-numbered and even-numbered extraordinary transfer functions, and calculates the average of the two values. An adding unit 7 and a subtracting unit 8 for calculating an error ε (k) ^<N> corresponding to the difference, and a converting unit for converting the data of the adding unit 7 and the subtracting unit 8 into power as shown in FIG. 9, a normalization operation unit 10 for normalizing the power with a transfer function, and a general-purpose computer in which each operation function of the power overall operation unit 11 is programmed.

In the above components, the input / output signal of the analog filter is A / D converted and then sent to the first arithmetic unit 3 to calculate the power spectrum and cross spectrum of the input signal and the output signal. Subsequently, the power spectrum and the cross spectrum are transferred to a computer that executes the arithmetic operations of the averaging units 4 and 5 in FIG. 1 via GPIB,
Therefore, the above operations are sequentially executed to calculate the random error ξ (k) ^<N> normalized by the transfer function, the overall error power Poa ε (k) ^<N>, and the transfer function. .

FIG. 7 shows how the random error contained in the estimated value of the transfer function changes under various conditions depending on the average number of times. The variance of the disturbance was varied from the example of FIG. In case of not collecting data, the filter Q is 2.5
The difference is that the measurements were performed for the cases (illustrated by the broken line) and 10 (illustrated by the solid line). Also in this case, as in FIG. 8, the magnitude of the random error included in the estimated value of the transmission error based on the relationship between the magnitude of the calculated random error and the average number of times,
Alternatively, it is possible to determine the average number of times required to fall within a certain error tolerance.

In the above description, an overall of 401 discrete frequencies k from DC to 400 (a value obtained by multiplying the value of k by 2π / 1024 is a normalized angular frequency) is used. When it is desired to estimate only the neighborhood, the overall part may be used.

[Advantages of the Invention] As described above, according to the present invention, when the transfer function is estimated by the discrete Fourier transform, only the random error included in the measured transfer function is extracted and the magnitude thereof is calculated, or the magnitude thereof is calculated. And the average number of times, the required average number is predicted and determined.As a result, the error range of the measurement transfer function can be clarified, and a clear guideline can be given when designing the system, or the required average number of times The predictive decision makes it possible to obtain a transfer function of desired accuracy in a minimum measuring time.

[Brief description of drawings]

1 and 2 are block diagrams showing an embodiment of the present invention, FIG. 3 is a block diagram of a signal transmission system in which the computer simulation of the present invention is performed, and FIG. 4 is a block diagram of the filter shown in FIG. FIG. 5 is a diagram showing a transfer function, FIG. 5 is a diagram showing the power of the random error extracted by the present invention when white noise is used as an input signal, and FIG. 6 is a normalized random chance when the S / N is 37 dB. FIG. 7 is a diagram showing an error, FIG. 7 and FIG. 8 are diagrams showing a relation between the normalized random error and the average number of times, and FIG. 9 is a block diagram showing a signal transmission system used in the theoretical study of the present invention.
FIG. 10 is a waveform diagram showing a model of the sampling and processing system of the input / output signal in the present invention. 1: A / D conversion unit, 3: First calculation unit 4,5: Averaging unit, 6: Second calculation unit 7: Addition unit, 8: Subtraction unit

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Masahisa Ohashi 2-4-1 Nishishinjuku, Shinjuku-ku, Tokyo Ono Sokki Co., Ltd. In-house Examiner Hiroyuki Kikui

Claims (6)

[Claims] 1. The input and output signals of the estimated signal transfer system are sequentially cut out through time windows of a predetermined functional form to obtain respective discrete Fourier transform data X _i (k), Y _i (k). [Where k is a discrete frequency, i is the number of the time window], and when using it to find the average value of N times [where N is an even number] of the transfer function on the discrete frequency k, an odd number of the above time window, Each N / 2 average transfer function based on every even numbered data Is calculated for each [where the superscript * represents a complex conjugate], and the error is obtained based on the difference between the two calculated values. 2. The input and output signals of the signal transmission system to be estimated are sequentially cut out through a time window of a predetermined function form, and discrete Fourier transform data X _i (k), Y _i (k) thereof are obtained. [Where k is a discrete frequency, i is the number of the time window], and when using this to find the average transfer function on the discrete frequency k within the specified tolerance, the cut-out data for each odd-numbered and even-numbered time window is used. Mean transfer function based Is calculated sequentially up to the appropriate time window number for each
L is the time window number at each time point, and the superscript * represents the complex conjugate]
The error is calculated based on the difference between the two calculated values, the relationship between the calculated error and each corresponding time window number is obtained, and the required average number of times is calculated from the corresponding time window number and the allowable error determined based on the relationship. A method of estimating a random error in a transfer function estimated value, which is characterized by performing prediction. 3. The input and output signals of the signal transmission system to be estimated are sequentially cut out through a time window having a predetermined function form, and discrete Fourier transform data X _i (k) and Y _i (k) of the data are obtained. [Where k is a discrete frequency, i is the number of the time window], and when using this to find the average transfer function on the discrete frequency k within the specified tolerance, the cut-out data for each odd-numbered and even-numbered time window is used. Mean transfer function based Are sequentially calculated [where L is the time window number at that point, and the superscript * represents a complex conjugate]. An error is calculated based on the difference between the two calculated values, and the calculated error and the allowable error are calculated. A method of estimating an accidental error in a transfer function estimation value, which is characterized by comparing and obtaining an average transfer function of an average number of times within an allowable error. 4. A sampling section for A / D converting the input and output signals of the signal transmission system to be estimated and storing the same in a memory, and a sampling section obtained by multiplying M points of the A / D converted data by a predetermined window function. As one time window data, discrete Fourier transform is performed on data for each time window from i = 1 to N-th (where N is an even number selected appropriately), and X _i (k), Y _i (K)
A first arithmetic unit for obtaining [where k is a discrete frequency],
Average transfer function based on Fourier transform data for every odd number and even number in the above time window In each of the transfer function estimation values, which is composed of an averaging part which calculates [wherein the superscript * represents a complex conjugate] and a second calculation part which calculates an error based on the difference between the two calculated values. Accidental error measuring device. 5. A sampling unit for A / D converting the input and output signals of the estimated signal transfer system and storing the same in a memory, and multiplying each A point of the A / D converted data by a predetermined window function. Is taken as one time window data and discrete Fourier transform is performed on the data for each time window to obtain X _i (k) and Y _i (k) [where k is the discrete frequency and i is the time window number] A first calculation unit and an average transfer function based on Fourier transform data for each of the odd-numbered and even-numbered time windows Is calculated sequentially for each up to a predetermined time window number [However,
L is the time window number at each time point, and the superscript * represents the complex conjugate]
The second arithmetic unit that calculates an error corresponding to each time window number based on the difference between the averaging unit and the two calculated values, and the relational expression between the calculation error and the time window number is obtained and set in advance based on the relational expression. And an erroneous error estimation device in the transfer function estimation value, which comprises an average number prediction unit that determines a time window number falling within the allowable error. 6. A sampling unit for A / D converting the input and output signals of the signal transmission system to be estimated and storing the same in a memory, and the A / D converted data multiplied by a predetermined window function for one time. Window data, a first calculation unit that obtains X _i (k) and Y _i (k) [where k is a discrete frequency] by performing a discrete Fourier transform on the data for each time window, and the time window Mean transfer function based on Fourier transform data for every odd and even number of Is calculated sequentially for each [where L is the time window number at each time point,
A superscript * represents a complex conjugate], a second arithmetic unit that sequentially calculates an error based on the difference between the two calculated values, and an allowable error by comparing the calculated error with a preset allowable error. And a comparison unit for extracting the average transfer function in, and an accidental error estimation device in the transfer function estimation value, which comprises: