JPH0738380A - Wavelet converting device - Google Patents

Abstract

PURPOSE:To easily and effectively reproduce the termination of data with fidelity. CONSTITUTION:When input data X1(i) is inputted to a conversion side 10, a termination data comprising means 31 comprises the data outside than termination data required for filter processing for the input data X1(i). A processed result is processed at a low-pass filter 12 and thin-out means 13, 14. When thinned out low frequency component and high frequency component are inputted to a reverse conversion side 20, the low frequency component is thinned out by an interpolating means 21. A termination data comprising means 32 comprises the data outside than the termination of the low frequency component by the amount required for the filter processing. The thinned out high frequency is interpolated by an interpolating means 22. A termination data comprising means 33 comprises the data outside than the termination of an interpolated high frequency component by the amount required for the filter processing. Those processed results are processed by a low-pass filter 23 and a high-pass filter 24, then, they are added by an adder 25.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is used in a device for processing digital data such as images and sounds, a coding device, etc., and is a wavelet transform using a symmetric filter of even filter length which can improve the reproduction quality of data. It relates to the device.

[0002]

2. Description of the Related Art Conventionally, as a technique in such a field,
For example, some documents were described in the following documents. Reference; 1980 IEEE ICASSP, Denver, CO. (1980-4) (US) JDJ
ohnston, “A Filter Family Designed for Use inQua
Drature Mirror Filter Banks) ”P.291-294 Conventionally, as a wavelet transform device or a subband splitting device, there is a system using a symmetrical filter with an even filter length described in the above document. 2 is a functional block diagram showing a configuration example of the conventional wavelet transform device described in the above document, which performs wavelet transform of input data X _I (i). Low frequency component X _L (2i) and high frequency component X _H (2i) of the thinned data
A conversion side 10 for outputting the inverse transform to output a low-frequency component of the wavelet transformed data X _L (2i) and the high frequency component X _H by performing inverse transformation of (2i) output data X _o (i) by thinning With side 20. Conversion side 10
And the inverse conversion side 20 are connected by, for example, a transmission line. The conversion side 10, a first low-pass filter a low frequency component obtained X _L (i) of the input data X _I (i) 1
1, a first high-pass filter 12 for extracting a high-frequency component X _H (i) of the input data X _I (i), and a low-frequency component X
_L first decimating means (i) to which thinned out every other data and outputs the data of the low frequency component X _L (2i) 13
When, a second decimating means 14 for outputting the data of the high-frequency component X _H (2i) by performing thinning every other data to the high-frequency component X _H (i), are provided. On the inverse transform side 20,
The first interpolating means 21 for outputting data of the low frequency component X _L ′ (i) by inserting one zero every other data for the low frequency component X _L (2i) of the thinned data, and A second interpolating means 22 for outputting data of the high frequency component X _H ′ (i) by inserting one zero every other data for the high frequency component X _H (2i) of the subtracted data, and the interpolated low Frequency component X _L ′
The second low-pass filter 23 for taking out the low frequency component X _L ″ (i) of the data (i) and the interpolated high frequency component X _H ′.
The second high pass filter 24 for extracting the high frequency component X _H ″ (i) of the data of (i), the low frequency component X _L ″ (i) and the high frequency component X _H ″ (i) are added and doubled. Output data X
and an adder 25 that is an addition unit that outputs _o (i). The first and second low-pass filters 11 and 23 and the first and second high-pass filters 12 and 24 are symmetric filters having even filter lengths.

Next, the principle and operation of the conventional wavelet transform device will be described. First, on the conversion side 10, the filter coefficient of the low-pass filter 11 of FIG.
Let the filter coefficient of the high-pass filter 12 be g (k). In the low-pass filter 11 and the high-pass filter 12, the low frequency component X _L (i) of the input data X _I (i) is input.
And the high frequency component X _H (i) are extracted and output.
This extraction process is performed using the input data X as expressed by the following equation (1).
It is expressed by the sum of products of _I (i) and filter coefficients h (k) and g (k).

[0004]

[Equation 1] Regarding the low-pass filter coefficient h (k), as shown in FIGS. 3 to 5, many symmetric low-pass filter coefficients (h (0) to h (N)) having an even filter length are described in the above document. . Although only half of the filter coefficients of even filter lengths are shown in FIGS. 3 to 5, assuming that those coefficients start from h (0), the low-pass filter 11 has the following equation (2). And is symmetrical about -1/2.

[0005]

[Equation 2] Regarding the high pass filter 12, QMF (Quad
so as to satisfy the rature Mirror Filter) condition, g (k) = (- a ^{1) k h (k) ···} (3). Therefore, the filter coefficient g (k) of the high-pass filter 12 is oddly symmetric about -1/2 as shown in the following expression (4).

[0006]

[Equation 3] In the first thinning means 13, the input low frequency component X
_L (i) thinning one data every one for, and outputs the low frequency component X _L (2i) of the input half. Further, in the second thinning means 14, the input high frequency component X
_Every other data is thinned out for every _H (i), and half the high frequency components X _H (2i) of the input are output. for that reason,
When the thinning process and the filter process are considered in the equation (1), the following equations (5) and (6) are obtained.

[0007]

[Equation 4] On the other hand, the inverse transform side 20, first, by the first interpolation means 21, with respect to the low frequency component X _L (2i) thinned out, as in the following equation (7), zero every one data 1 Insert one,
Further, the high-frequency component X _H (2i) decimated by the second interpolator 22 is converted into the data 1 by the following equation (7).
Insert one zero every other piece. x _L ′ (2i) = X _L (2i) x _L ′ (2i + 1) = 0 x _H ′ (2i) = X _H (2i) x _H ′ (2i + 1) = 0 (7) And the low-pass filter 23, the filter coefficient h
^* (k) has a filter coefficient h (k) of the low-pass filter 11 on the conversion side 10 which is inverted in the front-rear direction, as shown in the following equation (8), and performs the same processing as that of the low-pass filter 11. The low-pass filter 23 outputs the low frequency component X _L ″ (i) with respect to the low frequency component X _L ′ (i) which is the input data according to the following equation (9).

[0008]

[Equation 5] Similar to the low-pass filter 23, the high-pass filter 24 has a filter coefficient g (k) of the high-pass filter 12 on the conversion side 10 which is inverted in the front-back direction.
As shown in (11), the same processing as that of the high pass filter 12 is performed.

[Equation 6] The adder 25 adds the low-frequency component X _L ″ (i) from the low-pass filter 23 and the high-frequency component X _H ″ (i) from the high-pass filter 24, as shown in the following equation (12),
Further, in order to match the size of the input / output data, the data of the addition result is doubled and output data X ₀ (i) is output. X ₀ (i) = 2 (X _L ″ (i) + X _H ″ (i)) (12) In the filter system satisfying the above conditions, output data X _o (i)
And the input data X _I (i) become substantially equal. Therefore, the input data X _I (i) can be divided and reproduced.

[0009]

However, in the wavelet transform device having the above-mentioned configuration, since reproduction of the end of data such as voice and image having a finite data length is not taken into consideration, the end of data is reproduced faithfully. I can't. As an example, a method most often used as a method for reproducing the end of data is shown in FIGS. FIG. 6 (a)-
(D) is a diagram showing an example of edge reproduction of data in the conventional wavelet transform device shown in FIG. 2, where (a) is a first low-pass filter 11 and (b) is a second low-pass filter. 23, the figure (c) is the first high-pass filter 12, and the figure (d) is the second high-pass filter 24.
It is a figure which shows the processing content of. In this figure, the filter length is 4, the center of the filter is k = 0, and the low-pass filters 11, 23 are h (-2), h (-1), h (0).
And four coefficients of h (1) and high pass filter 1
2 and 24 are g (-2), g (-1), g (0) and g
It has four coefficients of (1). In this case,
The low-frequency component X _L (0) and the high-frequency component X _H (0) at the left end are
Each is calculated from the following equation (13).

[0010]

[Equation 7] Here, since X _I (-2) and X _I (-1) do not exist,
From the inside of each data, as shown in FIGS. 6A and 6C, according to the following equation (14), the data is folded and substituted. X _I (−2) = X _I (2), X _I (−1) = X _I (1) (14) On the inverse transform side 20, filter coefficients h ^* (k) and g ^* (k).
From the equations (8) and (10), the center is k = 0.
Where h ^* (-1), h ^* (0), h ^* (1) and h ^* (2), and g ^* (-1), g ^* (0), g ^* (1) and g ^* ( It turns out that it has 2). Therefore, on the inverse transformation side 20, the leftmost X
_In order to reproduce _I (0), the calculation according to the following expression (15) may be performed as in the expressions (9), (11) and (12).

[Equation 8] In X ₀ ′ and X _H ′, one zero is inserted every other data, so that X _L ′ (1) and X _H ′ (1) become zero. Further, _XL '(-1) and _XH ' (-1) are respectively _XL '
Since (1) and X _H ′ (1) can be substituted, X ₀ (0) becomes equal to the input X _I (0), and the left end can be faithfully reproduced. However, at the right end, when the data is reproduced by the same method as at the left end, when the data length is an even number, the conversion end 10 thins out the right end (2N-1th data). On the reverse conversion side 20, in order to reproduce the right end (2N-1st),
(2N-2) th and (2N-1) th (= 0) and 2
Nth (because it does not exist, substitute 2N-2nd),
(2N + 1) th (= 0) requires four data, _{and, X L (2N) = X} L (2N-2)
Must meet the conditions of. However, FIG. 6 (b)
In the conventional edge reproduction method such as
Looking calculates _L (2N) and X _L (2N-2), obviously X _L (2N-2) and X _L (2N) are not equal. Therefore,
X _I (2N-1) cannot be faithfully reproduced. Similar results are obtained with the high pass filters 12 and 24. _XL (2N-2) = h (-2) X _I (2N-4) + h (-1) X _I (2N-3) + h (0) X _I (2N-2) + h (1) X _I ( _{2N-1) X L (2N} ) = h (-2) X I (2N-2) + h (-1) X I (2N-1) + h (0) X I (2N-2) + h (1) X _I (2N−3) (16) Similarly, when the data length is odd, FIG.
From (b), the following expression (17) for faithfully reproducing the right end
It can be seen that the condition of is not satisfied. Therefore, the rightmost data is not faithfully reproduced. . X _L (2N-2) = X _L (2N + 2) X _H (2N-2) = X _H (2N + 2) (17) The present invention addresses the end of data as a problem that the prior art has. In order to solve the problem that faithful reproduction is not possible, an object of the present invention is to provide a wavelet transform device that reproduces the end of data faithfully and simply by adding end data forming means.

[0011]

In order to solve the above-mentioned problems, a first aspect of the present invention has a symmetrical filter having an even filter length and performs a wavelet conversion of input data, and a wavelet-converted data. The following means is provided in the wavelet transform device configured with the inverse transform side for performing the inverse transform of. Here, on the conversion side, a first low-pass filter that extracts a low-frequency component of the input data, a first high-pass filter that extracts a high-frequency component of the input data, and a low-frequency component extracted by the first low-pass filter. A first thinning means for thinning out one data every other data for the component, and a second thinning means for thinning out one data every other data for the high frequency component extracted by the first high-pass filter. ing. Also, on the inverse transform side, zero is set every other data for the low frequency component of the wavelet transformed data.
First interpolating means for inserting and interpolating, and second interpolating means for interpolating by inserting one zero for every other data with respect to the high-frequency component of the wavelet-transformed data, and the first interpolating means The second to extract the low frequency component interpolated by
Low-pass filter, a second high-pass filter for taking out the high-frequency component interpolated by the second interpolation means, and a low-frequency component and a high-frequency component respectively taken out by the second low-pass filter and the second high-pass filter. Is added and the addition result is doubled and output. Further, in the present invention, on the conversion side, there is provided a first end data forming means for forming the data outside the end data necessary for the filter processing with respect to the input data,
It is provided on the input side of the first low-pass filter and the first high-pass filter. Further, on the inverse transform side, the second end data forming means for forming the data outside the end of the low frequency component interpolated by the first interpolating means by the number necessary for the filter processing is provided with the first end data forming means. It is provided between the interpolating means and the second low-pass filter. Further, the third end data forming means for forming the data outside the end of the high frequency component interpolated by the second interpolating means by the number necessary for the filter processing is provided with the second interpolating means and the second interpolating means. It is provided between the high-pass filter and. In the second invention, the first end data forming means of the first invention sets the data outside the end of the input data with respect to the input data,
It has a function of sequentially folding the internal data outward from the end of the input data. In the third invention, the first
The second end data forming means of the invention of claim 1 inserts one zero in front of the left end for the input low frequency component, and for the data string of the inserted low frequency component, the data string Has a function of sequentially folding data outside the end of the data string to data outside the end of the data string (not including the end data). In the fourth invention, the third end data forming means of the first invention inserts one zero before the left end of the input high-frequency component, and inserts the zero into the data string of the high-frequency component. On the other hand, it has a function of sequentially inverting the sign and folding the data outside the end of the data string and the data inside the end of the data string (not including the end data) to the outside.

[0012]

According to the first aspect of the present invention, since the wavelet transformation device is constructed as described above, when the input data is input to the transformation-side first end data forming means, the first end data forming means is formed. Then, the data outside the end data necessary for the filter processing is constituted with respect to the input data. This first
The low-frequency component is the first
After being taken out by the low pass filter of No. 1, the thinning processing is performed by the first thinning means. The high-frequency component of the processing result of the first end data forming means is taken out by the first high-pass filter, and the thinning-out processing is performed by the second thinning-out means. On the inverse transform side, the low frequency component of the wavelet transformed data is interpolated by the first interpolating means and then sent to the second end data forming means. The second end data forming means forms the data outside the end of the low frequency component interpolated by the first interpolating means by the number required for the filter processing. A low frequency component is extracted from the processing result of the second end data forming means by the second low pass filter. The second interpolation means performs interpolation processing on the high frequency component of the wavelet-transformed data, and sends the interpolation result to the third end data forming means. The third end data forming means forms the data outside the end of the high frequency component interpolated by the second interpolating means by the number necessary for the filter processing. From the processing result of the third end data forming means, a high frequency component is taken out by the second high pass filter. The low-frequency component extracted from the second low-pass filter and the high-frequency component extracted from the second high-pass filter are added by the adding means, and further, they are doubled and output as output data. According to the second aspect, when the input data is input to the first end data forming unit, the first end data forming unit inputs the data outside the end of the input data to the end input. The internal data is sequentially folded back from the end of the data to the side, and the processing result is sent to the first low-pass filter and the first high-pass filter. According to the third aspect, when the low-frequency component interpolated by the first interpolating means is sent to the second end data forming means, the second end data forming means converts the low-frequency component into an input low-frequency component. On the other hand, insert one zero in front of the left edge. Then, with respect to the low frequency component data string in which zeros are inserted, the data outside the end of the data string and the data inside the end of the data string (not including the end data) are sequentially folded back to the outside. Then, the processing result is sent to the second low-pass filter. According to the fourth aspect, when the high frequency component interpolated by the second interpolating means is sent to the third end data composing means, the third end data composing means prepares for the input high frequency component. , Insert one zero in front of the left edge. Then, with respect to the data string of the high-frequency component in which zeros are inserted, the data outside the end of the data string and the data inside the end of the data string (not including the data) are sequentially inverted in the sign to the outside. Fold it back to configure
The processing result is sent to the second high pass filter. Therefore, the above problem can be solved.

[0013]

FIG. 1 is a functional block diagram of a wavelet transform device using an even filter length symmetric type filter according to an embodiment of the present invention. Elements common to those shown in FIG. The reference numeral is attached. In this wavelet transform device, as in the conventional case, the transform side 10 has a first low-pass filter 11, a first high-pass filter 12, and first and second thinning means 13 and 14, and
On the inverse transformation side 20, the first and second interpolating means 21, 22 and the second low pass filter 23 and the second high pass filter 2 are provided.
4 and an adder 25 which is addition means, except that the following means are added. That is, the conversion side 10 is provided with the first end data forming means 31 in front of the low-pass filter 11 and the high-pass filter 12. Further, on the inverse transformation side 20, a second end data forming means 32 is provided between the first interpolating means 21 and the second low-pass filter 23, and the second interpolating means 22 and the second high-pass filter are provided. Between 24 and 3
End data forming means 33 is provided. The first end data forming means 31 is arranged outside the end of the input data X _I (i) by the number of the input data X _I (i) required for the filter processing.
_It has a function of sequentially returning from the end of _I (i) to form data. The second end data forming means 32 first sets zero to the front of the left end data for the low frequency component _XL '(i) interpolated by the first interpolating means 21 of the inverse transform side 20.
Insert the individual pieces, and fold back the data as many times as necessary for the filter processing from the left end to the front to form the end data.At the right end, fold back as much as the data necessary for the filter processing from the data before the right end to the back. It has a function to configure end data. Third end data forming means 33
Of the high-frequency component X _H ′ (G) interpolated by the second interpolating means 22 on the inverse transform side 20, first, insert one zero before the left-end data, and then perform the filtering process. The end data is formed by sequentially folding back the data from the left end by the number, and at the right end, only the number necessary for the filter processing,
It has a function of forming the right end data by sequentially folding back the data before the right end.

7 (a) to 7 (d) are diagrams showing an example of edge reproduction of data in the wavelet transform device of FIG. 1, in which FIG. 7 (a) shows the first low-pass filter 11 and FIG. 7 (b). Is a diagram showing the processing contents of the second low-pass filter 23, FIG. 7C is the first high-pass filter 12, and FIG. 7D is a diagram showing the processing contents of the second high-pass filter 24. The operation and effect of FIG. 1 will be described with reference to this figure. First,
Conventional low-pass filter 11 and high-pass filter 12
The center of the filter coefficients h (k) and g (k) at
Move to 1. That is, the filters 11 and 12 are made to be symmetrical about 1/2. Therefore, the equations (2) and (4) are the following equations (18) and (19).

[0015]

[Equation 9] Therefore, the low-pass filter 11 and the high-pass filter 1
The processing of No. 2 is expressed by the following equations (20) and (21), respectively.

[0016]

[Equation 10] In the example of FIG. 7, if the filter length is 4 as in the conventional example of FIG. 6, the low frequency component X _L (i) and the high frequency component X _H (i)
Are respectively expressed by the following equation (22).

[0017]

[Equation 11] In this equation (22), the end data forming means 31
For the left edge of the input data X _I (i),

[Equation 12] Since the end data is configured so that X _I (−1) = X
It becomes _I (0). At the right end of the input data X _I (i), if the end data is M in the end data constructing means 31,

[Equation 13] The edge data is configured so that These data are filtered by the low-pass filter 11 and the high-pass filter 12 and then thinned by the thinning means 13 and 14. On the reverse conversion side 20, interpolation processing is performed on the thinned data by the interpolation means 21 and 22, and the processing result is sent to the end data forming means 32 and 33.
In the end the data structuring unit 32, first, 'by inserting one zero before (i) X _L' interpolated by the interpolation means 21 the low frequency component X _L and (-1) = 0. And

[Equation 14] The leftmost data is configured so that Inverse conversion side 20
Then, since the filter coefficient h ^* (k) of the low-pass filter 23 is given by the equation (8), the processing of the low-pass filter 23 in the example of FIG.

[Equation 15] Becomes Therefore, in order to reproduce the leftmost data, the data shown in FIG.
As in (b), x _L (−2) = X _L (0) is a necessary condition. On the other hand, on the conversion side 10, the above (2
Using equations (2) and (23), _XL (-2) = h (-1) _XI (2) + h (0) _XI (1) + h (1) _XI (0) + h (2 ) X _I (0) _XL (0) = h (−1) X _I (0) + h (0) X _I (0) + h (1) X _I (1) + h (2) X _I (2)・ ・ It turns out that it becomes (27). When the symmetry of the filter coefficient h (k) in the low-pass filter 11 is put in, that is, when h (-1) = h (2) and h (0) = h are substituted, _XL (-2) = _XL (0 ). If the data length is an even number (2N),
In the end data forming means 32, according to the following equation (28), (2
N-1) is used as the axis to fold the data.

[Equation 16] In this case, the low-pass filter 23 is X _L "(2N-1)
In order to reproduce, as shown in FIG. 7B, the following equation (29)
Need to be satisfied. Meanwhile _{X L (2N-2) =} X L (2N) ··· (29), the conversion side 10, tentatively to constitute X _L (2N), the use of the (22) and (24) , X
_L (2N) and X _L (2N-2) becomes the following equation (30). _XL (2N) = h (-1) X _I (2N-1) + h (0) X _I (2N-1) + h (1) X _I (2N-2) + h (2) X _I (2N-3) ) _XL (2N-2) = h (-1) X _I (2N-3) + h (0) X _I (2N-2) + h (1) X _I (2N-1) + h (2) X _I ( 2N-1) (30) Similarly, the filter coefficient h in the low-pass filter 11 is
Taking symmetry _{(k), X L (2N} ) and X _L (2N-
It can be seen that 2) are equal. Therefore, it is understood that the end reproduction condition of the low frequency component is satisfied by using the end data forming means 31 and 32. If the data length is an odd number (2N + 1), as it can be seen from FIG. 7 (b), since _{X L "X L '(2N} + 1) in order to play (2N) (= 0) may be added to, clearly The condition is satisfied: the end data forming means 33.
Then, first, one zero is inserted before the left end of the high frequency component X _H ′ (i) interpolated by the interpolating means 22 to obtain X _H ′.
(-1) = 0. And at the left end of the data,
The sign of the data inside the end data is inverted and folded back outside the end according to the following expression (31) with X _H ′ (−1) as the axis.

[0018]

[Equation 17] On the inverse transform side 20, as in the case of the low frequency component, in order to reproduce the high frequency component X _H ″ (0) at the left end, the following equation (32)
Should be satisfied. X _H (−2) = − X _H (0) (32) On the other hand, when X _H (−2) is configured on the conversion side 10,
From the expressions (22) and (23), X _H (−2) and X _H (0) are obtained as in the following expression (33). X _H (−2) = g (−1) X _I (2) + g (0) X _I (1) + g (1) X _I (0) + g (2) X _I (0) X _H (0) = g (-1) X _I (0) + g (-1) X _I (0) + g (1) X _I (1) + g (2) X _I (2) (33) Further, in the high pass filter 12 Filter coefficient g
Including the odd symmetry of (k), that is, g (-1) =-g
Substituting (2) and g (0) =-g (1), X _H (-
It can be seen that 2) = − X _H (0). At the right end, if the data length is M in the end data forming means 33, the end data (M-1) is used as an axis,

[Equation 18] The edge data is configured so that If the data length is an even number, as shown in FIG. 7 (d), in order to reproduce the _{X H "(2N-1)} , X H (2N-2) = - X H (2N) ··· (35 ), On the other hand, the conversion side 1
At 0, X _H (2N) is calculated using the equations (21) and (24).
And X _H (2N) and X _H (2N-2) are expressed by the following formula (3
It becomes like 6). X _H (2N) = g (-1) X _I (2N-1) + g (0) X _I (2N-1) + g (1) X _I (2N-2) + g (2) X _I (2N-3) ) X _H (2N-2) = g (-1) X _I (2N-3) + g (0) X _I (2N-2) + g (1) X _I (2N-1) + g (2) X _I ( 2N-1) (36) Substituting the odd symmetry of the filter coefficient g (k) in the high-pass filter 12, as in the case of the left end, (35)
It can be seen that the condition of the expression is satisfied. When the data length is odd, as can be seen from FIG. 7 (d), X _H ″ at the right end
(2N) can be reproduced as in the case of the low frequency component. The outputs of the low-pass filter 23 and the high-pass filter 24 are added by the adder 25, and the addition result is doubled and output as output data X _o (i).

As described above, in this embodiment, since the end data forming means 31, 32 and 33 are provided, the end of the data can be reproduced faithfully and efficiently. In the above embodiment has been decimated transform side 10 the low frequency component X _L (2i) and the high frequency component X _H (2i) is has been directly input to the inverse transform side 20, decimation means transform side 10 Even if data processing or the like is performed on the outputs of 13 and 14, the processing results are input to the interpolating means 21 and 22 of the inverse transform side 20, the same effect as in the above embodiment can be obtained.

[0020]

As described above in detail, according to the first aspect of the invention, the input of the first low-pass filter and the first high-pass filter on the transform side of the wavelet transform device having the symmetrical filter of even filter length. The first end data forming means for forming the external data at the end of the input data is provided on the side, and the first and second interpolating means and the second low pass filter and the second high pass filter on the inverse conversion side are provided. A second end data forming means for forming external data at the end of the interpolated low frequency component and a third end data forming means for forming external data at the end of the interpolated high frequency component are provided between them. Therefore, the end of the data can be reproduced faithfully and efficiently. According to the second, third and fourth inventions, the end of the data can be more easily reproduced depending on whether the data length is even or odd.

[Brief description of drawings]

FIG. 1 is a functional block diagram of a wavelet transform device showing an embodiment of the present invention.

FIG. 2 is a functional block diagram of a conventional wavelet transform device.

FIG. 3 is a diagram showing symmetric low-pass filter coefficients (h (0) to h (N)) having even filter lengths.

FIG. 4 is a diagram showing symmetrical low-pass filter coefficients (h (0) to h (N)) having even filter lengths.

FIG. 5 is a diagram showing symmetrical low-pass filter coefficients (h (0) to h (N)) having even filter lengths.

FIG. 6 is a diagram showing an example of edge reproduction of data in the wavelet transform device of FIG.

7 is a diagram showing an example of edge reproduction of data in the wavelet transform device of FIG. 1. FIG.

[Explanation of symbols]

10 conversion side 11,23 first and second low-pass filters 12,24 first and second high-pass filters 13,14 first and second thinning-out means 20 reverse conversion side 21,22 first and second interpolation Means 25 Adder 31, 32, 33 First, second and third end data constituent means X _I (i) Input data X _o (i) Output data

Continuation of the front page (51) Int.Cl. ⁶ Identification code Office reference number FI Technical indication location H03H 17/00 A 8842-5J 21/00 8842-5J H03M 7/30 A 8522-5J

Claims (4)

[Claims] 1. A symmetric filter having an even filter length, and a first low-pass filter for extracting a low-frequency component of the input data and a high-frequency component of the input data on a transform side for performing a wavelet transform of the input data. First to take out
Of the high-pass filter and the low-frequency component extracted by the first low-pass filter, the first thinning-out means for thinning out one data every other data, and the high-frequency component extracted by the first high-pass filter. A second thinning means for thinning out one data every other data, and on the inverse transform side for performing the inverse transform of the wavelet transformed data, the low frequency component of the wavelet transformed data becomes zero every other data. A first interpolating means for inserting and interpolating, and a second interpolating means for interpolating by inserting one zero for every other data with respect to the high-frequency component of the wavelet-transformed data, and the first interpolating means. A second low-pass filter for taking out the low-frequency component interpolated by the interpolating means and a second high-pass filter for taking out the high-frequency component interpolated by the second interpolating means. Filter and an adding means for adding the low-frequency component and the high-frequency component respectively taken out by the second low-pass filter and the second high-pass filter and doubling the addition result and outputting the result. In the above, first end data forming means for forming data outside the end data necessary for filter processing with respect to the input data is provided on the input side of the first low-pass filter and the first high-pass filter, The second end data forming means for forming the data outside the end of the low frequency component interpolated by the first interpolating means by the number necessary for the filter processing is the first interpolating means and the second low-pass means. Third end data, which is provided between the filter and the outside of the end of the high frequency component interpolated by the second interpolating means, is constituted by the number required for the filter processing. The data structure means, the wavelet transform unit, characterized in that provided between said second interpolation means and said second high-pass filter. 2. The function of the first end data structuring means, wherein the data outside the end of the input data with respect to the input data is sequentially folded back to the outside from the end of the end input data. The wavelet transformation device according to claim 1, further comprising: 3. The second end data forming means inserts one zero before the left end of the input low frequency component,
Data outside the end of the data string with respect to the zero-inserted low-frequency component data string,
2. The wavelet transform device according to claim 1, wherein the wavelet transform device has a function of sequentially folding the inner data not including the data to the outer side. 4. The third end data forming means inserts one zero in front of the left end of the input high frequency component,
Data outside the end of the data string with respect to the high-frequency component data string in which the zero has been inserted is calculated from the end of the data string
2. The wavelet transform device according to claim 1, wherein the wavelet transform device has a function of sequentially inverting the sign and folding back the inner data that does not include the end data.