JPH08317254A - Ghost elimination device - Google Patents

Abstract

PURPOSE: To reduce the ghost left unerased even in the case of presence of a ghost between the positions of taps discretely existing in a filter. CONSTITUTION: This ghost elimination device is provided with a largest/maximal value detection part 4 which obtains absolute values of correlations between a reference signal (r) and an intermediate signal x' generated from the reference signal (r) and an input signal (x) in the position of a tap for the largest/maximal absolute value absolute value and in positions before and after this position, a largest/maximal value correction part 5 which obtains an approximate curve from absolute values of correlations obtained by the largest/maximal value detection part 4 and uses this approximate curve to obtain the ghost position for the largest/maximal value absolute value of correlations, and a tap coefficient distribution part 6 which corrects the tap coefficient in positions of two taps on both sides of the ghost position obtained by the maximum correction part 5 by successive correction type control.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a ghost eliminating device for eliminating a ghost contained in an input signal of a television receiver or the like.

[0002]

2. Description of the Related Art When a radio wave transmitted directly from a transmitting antenna of a broadcasting station and a radio wave reflected by a building or a mountain are simultaneously received by a receiving antenna, images of both radio waves are shifted. The so-called ghost disorder occurs.

In order to remove this ghost disturbance, a ghost removing device is used which processes an input signal with a filter circuit to remove the ghost signal.

Generally, the filter circuit uses a transversal filter to form an FIR type configuration (Finite Impulse Response digital filter) shown in FIG. 6 and an IIR type configuration (Infinite type) shown in FIG. Impulse Response digital filter, cyclic digital filter), or both of these are used in FIG.
The configuration shown in is used. The transversal filter in FIGS. 6 to 8 is a circuit as shown in FIG. 9, and is composed of a delay device for each fixed time, a storage device for storing tap coefficients, a multiplier, and an adder. The tap coefficient is set corresponding to the delay time and magnitude of the ghost.

The methods for calculating the tap coefficients of the transversal filter are roughly classified into a batch calculation method and a sequential correction method. Here, a widely used iterative correction method will be described.

It is assumed that the input signal is x _i , the output signal of the filter circuit is y _i , the reference signal is r _i , and the number of taps of the transversal filter is N. Letting the error signal be e _i , equation (2
Defined in 1).

E _i = y _i −r _i (i = 0 to N−1) (21) The square integral value E of the error signal e _i shown in Expression (22) as an evaluation function representing the magnitude of the error. To use.

[0008]

[Equation 1]

MSE generally used in the iterative correction method
In the (Mean Square Error, least square error) method, the correction of the tap coefficient is repeated so that the evaluation function E shown in the above equation (22) becomes small. It has been mathematically proved that the evaluation function E converges. That is, the formula (2
As in 3), the correlation calculation result of the input signal x _i and the error signal e _i is defined as s _i , the i-th tap coefficient c _i ⁽ⁿ⁾ is set, and α is a small coefficient. Is the expression (2
4). Then, c _i ^{(n) is changed} to c _i ^{(n + 1)}
By updating to, the evaluation function E gradually decreases.

[0010]

[Equation 2]

C _i ^{(n + 1)} = c _i ⁽ⁿ⁾ −αs _i (i = 0 to N−1) (24) Here, the coefficient α is an experimen- tal balance between convergence and stability of tap coefficients. Can be decided. If the coefficient α is small, the stability is good but the convergence is poor. If the coefficient α is large, the convergence is fast but the stability is poor, and the output diverges.

As shown in FIG. 10, in the ghost removing apparatus using the successive correction method, first, the input signal x is input to the filter circuit 17, the output signal y is output, and the reference signal generating unit 11 outputs the signal. A reference signal r is generated. Next, in the error signal generator 18, the reference signal r is subtracted from the output signal y of the filter circuit 17 to generate the error signal e. Next, in the correlation calculation unit 13, the calculation shown by the above equation (23) is performed to input the input signal x and the error signal e.
The correlation s with Next, in the tap coefficient calculation unit 16, the calculation shown in the above equation (24) is performed, and the tap coefficient c
Ask for. This is sent to the filter circuit 17 to correct the tap coefficient.

Then, the output signal y is calculated again, and the above correction process is repeated until the evaluation function E becomes small to some extent. By repeating the modification of the tap coefficient sufficiently many times, the final tap coefficient is obtained.

FIG. 11 shows signal waveforms in the above processing steps.
Shown in The ghost signal is removed from the input signal x to obtain the output signal y. Here, an equalization pulse is used as the reference signal.

The following method has been considered as one of the speed-ups of this method. That is, FIG.
First, as shown in FIG.
Generate Then, in the intermediate signal generator 22, the reference signal r is subtracted from the input signal x to obtain the intermediate signal x ′.
Generate Next, the correlation calculator 23 obtains the correlation s between the reference signal r and the intermediate signal x ′. Assuming that the number of taps corresponding to the width of the reference signal r is M, the correlation s is expressed by the formula (2
Given by 5).

[0016]

(Equation 3)

Next, the maximum / maximum detecting section 24 detects the position where the absolute value of the correlation s becomes the maximum value or the maximum value.

Then, in the tap coefficient calculator 26,
A tap coefficient c corresponding to the detected position is obtained. The tap coefficient c _i is set to be 1 when the reference signal r and the intermediate signal x ′ exactly match, and is calculated by the equation (26).

[0019]

[Equation 4]

This is sent to the filter circuit 27 to correct the tap coefficient. At the same time, the intermediate signal generation unit 22 updates only the area of the intermediate signal x ′ that changes depending on the corrected tap coefficient, and repeats the above correction processing until the evaluation function E becomes small to some extent. The final tap coefficient is obtained by repeating the correction of the tap coefficient several times.

FIG. 13 shows signal waveforms in the above processing steps.
Shown in An output signal y from which the ghost signal has been removed is obtained from the input signal x.

In this ghost removal processing, the number of tap coefficients to be modified at one time and the number of repetitions of modification are reduced as compared with the above-described processing of modifying all N taps by the MSE method, so that the amount of calculation is reduced. It is possible to process at high speed.

[0023]

The position of the ghost signal is a continuous value and the position of the tap of the filter is a discrete value. Therefore, as described above, in the method of correcting only the tap coefficient corresponding to the maximum value or the maximum value of the absolute value of the correlation between the signal including the received ghost signal and the reference signal, the ghost The position of the signal and the position of the tap coefficient will deviate within the discrete interval of the position of the tap. Due to this shift, the ghost remains, and there is a problem that the ghost cannot be removed with good characteristics.

FIG. 14A shows the correlation between the actual ghost and the tap position. As shown in the figure, here, the actual ghost exists between the positions of the taps for which the correlation is calculated. In this case, the correlation in which the absolute value is maximum or maximum deviates from the actual ghost. 14
(B) shows the calculated tap coefficient and the actual ghost. At this time, the calculated position and size of the tap coefficient are different from the actual position and size of the ghost. FIG. 15A shows the equalized pulse waveforms corresponding to the calculated tap coefficient and the actual ghost. In the figure, the solid line shows the waveform corresponding to the actual ghost signal, and the broken line shows the waveform corresponding to the calculated tap coefficient. FIG. 15B shows the waveform of the ghost signal remaining after the latter is subtracted from the former. As shown in the figure, a large ghost disappears and remains at the edge of the waveform. In addition to the edge portion, a large amount of the remaining portion remains.

As described above, in the ghost elimination device in which the tap coefficient is provided only at the position where the absolute value of the correlation is maximum or maximum, when the ghost exists in the middle of the tap positions discretely present in the filter, , The ghost disappearance becomes large. This is a major problem as a ghost remover because the purpose of the ghost remover is to remove all ghosts.

The present invention has been made in view of the above problems, and an object of the present invention is to provide a ghost removing device which has a small amount of erasure even when a ghost exists in the middle of discrete tap positions in a filter. There is.

[0027]

In order to solve the above-mentioned problems, the ghost elimination device according to the first aspect of the invention is based on the correlation between an input signal containing a ghost signal and a reference signal, and the position of a tap in a transversal filter. In the ghost removing apparatus that corrects the tap coefficient in the sequential correction control, the maximum / maximum detection unit that obtains each correlation value at the position of the tap at which the absolute value of the correlation is maximum or maximum and the positions before and after this position, From each of the correlation values obtained by the maximum / maximum detection unit, an approximate curve of the correlation is obtained,
Using the above-mentioned approximate curve, the maximum / maximum correction part for _{obtaining the} ghost position p _{real at} which the absolute value of the correlation becomes maximum or maximum, and the two taps sandwiching the ghost position obtained by the maximum / maximum correction part It is characterized in that it is provided with a tap coefficient correction unit that corrects the tap coefficient at the positions p ₁ and p ₂ by successive correction type control.

According to a second aspect of the ghost elimination device of the present invention, in the ghost elimination device of the first aspect, the maximum / maximum correction unit obtains the absolute value s _real of the correlation at the position p _real using the approximate curve. , The tap coefficient correction unit obtains the tap coefficient c _real indicating the actual magnitude of the ghost based on the absolute value s _{real of the} correlation, and c ₁ = c _real × (p ₂ −p _real ) c ₂ = c _real × By (p _real −p ₁ ), each tap coefficient c _{1 at} the positions p ₁ and p ₂ is
It is characterized by finding c ₂ .

[0029]

With the configuration of the ghost elimination device according to claim 1, when an input signal including a ghost signal is input,
The maximum / maximum detector detects the absolute value of each correlation at the position p of the tap at which the absolute value of the correlation s between the input signal and the reference signal becomes maximum or maximum and the positions p−1 and p + 1 that are positions before and after the position p. The values s _p , s _p-1 and s _{p + 1} are obtained.

Next, the maximum / maximum correction unit obtains an approximated curve of the correlation s from the absolute values s _p , s _p-1 and s _{p + 1 of} each of the above correlations, and uses the above described approximated curve to determine the ghost position. As a result, the position p _{real at} which the absolute value of the correlation s becomes maximum or maximum is obtained.

Next, the tap coefficient correction unit obtains the positions p ₁ and p ₂ of the two taps sandwiching the ghost position p _real, and the tap coefficients of the taps in the transversal filter are obtained at the positions p ₁ and p ₂ . It is corrected by the sequential correction type control.

Therefore, the tap coefficients are corrected at the positions p ₁ and p ₂ of the two taps sandwiching the position p _real where the absolute value of the correlation s is maximum or maximum.

As a result, unlike the ghost removing device in which the tap coefficient is provided only at the position where the absolute value of the correlation becomes maximum or maximum, even when the ghost exists in the middle of the tap positions discretely present in the filter, the ghost exists. Can be reduced.

With the configuration of the ghost eliminating device according to the second aspect, the maximum / maximum correction unit obtains the absolute value s _real of the correlation at the position p _real using the above approximation curve.

Then, the tap coefficient correction unit obtains the tap coefficient c _real indicating the actual magnitude of the ghost based on the absolute value s _{real of the} correlation, and c ₁ = c _real × (p ₂ −p _real ) c ₂ = c _real × (p _real −p ₁ ), each tap coefficient c _{1 at} the positions p ₁ and p ₂
Find c ₂ . Then, at the positions p ₁ and p ₂ , the tap coefficients of the taps in the transversal filter are corrected to c ₁ and c ₂ by the successive correction control.

Therefore, the two tap coefficients c ₁ and c ₂
Is approximately equal to the actual ghost size, and 2
Each of the two tap coefficients c ₁ and c ₂ becomes larger as the position is closer to the actual ghost position. As a result, the ghost can be removed more accurately, and the remaining ghost can be reduced.

[0037]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The following will describe one embodiment of the present invention with reference to FIGS. The ghost removing apparatus according to the present embodiment removes the ghost signal by correcting the tap coefficient at the tap position in the transversal filter by the successive correction control based on the correlation between the input signal including the ghost signal and the reference signal. It is a ghost removing device.

As shown in FIG. 1, a reference signal generator 1, an intermediate signal generator 2, a correlation calculator 3, a maximum / maximum detector 4,
A maximum / maximum correction unit 5, a tap coefficient distribution unit (tap coefficient correction unit) 6, and a filter circuit 7 using a transversal filter are connected in this order. And
The input signal x is input to the intermediate signal generator 2 and the filter circuit 7, and the filter circuit 7 outputs the output signal y. The output of the tap coefficient distribution unit 6 is also input to the intermediate signal generation unit 2. Further, the output (reference signal r) of the reference signal generator 1 is also input to the correlation calculator 3.

Next, the ghost removing operation with the above configuration will be described. It is assumed that the input signal is x _i , the output signal of the filter circuit is y _i , the reference signal is r _i , and the number of taps of the transversal filter is N.

An input signal including a ghost signal is input as x. On the other hand, the reference signal generator 1 generates the reference signal r. Then, the intermediate signal generator 2 subtracts the reference signal r from the input signal x to generate the intermediate signal x ′, as shown in Expression (1).

X ′ _i = x _i −r _i (i = 0 to N−1) (1) The intermediate signal x ′ is an index of the error of the input signal x with respect to the reference signal r. The square integral value E of the intermediate signal x ′ _i shown in Expression (2) is used as the evaluation function representing the magnitude of this error.

[0042]

(Equation 5)

The correlation calculator 3 calculates the correlation s between the reference signal r and the intermediate signal x '. That is, when the number of taps corresponding to the width of the reference signal r is M, the correlation s is given by the equation (3).

[0044]

(Equation 6)

Next, the maximum / maximum detector 4 determines the correlation s
The absolute values s _p , s _p-1 and s _{p + 1} of each correlation are detected at the position p of the tap where the absolute value of is maximum or the maximum and the positions p-1 and p + 1 which are positions before and after the position _p .

Next, the maximum / maximum correction unit 5 determines the positions p, p.
Absolute values s _p , s _p−1 , s of each correlation at −1, p + 1
The position and size of the ghost are corrected from _{p + 1} as follows.

That is, first, an approximate curve for the relationship between the position and the correlation is obtained. In this embodiment, a quadratic function is approximated as shown in FIG. Although a quadratic function is selected as the approximate curve here, the present invention is not limited to this.

Next, the position where the absolute value of the correlation s is maximum or maximum, that is, the corrected ghost position p _real and the tap coefficient c _real indicating the ghost size are calculated from the peak value in the above approximation curve. Ask. p _real and c
_{The real} is calculated by the equations (4) to (8), respectively. That is, if m = s _p −s _p−1 (4) and n = s _p −s _{p + 1} (5),

[0049]

(Equation 7)

[0050]

(Equation 8)

[0051]

[Equation 9]

It is

As described above, based on the absolute value of the correlation at the position p where the absolute value of the correlation is maximum or maximum and the adjacent position, the absolute value of the correlation is maximized by correcting the ghost position using the approximate curve. Alternatively, it is possible to obtain a value closer to the actual position and size of the ghost, as compared with the ghost removing device in which the tap coefficient is provided only at the maximum position.

Next, as shown in FIG. 3, the tap coefficient distribution unit 6 performs two tap positions p ₁ and p ₂ sandwiching the ghost position p _real and each position p ₁ and p _{2 as} follows.
Then, the magnitudes c ₁ and c ₂ of the tap coefficient at are obtained. Note that p ₁ and p ₂ are p−1 and p, respectively,
It is either p + 1.

That is, first, p ₁ and p ₂ are expressed by equation (9),
It is calculated by the equation (10). p ₁ = INT (p _real ) (9) p ₂ = p ₁ +1 (10) Here, INT (X) gives the integer part of X.

Next, at the positions p ₁ and p ₂ , the tap coefficient c
By distributing _real , the tap coefficient magnitudes c ₁ and c ₂ corresponding to the positions p ₁ and p ₂ are obtained. In the present embodiment, for example, as shown in Expressions (11) and (12), c _real is distributed to the positions p ₁ and p ₂ with the ratio of p ₂ −p _real and p _real −p ₁ . However, the distribution method is not limited to this. c ₁ = c _real × (p ₂ −p _real ) (11) c ₂ = c _real × (p _real −p ₁ ) (12) As described above, p ₁ , p ₂ , c ₁ , and c ₂ are Desired.

As in the above equations (9) to (12), p
_{When 1} , p ₂ , c ₁ , and c ₂ are determined, the conditions of Expressions (13) to (16) are satisfied. p ₁ ≦ p _real ≦ p ₂ (13) When p ₁ = p _real c ₁ = c _real (14) When p ₂ = p _real c ₂ = c _real (15) c ₁ + c ₂ = c _real (16) However, the distribution method is not limited to the one that satisfies Expression (16).

These p ₁ , p ₂ , c ₁ and c ₂ are sent to the filter circuit 7. In the filter circuit 7, it corrects the tap coefficients c _1, c _2, respectively, in the tap position p _1, p _2.

The tap coefficients c ₁ and c ₂ are also input to the intermediate signal generator 2. The intermediate signal generating unit 2, 'among the regions of the _{i (i = 0~N-1)} , an intermediate signal x whose value changes by a modification of the tap coefficients' intermediate signal x only in the region of _i, and updates the value .

The above correction process is repeated until the evaluation function E becomes small to some extent. The final tap coefficient is obtained by repeating the correction of the tap coefficient several times.

As described above, in the present embodiment, of the N taps, only the two tap positions p ₁ and p ₂ need to be modified, and the number of tap coefficients modified at one time is reduced. be able to. Further, since the tap coefficient is corrected only at the tap position closest to the actual ghost position, the number of times of necessary correction repetition can be reduced. Thereby, it is possible to reduce the amount of calculation and process at high speed.

If there are a plurality of ghost signals and the absolute values of the above correlations are maximum at a plurality of positions,
The above operation may be performed for the plurality of maximum positions.

FIG. 4A shows the actual ghost and the correlation at the tap position. Here, the actual ghost exists in the middle of the positions of the taps for which the correlation is calculated. In this case, the correlation in which the absolute value is maximum or maximum deviates from the actual ghost.

FIG. 4B shows the tap coefficient calculated by the procedure described in this embodiment and the actual ghost. The two calculated tap coefficients sandwich the actual ghost. Also, the tap coefficient c indicating the magnitude of the ghost
_{Since the real} is distributed as shown in the above equations (11) and (12), the sum of the _two tap coefficients c ₁ and c ₂ is almost equal to the actual magnitude of the ghost. Furthermore, by the above distribution method, two tap coefficients c ₁ and c
The ratio to ₂ is the tap position p as shown in equation (17).
_It increases as the distance between ₂ and the actual ghost position p _real increases, and decreases as the distance between the tap position p ₁ and the actual ghost position p _real increases. c ₁ / c ₂ = (p ₂ −p _real ) / (p _real −p ₁ ) (17) That is, the two tap coefficients c ₁ and c ₂ are the ghosts at the tap positions p ₁ and p ₂ respectively. It is set such that the closer it is to the position of, the larger it becomes. Thereby,
The ghost can be removed more accurately, and the remaining ghost can be reduced.

FIG. 5 shows how the ghost is removed as described above. That is, FIG. 5A shows equalized pulse waveforms respectively corresponding to the calculated tap coefficient and the actual ghost. In the figure, the solid line represents the waveform corresponding to the actual ghost signal, and the broken line represents the waveform corresponding to the calculated two tap coefficients. On the other hand, FIG.
(B) shows the remaining waveform obtained by subtracting the latter, that is, the waveform corresponding to the calculated two tap coefficients from the former, that is, the waveform corresponding to the actual ghost signal. FIG.
Compared to the conventional technique shown in (b), the unerased portion of the edge of the waveform is small, and the unerased portion other than the edge portion is also small.

As described above, even with respect to the ghost existing in the middle of the tap positions, the remaining taps can be reduced by providing tap coefficients at two positions sandwiching the ghost.

In the above embodiment, the maximum and the maximum of the absolute value of the correlation are corrected by approximation with a quadratic function, but the approximation curve is not limited to this, as described above. For example, an nth degree polynomial such as a cubic function may be used.
Another functional system may be used.

Further, in the above-described embodiment, each processing is divided into corresponding processing units, but it may be processed by one arithmetic unit, or by a general-purpose CPU (central processing unit), a computer is used. The processing may be performed by a program.

[0069]

As described above, the ghost elimination device according to claim 1 of the present invention determines the tap coefficient at the tap position in the transversal filter based on the correlation between the input signal including the ghost signal and the reference signal. In a ghost elimination device that corrects by successive correction type control, a maximum / maximum detection unit that finds each correlation value at a tap position where the absolute value of the correlation is maximum or maximum and positions before and after this position, and the maximum / maximum A maximum / maximum correction unit that obtains an approximate curve of the correlation from the correlation values obtained by the detection unit and obtains a ghost position p _{real at} which the absolute value of the correlation becomes maximum or maximum using the approximate curve. A tap coefficient that corrects the tap coefficient by successive correction control at the positions p ₁ and p ₂ of the two taps that sandwich the ghost position determined by the maximum / maximum correction unit. This is a configuration including a number correction unit.

Therefore, even when the ghost exists in the middle of the tap positions discretely existing in the filter,
This has the effect of reducing the remaining ghost.

In the ghost removing apparatus according to the second aspect, in the ghost removing apparatus according to the first aspect, the maximum / maximum correction unit obtains the absolute value s _real of the correlation at the position p _real using the approximate curve. , The tap coefficient correction unit obtains the tap coefficient c _real indicating the actual magnitude of the ghost based on the absolute value s _{real of the} correlation, and c ₁ = c _real × (p ₂ −p _real ) c ₂ = c _real × By (p _real −p ₁ ), each tap coefficient c _{1 at} the positions p ₁ and p ₂ is
This is a configuration for obtaining c ₂ .

Therefore, it is possible to remove the ghost with higher accuracy and reduce the remaining ghost.

[Brief description of drawings]

FIG. 1 is a block diagram showing a schematic configuration of an entire ghost removing apparatus according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram showing a method of correcting the position and size of a ghost in the ghost removing device of FIG. 1 by using a quadratic function approximation.

FIG. 3 is an explanatory diagram showing a distribution method of tap coefficients in the ghost removing device of FIG. 1.

4A and 4B are explanatory diagrams showing a state of tap coefficient distribution processing in the ghost elimination device of FIG. 1.

5A and 5B are explanatory diagrams showing a state of ghost removal processing in the ghost removal apparatus of FIG.

FIG. 6 is a block diagram showing a configuration of an FIR type filter circuit using a transversal filter.

FIG. 7 is a block diagram showing a configuration of an IIR type filter circuit using a transversal filter.

FIG. 8 is a block diagram showing a configuration of a filter circuit having both FIR type and IIR type using a transversal filter.

FIG. 9 is a block diagram showing a configuration of a transversal filter used in a conventional ghost removing device.

FIG. 10 is a block diagram showing a configuration of a ghost removing apparatus using a conventional iterative correction method.

FIG. 11 is an explanatory diagram showing a signal waveform in a process of a ghost removing apparatus using a conventional iterative correction method.

FIG. 12 is a block diagram showing a configuration of a ghost removing apparatus using a conventional iterative correction method.

FIG. 13 is an explanatory diagram showing a signal waveform in a process of a ghost removing apparatus using a conventional iterative correction method.

FIGS. 14A and 14B are explanatory diagrams showing a state of tap coefficient calculation processing in the conventional ghost removing device.

15 (a) and 15 (b) are explanatory views showing the occurrence of unexposed ghost in the conventional ghost removing device.

[Explanation of symbols]

 1 Reference signal generation unit 2 Intermediate signal generation unit 3 Correlation calculation unit 4 Maximum / maximum detection unit 5 Maximum / maximum correction unit 6 Tap coefficient distribution unit (tap coefficient correction unit) 7 Filter circuit

Claims (2)

[Claims] 1. A ghost removing apparatus that corrects a tap coefficient at a tap position in a transversal filter by successive correction control based on a correlation between an input signal including a ghost signal and a reference signal. From the maximum / maximum detection unit that obtains the maximum or maximum tap position and the correlation values at the positions before and after this position, and the correlation values obtained by the maximum / maximum detection unit,
The approximate curve of the correlation is obtained, and the ghost position p _real at which the absolute value of the correlation is maximum or maximum is obtained using the approximate curve.
And a maximum / maximum correction unit that obtains, and a tap coefficient correction unit that sequentially corrects the tap coefficient at _two tap positions p ₁ and p ₂ that sandwich the ghost position obtained by the maximum / maximum correction unit. And a ghost removing device. 2. A maximum-maximum correction unit, together with the absolute value s _{re al} correlation at position p _real by using the approximate curve, the tap coefficient correction portion, based on the absolute value s _real correlation, actual obtains the tap coefficients c _real showing a ghost size, by _{c 1 = c real × (p} 2 -p real) c 2 = c real × (p real -p 1), each in the position p _1, p ₂ Tap coefficient c ₁ ,
The ghost removing apparatus according to claim 1, wherein c ₂ is obtained.