JPH04278668A - Two-dimensional method and device for discrete cosine transformation - Google Patents

Abstract

PURPOSE: To carry out the two-dimensional DCT at a high speed by performing the two-dimensional DCT processing to the (N×N) digital data through N times of one-dimensional DCT, the addition and a shift process. CONSTITUTION: A buffer 100 inputs the (N×N) digital data, and a reconstruction part 200 rearranges the digital data into N pieces of groups so as to ensure the addition of cosine functions equal to the core of the one-dimensional DCT and in order to transform the multiplication of cosine functions, i.e., the core of the two-dimensional DCT into the addition of cosine functions. A 1st adder 300 performs the addition or subtraction of the groups of odd order numbers corresponding to the groups of even order numbers adjacent to each other among those N pieces of rearranged groups and generates N/2 pieces of groups. These generated groups are sent to a one-dimensional pct part 400 where the one-dimensional DCT data to the 2/N pieces of groups are generated. A 2nd adder 500 generates the two-dimensional DCT data by carrying out the addition/ subtraction and a shift operation to the one-dimensional DCT data at log2 N pieces of stages.

Description

[Detailed description of the invention]

0001

TECHNICAL FIELD The present invention relates to a two-dimensional discrete cosine transform (hereinafter referred to as "two-dimensional DCT") method and apparatus for a data transmission system, and particularly to a two-dimensional discrete cosine transform (hereinafter referred to as "two-dimensional DCT") method and apparatus.
The present invention relates to a method and apparatus that can perform two-dimensional DCT at high speed by shortening calculation time.

0002

2. Description of the Related Art Generally, when transmitting data, the transmitting side compresses the amount of data and transmits it, and the receiving side converts the compressed data into original data and processes it. When converting data compressed as described above, the two-dimensional DCT method is currently widely used. At this time, let the two-dimensional data string be [X1j:i,j=0,1,2...N-1], and 2
The column of dimensional DCT is [Ymn: m, n=0, 1, 2...N-
1], the two-dimensional DCT can be expressed as shown in Equation 1.

0003

[Equation 1] Here, the scale factor is 4U(m) U(n)
/N2 is omitted for convenience, and the above equation 1 becomes the following equation 2 when defined in the non-normalized DCT form Ymn (non-normal form)
It becomes a ceremony.

0004

[Mathematical 2] Therefore, looking at the above formula 2, ymn (non-normal form D
CT) is repeated N times in the row direction by executing N-1 Σ COS(2i+1)mπ i=0 and then N-1 Σ COS(2j+1)nπ/2N j=0 It is expressed by one-dimensional DCT of .

[0005] That is, the two-dimensional DCT of the above two equations is as follows:
It can be expressed as an expression.

[0006]

##EQU00003## Therefore, when performing DCT on N.times.N two-dimensional digital data using the above equations 2 and 3, a configuration as shown in FIG. 1 is required. That is, input N×
N times of 1 in the row direction for N two-dimensional digital data
After performing the dimensional DCT, the result is transposed in matrix form by a matrix transposer 2.
By again performing N one-dimensional DCTs on the resultant output in the column direction, Ymn, which is a two-dimensional DCT, can be obtained.

However, when performing two-dimensional DCT on N×N two-dimensional digital data using the above method, by using 2N one-dimensional DCTs, D
Although it has been difficult to implement CT calculation time software, for example, M. A. Haque's “Two-dimensional fast cosine transform (A
two - dimensionalfast co
sine transform)” [ IEEETr
ans. Acoust. , Speech, Signa
lProcessing, Vol. ASSP-3
3, PP. 1532-1539, Dec. 1985
] and C. Ma's “fast recursive two-dimensional cosine transform (
A fast recursive two dime
cosine transform)
” [Intelligent Robotsand
Computer Vision: Seven
h in a Series, David P. Cas
asent, Editor, Proc. SPIE10
02, PP. 541-548, 1988], etc.

In the above-mentioned publications, one-dimensional DC
Several methods have been proposed for performing two-dimensional DCT without using T. Therefore, when performing two-dimensional DCT using the method described above, it was necessary to configure separate hardware independent of the one-dimensional DCT circuit, but the number of multiplications when performing DCT is also lower than in the conventional method. 2
Since the reduction is about 5%, the DCT operation time remains long, making it difficult to realize high-speed DCT.

[0009]

SUMMARY OF THE INVENTION Therefore, it is an object of the present invention to convert N×N digital data into two-dimensional DCT by N times of one-dimensional DCT, addition, and shift steps.
An object of the present invention is to provide a method and apparatus that can perform CT processing and perform two-dimensional DCT at high speed.

Another object of the present invention is to convert the multiplication form of a cosine function into an addition form in the two-dimensional DCT when N×N digital data is subjected to two-dimensional DCT, and to create a sum of one-dimensional transformations. An object of the present invention is to provide a method and apparatus that can reduce the number of multiplications.

Still another object of the present invention is to receive N×N digital data, rearrange the multiplication form of a cosine function of a two-dimensional DCT into an addition form, and perform a first addition on the rearranged digital data. Provides a method and apparatus capable of performing two-dimensional DCT by performing N times of one-dimensional DCT using the result value of the first addition, and then performing second addition. It's about doing.

Another object of the present invention is that when N×N digital data is subjected to two-dimensional DCT, the one-dimensional transformation form is
By making it the same as the dimensional DCT, N times one-dimensional D
N× so that two-dimensional DCT results can be obtained with CT
An object of the present invention is to provide a method and apparatus capable of rearranging N digital data into N groups.

Another object of the present invention is to first add and subtract N/2 groups of odd group data and N/2 groups of even group data with the rearranged N groups of data when performing two-dimensional DCT; One-dimensional D with this result value
Execute CT and convert this one-dimensional DCT result value to log2 N
The object of the present invention is to provide a method and apparatus capable of performing two-dimensional DCT by performing second addition and subtraction at the ends.

Another object of the present invention is to perform two-dimensional DCT on N×N digital data, and in a system that executes one-dimensional DCT in a pipeline structure, N/2 of rearranged N groups of data is During the first addition of group data, one-dimensional DCT is performed on the remaining N/2 group data, and while one-dimensional DCT is performed on the first added N/2 group data, two-dimensional DCT is performed on the remaining N /2
By first adding the group data, one-dimensional D
The object of the present invention is to provide a method and apparatus that can compress the number of CT operations to N/2 times.

[0015]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be explained in detail below with reference to the drawings.

FIG. 2 shows a two-dimensional DC for implementing the present invention.
FIG. 2A is a configuration diagram of a two-dimensional DCT, and FIG. 2B is a configuration diagram of a two-dimensional IDCT.

The configuration of the two-dimensional DCT will be explained with reference to FIG. 2A. The buffer 100 receives N×N two-dimensional digital data. The reconstruction unit 200 receives the output of the input buffer 100 as input. This reconstruction unit 20
0 is the kernel of the two-dimensional DCT, in order to convert the multiplication of the cosine function into the addition of the cosine function, the data is divided into N pieces so that the addition of the cosine function is the same as the kernel of the one-dimensional DCT. Rearrange into groups. 1st
The adder 300 inputs the output of the rearrangement section 200 and adds data to or from adjacent even-numbered groups of the rearranged N groups to odd-numbered groups corresponding thereto. By adding or subtracting the data, N/2 groups of addition data and subtraction data are generated. The N/2 groups of addition data and subtraction data are sent to a one-dimensional DCT section 400, which generates one-dimensional DCT data for the N/2 groups of addition and subtraction data.
Perform dimensional DCT operations. The second adder 500 receives the output of the one-dimensional DCT section 400 and generates two-dimensional DCT data by performing addition, subtraction, and shift operations in log2N stages. Output buffer 6
00 buffers the output of the second adder 500.

In addition, the two-dimensional inverse DCT (hereinafter referred to as
(referred to as two-dimensional IDCT) is a two-dimensional DC as shown in Figure 2A.
It is executed in the reverse order of execution of T.

FIGS. 3A and 3B show 8×8 input data
FIG. After inputting 8×8 input data as shown in FIG. 3A, the data are rearranged into eight groups such that the sum of the cosine functions is the same as the kernel of the one-dimensional DCT. As a result, multiplication of cosine functions, which is the core of two-dimensional DCT, can be converted into the form of a sum of cosine functions.

FIGS. 4A to 4C are diagrams showing an example of an 8×8 DCT. In this embodiment, the first adder 300 (i.e., 301-308) inputting the rearranged 8 groups of data has groups (R1a, R3a,
The data sets of R5a, R7a) are added or subtracted from the data of adjacent groups (R1b, R3b, R5b, R7b) at a ratio of 1:1, respectively, to obtain added data and subtracted data of the two groups. occurs. 1-dimensional D
The CT section 400 (i.e., 401-408) inputs the output of the first addition section 300, and performs one-dimensional DCT on each of the eight groups of data for the addition data and subtraction data.
do. Further, the second adder 500 inputs the DCT data from the one-dimensional DCT unit 400, performs addition/subtraction and shift operations in log2 N stages, and converts the data into two-dimensional DC data.
Generate T data.

At this time, in FIGS. 4A to 4C, ○ means an adder, and the dotted line part represents a transfer factor.
factor) is “-1”, the solid line part means the transfer factor is “1”, and the [→] symbol with 1/2 means multiplication by 1/2. , which is equivalent to a shift operation. FIG. 4A shows that the rearranged data set X1j of 8 groups is added and subtracted between the data of any odd numbered group and its adjacent group, and then one-dimensional DCT is applied to these added data and subtracted data. is executed and the addition group data fp
1 and subtraction group data gp1 are shown.

FIG. 4B shows the second addition group data fp1.
ymn is added to generate two-dimensional DCT data ymn. Figure 4C shows subtracted group data gp
1 shows a process in which a second addition is performed on 1 to generate two-dimensional DCT data ymn.

FIGS. 5A to 5C are block diagrams of the 8×8 IDCT, and illustrate that the 8×8 IDCT is executed in the reverse order of the execution order of the 8×8 DCT shown in FIG.

FIG. 6 shows another configuration of the first adder 300 and one-dimensional DCT section 400 in FIG. Figure 6 shows the input 2
Even if the first (main) addition operation is performed after performing one-dimensional DCT on the dimensional data, the one-dimensional DC after the main addition is
This figure shows that the operation is the same as the T operation.

FIG. 7 is a diagram showing another embodiment of the 8×8 DCT. According to the figure, by using multiplexers 701 and 702 and demultiplexers 801 and 802, the configuration of one-dimensional DCT section 400 is compressed to 1/2.

The present invention will be explained in detail based on the above configuration with reference to the drawings.

In the case of DCT of N×N two-dimensional digital data, the present invention greatly reduces the number of multiplications by realizing the two-dimensional DCT calculation by N one-dimensional DCT operations. We propose a structure that can perform two-dimensional DCT at high speed, improve regularity, and achieve high integration.

For this purpose, multiplication of cosine functions in the row and column directions, which is the core of two-dimensional DCT, is converted into addition of cosine functions. Furthermore, the transformed data set must be rearranged into N one-dimensional data groups so that this transformed data data is the same as the kernel of the one-dimensional DCT. Therefore, when inputting N×N two-dimensional digital data and converting the multiplication of cosine functions, which is the core of two-dimensional DCT, into the sum of cosine functions, the rearranging unit 200 converts the sum of the cosine functions into a sum of cosine functions. The input data is rearranged into N groups such that the kernel is the same as the kernel of the one-dimensional DCT.

Thereafter, each group of the rearranged N groups of data has its own characteristics, and the first adder 300 adds and subtracts the data of each group according to these characteristics. Therefore, the first adder 30
0 inputs N group data and executes the addition or subtraction process, but at this time, all N/2 group data are added by two data, while the remaining N/2 For groups of , one data set is subtracted from the other data set. Therefore, the result data from the first adder 300 consists of addition data for the first N/2 groups and subtraction data for the remaining N/2 groups.

The addition data and subtraction data output from the first adder 300 are each converted into DCT data by a one-dimensional DCT section 400;
The output of 0 is subjected to subtraction in log2N stages and shifted by the second adder 500 to form a two-dimensional D
CT data ymn is obtained. Therefore, among the finally obtained two-dimensional DCT data ymn, those where n is an even number are the sum of the results obtained by adding all the data on both sides in the first adder 300 and performing one-dimensional DCT. ,on the other hand,
When n is an odd number, the first adder 300 subtracts one data from the other data and performs one-dimensional DCT, resulting in the sum of the results.

Let's take a look at the process of performing two-dimensional DCT on N×N two-dimensional digital data with the above content. As defined above, the column of two-dimensional data number is [Xij:i, j=0,
1,...,N-1], and the sequence of two-dimensional DCT numbers is [
Ymn:=0, 1,...,N-1], this relationship is expressed as in the following four equations.

[0032]

[Equation 4] Here, the scale factor is 4U(m) U(n)
/N2 is omitted for convenience, and the denormalized D of Ymn
The CT morphology is

[0033]

[Math 5] becomes.

Therefore, the normalized Ymn is

003
5]

[Math 6] It is expressed as

In this case, the multiplication of the cosine function of the kernel of the two-dimensional DCT can be expressed as the addition of cosine functions as shown in Equation 7 below.

[0037]

[Equation 7] Here, using the above equation 7, the two-dimensional D of the above equation 5
Ymn of CT can be expressed by the following 8 formulas.

[0038]

[Math. 8] Here, m, n=0, 1, 2, . . . , N-1.

Here, for convenience, the two-dimensional DCT is transformed into one-dimensional DCTAmn and Bmn using the law of cosine addition.
and is defined by the following equations 9 and 10.

[0040]

[Math. 9]

[0041]

[Formula 10] Therefore, the two-dimensional DCT result ymn can be expressed by the following equation 11.

[0042]

[Equation 11] Now, by rearranging the data in the above Amn and Bmn, the above ymn can be expressed by the addition of N one-dimensional DCTs, so the N×N DCT is N independent one-dimensional DCTs.
This is realized by In order for the transformation kernel shown by equations 9 and 10 above to be the same as the one-dimensional transformation kernel, [(2i+
1) m±(2j+1)n] is a certain integer (2i+1)
It must be expressed in double form. In order to satisfy this condition, the remainder after dividing (2j+1) by 2N must be the same as the remainder when dividing a multiple of (2i+1) by 2N, or the multiple of (2i+1) must be subtracted from 2N. It must be the same as the remainder when divided by 2N. That is, the above relationship must satisfy the following equation 12 or 13.

[0043]

[Math. 12]

[0044]

[Formula 13] In Equation 12 or 13 above, p must be an odd number between 1 and N-1, which means that p outside this region can be obtained by substituting a certain p within this region. This is to generate the same sequence of j numbers. Therefore, the above 12
Equation or Equation 13 can be expressed as Equation 14 or Equation 15.

[0045]

[Math. 14]

[0046]

[Math. 15] At this time, p=1, 3, 5,..., N-1.

Here, when i changes from 0 to N-1, the variable j determined by the above equation 12 or 13
It can be easily understood that the columns are different from each other. Therefore, the two-dimensional data of size N×N is
It is possible to separate into N data sets that satisfy the relational expressions of Equation 2 or Equation 13. Therefore, the transformation kernel of Equation 8 above for each data set is the same as the kernel of one-dimensional DCT. Therefore, in order to mutually separate the j sequences generated by equations 14 and 15, respectively, for p = 1, 3, 5, ..., N-1, the following equations 16 and 17 are defined. Ru.

[0048]

[Math. 16]

[0049]

[Formula 17] At this time, p=1, 3, 5,..., N-1. That is,
For a given p, [j(p;a): i=0,1,2
,...,N-1] is the j sequence generated by the above equation 12, and [j(p;b):i=0,1,2,...,N-1
] is a sequence of j numbers generated by Equation 13 above. Therefore, two-dimensional input data and [Xij:i,j=0
, 1, 2, ..., N-1] are [Xij (p; a): where i = 0, 1, 2, ..., N-1] and [Xij (p; b
): Here, by separating into N one-dimensional data of i=0,1,2,...,N-1], the above equation 8 can be expressed as addition of one-dimensional DCT. Here, Expressions 18 and 19 can be expressed as follows by expressing the set of one-dimensional data as Rpa and Rpb, respectively.

[0050]

[Math. 18]

[0051]

[Formula 19] The exact value obtained by dividing pi+(p-1)/2 by N is, however, the remainder of said division is
It can be known from Equation 19. That is, since you must know the quotient of the division result and the remainder when performing the division, pi+(p-1)/2
By defining a sequence qp1 of integers representing dividing by N, it can be expressed by the following equations 17 and 18 without using "mod" in equations 18 and 19 above.

[0052]

[Math. 20]

[0053]

[Math. 21] At this time, p=1, 3, 5,..., N-1.

By using data rearrangement in the above equations 20 and 21, Amn and Bmn expressed in the above equations 10 and 11 can be expressed as the following equations 22 and 23.

[0055]

[Math. 22]

[0056]

[Math. 23] Here, p is an odd number.

[0057] Also, here, the above Tpa (m, n), T
pb (m, n), Spa (m, n) and Spb (m,
n) is expressed by Equations 24 to 27 below.

[0058]

[Math. 24]

[0059]

[Math. 25]

[0060]

[Math. 26]

[0061]

[Formula 27] Therefore, ymn expressed by Equation 11 can be rewritten as shown in Equation 28 below.

[0062]

[Formula 28] Therefore, in order to prove that the above ymn is an addition of one-dimensional DCT, Tpa(m,n), Tpb(m
, n), Spa (m, n) and Spb (m, n) are 1
It suffices to show that it is indicated by addition of dimensional DCT. For this purpose, by substituting the above equation 20 into the corresponding term of equation 24, we get
It can be expressed by Equation 29 below.

[0063]

##EQU29## The above equation 29 can be expressed again in terms of when n is an odd number and when it is an even number, as shown in equations 30 and 31 below.

[0064]

[Math. 30]

[0065]

[Math. 31] At this time, n is an odd number.

Further, by substituting the above equation 11 into equation 25, the following equation 32 is obtained.

[0067]

[Equation 32] However, the above Equation 32 can be changed to Equation 33 depending on whether n is an odd number or an even number.
, 34.

[0068]

[Math. 33] At this time, n is an even number.

[0069]

[Math. 34] At this time, n is an odd number.

Similarly, formula 26 is added to the corresponding term of formula 10.
By substituting , Spa (m, n) becomes the following formula 35,
It can be expressed as

[0071]

[Math. 35] n is an even number.

[0072]

[Math. 36] n is an odd number.

Further, by replacing equation 21 with the corresponding term in equation 27, Spb can be expressed in the form of equations 37 and 38 below.

[0074]

[Math. 37] Here, n is an even number.

[0075]

[Math. 38] Here n is an odd number.

Therefore, the above equations 30 to 38 can be transformed into equation 2.
By substituting into each term of 8, ymn becomes the following equation 39, 4
It can be expressed as 0.

[0077]

[Math. 39] Here n is an even number.

[0078]

[Math. 40] Here n is an odd number.

However, Equations 41 and 42 below are based on the input data sequence [X1j(p;a) +X1j
(p;b)] corresponds to one of the one-dimensional DCTs.

[0080]

[Math. 41]

[0081]

[Formula 42] In other words, fpl, which indicates the result of performing one-dimensional DCT by performing the first addition on the rearranged data, can be expressed by the following formula 43, but formulas 41 and 42 are arbitrary. of l(
It can be understood that this applies to either +fpl or -fpl for l=0, 1, 2, . . . , N-1).

[0082]

[Equation 43] Also, the first
gp showing the result of executing one-dimensional DCT with subtraction of
l can be expressed by the following equation 44.

[0083]

[Formula 44] At this time, gpl defined by Equation 44 is given by any l(l
=0,1,2,...,N-1), the following equation 45,4
This corresponds to either +gpl or -gpl shown in 6.

[0084]

[Math. 45]

[0085]

[ymn:m, n=
Note that only 0, 1, 2, ..., N-1] are required. This means that only N one-dimensional DCTs are needed to calculate an N×N two-dimensional DCT.

In addition to the gpl and fpl calculations described above, the process by which the second addition and subtraction are performed will now be seen. It can be seen that ymn, which is a two-dimensional DCT, is expressed by the sum of fpl and gpl, as shown in Equations 44 and 44. At this time, fpl to find ymn
The second addition of and gpl is a DFT (discrete Fourier transform:
Discrete Fourier Transfer
m) and DCT (Discrete Cosine T
It constitutes the butterfly stage in the algorithm. From the above explanation, it can be seen that the following equation 47 holds true when n is an even number.

[0087]

[Formula 47] The above equation means that when any l (l=0, 1, 2, . . . N-1) is given, the following equations 48 and 49 hold true.

[0088]

[Math. 48]

[0089]

[Formula 49] Also, from the above, when n is an odd number, the following formula 5
It can be seen that 0.51 holds true.

[0090]

[Number 50]

[0091]

[Equation 51] Therefore, fpl, which represents the result of the one-dimensional DCT obtained by performing the first addition shown in Equations 48 and 49 for the one-dimensional DCT, is always the same as ±f(N-P)l. therefore, a butterfly structure can be formed. Also, the one-dimensional DCT obtained by performing the first subtraction shown in Equations 50 and 51 for the one-dimensional DCT
Since gpl, which indicates the result of , always appears together with ±g(NP)(N-1), it is possible to form a butterfly configuration for this as well.

The process of implementing two-dimensional DCT according to the present invention will be explained with reference to FIG. 2A. After storing N×N two-dimensional digital data in the input buffer 00, the re-arranging unit 20
0 rearranges N×N two-dimensional digital data into N groups based on Equations 20 and 21 above. From now on, the first
The adder 300 calculates (X1
j(p;a) +X1j(p;b) ) and (-1)
To perform the operation qpl(X1j(p;a)-X1j(p;b)), butterfly-style addition and subtraction operations are performed. In this case, when n is an even number, the rearranged data of adjacent groups are added and subtracted. On the other hand, if n is an odd number, one subtraction operation of the data sets of the adjacent group is performed. The data subjected to the first addition and first subtraction operations by the first adder 300 is sent to the one-dimensional DCT section 400, where the above equation 43,
First-order DCT is performed using a method such as No. 44. The output at this time is f indicating the one-dimensional DCT result of the first addition data.
pl and appears in the form of gpl indicating the one-dimensional DCT result of the first subtraction data.

Then, the second adder 500 calculates the f
Input pl and gpl, perform the second addition in butterfly form, and then output the two-dimensional DCT ymn. Thereafter, the output of the second adder 500 is sent to the output buffer 600.
Here, the data is rearranged to suit the output format and output to a coder.

As described above, the two-dimensional DCT data is again inversely transformed using the configuration shown in FIG. 2B. That is, FIG. 2B is 2
2 is a block diagram of a dimensional IDCT (two-dimensional inverse discrete cosine transform), showing that the execution order is reverse to that of the two-dimensional DCT. FIG.

Now, the process of performing two-dimensional DCT on 8×8 two-dimensional digital data according to the present invention will be specifically explained.

First, when N=8, by equation 8, 2
The dimension DCT ymn is expressed as follows.

[0097]

##EQU52## Here, m, n=0, 1, 2, 3, 4, 5, 6, 7.

In addition, Amn and Bm in the above formulas 9 and 10
n is also as follows.

0099

[Math. 53]

[0100]

[Equation 54] At this time, if it is established that the above Amn and Bmn are the same as the 8-point DCT through the data rearrangement process, the 2-dimensional DCT can be calculated from 8 independent 1-dimensional DCTs. I understand. Therefore, in order for the transformation kernel indicated by Amn and Bmn above to be the same as the one-dimensional transformation kernel,
[(2i+1)m±(2j+1)n) must be expressed as a multiple of (2i+1), and in order to satisfy this condition, (2j+1) is mod 2N of (2i+1)
or (2i+1)+N mod 2N. Therefore, the 8×8 two-dimensional input data is
If the data is divided into 8 groups consisting of
It becomes T. Therefore, if N=8, the result is p=1,
3, 5, 7, and 8 based on equations 16 and 17.
i to divide ×8 input data into 8 groups
and the value of j is determined.

[0101] Therefore, input data [X1j:ij=0,
1, 2, 3, 4, 5, 6, 7] are divided into eight groups as shown below according to the above equations (17) and (18).

R1a={X00,X11,X22,X33,X4
4,X55,X66,X77} R1b={X07,
X16,X25,X34,X43,X52,X61,X
70} R3a={X01, X14, X27, X32
,X45,X50,X53,X75} R3b={X
06,X13,X20,X35,X42,X57,X6
4,X71} R5a={X02,X17,X24,
X31, X46, X53, X60, X75} R5b
={X05,X10,X23,X36,X41,X54
,X67,X72} R7a={X03,X12,X
21,X30,X47,X56,X65,X74}
R7b={X04,X15,X26,X37,X40,
X51, X62, X73} Also, the sequence qpi for p=1, 3, 5, 7 is as follows.

q1i={0,0,0,0,0,0,0,0}q3i=
{0,0,0,1,1,2,2,2}q5i={0,0
,1,2,2,3,4,4}q7i={0,1,2,3
, 3, 4, 5, 6} Therefore, when attempting to perform two-dimensional DCT on 8×8 input data as shown in FIG. In order to convert into the form of cosine addition, Fig.
Rearrange the 8 input data as one group into 9 groups as shown below.

Hereinafter, a process of performing two-dimensional DCT in the form of eight one-dimensional DCTs using the eight groups of rearranged data will be described. Here, Amn and Bmn expressed in the above equations 22 and 23 are as follows when N=8.

Amn=[T1a(m,n) +T1b(m,n)
+T3a(m,n) +T3b(m,n)
+T5a (m, n) +T5b (m, n) +
T7a (m, n) + T7b (m, n) ] Bmn
=[S1a(m,n) +S1b(m,n) +S3a
(m, n) +S3b(m, n) +
S5a(m,n) +S5b(m,n) +S7a(m
,n) +S7b(m,n)] Here, Tpa(m,
n) , Tpb (m, n) , Spa (m, n) and Spb (m, n) are expressed by the above equations 30 and 31, respectively.
, Equations 33 and 34, Equations 35 and 36, and Equations 37 and 38. Therefore, according to equations 39 and 40, ym
When n is an even number and p is an odd integer,

[0106]

[Math. 55] and when n is an odd number and p is an odd number,

[0107]

[Number 56] becomes.

However, here, the above ymn,

01
09]

[Math. 57] and,

[0110]

[Formula 58] is the given m. Sequence of 2N input data for n [X1j(p;a) +X1j(p;b) )]
This corresponds to the one-dimensional DCT of

Similarly,

[0112]

[Math. 59] and,

[0113]

[Formula 60] corresponds to the one-dimensional DCT of the sequence of input data for given m and n, so qp
l can be defined. Therefore, fpl can be defined as shown in Equation 43 above. Therefore, the first adder 300 calculates (X1j(p;a) +X1j(p
;b)) After executing ), the first addition data is generated, and (-1)qpl(X1j(p;a) -X1j(
p; b) After executing ), first subtraction data is generated.

That is, the first adder 300 generates first addition data and first subtraction data using the rearranged eight group data. That is, the adders (301 to
304) are R1 groups (R1a, R1b), R
3 group (R3a, R3b), R5 group (R
5a, R5b) and R7 group (R7a, R7b
) are added to generate first addition data. The adders (305 to 308) generate first subtraction data by subtracting the other from any one of the reordered data sets of the R1 group, R3 group, R5 group, and R7 group.

When the first adder 300 generates the first addition data and the first subtraction data, the one-dimensional DCT section 400 uses eight one-dimensional DCTs to calculate the
DCT is performed on the first addition data and the first subtraction data. That is, the one-dimensional DCT elements (401-404) generate fpl data after inputting the first addition data from the adder (301-304), while the one-dimensional DCT elements (405-408) GPL data is generated after inputting the first subtraction data of the subtracters (305 to 308). Therefore, in order to calculate the 8x8 DCT sequence ymn, only fpl and gpl are required, which means that only 8 one-dimensional DCTs are required when calculating the 8x8 DCT. That means.

As mentioned above, ymn occurs in the form of the sum of fpl and gpl, but here, in order to capture the relationship that exists between ymn, fpl, and gpl, several arbitrarily selected m Let's observe this for n.

y30=1/2(f13+f13+f33+f33
+f53+f53+f73+f73) y52=1/
2(f17+f13-f35+f31-f51+f55
-f73-f77) y34=1/2(f17+f1
1-f31-f37-f57-f51+f71+f77
) y26=1/2(0 +f14-f34-f4
0+f50+f54-f74+ 0) y41=1
/2(g15+g13+g37+g31-g57+g5
1-g75+g73) y03=1/2(g13+g
13-g37-g37+g51-g51-g75-g7
5) y35=1/2(0 +g12-g32-g
34+g54-g56+g76+g70) y57=
1/2 (-g14+g12+g36-g30+0+g5
2-g76-g74) At this time, if n is an even number, fpl always appears with ±f(N-p1) in the above equations 48 and 49, so a butterfly form can be created. On the other hand, if n is an odd number, gpl always appears together with ±g(n-p1) in equations 50 and 51 above, so
You can create a butterfly shape.

Therefore, when N=8, the above example can be shown as follows.

y30=1/2 {(f13+f73)+(f13+f7
3)+(f33+f53)+(f33+f53)}y5
2=1/2 {(f17-f77)+(f13-f73)
-(f35+f55)+(f31-f51)}y34=
1/2 {(f17+f77)+(f11+f71)-(
f31+f51)+(f31+f51)}y26=1/
2{(0+0)+(f14-f74)-(f34-f5
4)-(f30+f51)}y41=1/2{(g15
+g73)+(g13-g75)+(g37+g51)
+(g31-g57)}y03=1/2{(g13-g
75)+(g13-g75)-(g37+g51)-(
g37-g57)}y35=1/2{(0+g70)+
(g12+g76)-(g32+g56)-(g34-
g54)}y57=1/2{-(g14+g74)+
(g12-g76)+(g36+g52)-(g30-
0)} Therefore, in order to observe the operation of the first adder 500, the above y30=1/2[(f13+f73)+(
f13+f73)+(f33+f53)+(f33+f
53)] as an example, (f13+f73), (f1
3+f73), (f33+f53), (f33+f53
) is executed by the adder 501, and (f13+f73)+(
f13+f73) and (f33+f53)+(f33
+f53) is executed in the adder 502, and [(f13+f
73)+(f13+f73)]+[(f33+f53)
+(f33+f53)] is executed by the adder 503, and “
1/2'' is executed by shifter 504.

Observing the configuration of FIG. 4, in FIG. 4A, the first adder 300 adds the first addition data and the first subtraction data in order to supply the rearranged data X1j to the one-dimensional DCT section 400. Generate data. One-dimensional DCT400
is a DCT on the first addition data and first subtraction data.
By applying , fpl and gpl are output.

On the other hand, the second adder 500 configured as shown in FIG. 4B calculates ymn, where n is an even number, from fpl generated by the one-dimensional DCT unit 400. Further, the second adder 500 configured as shown in FIG. 4C calculates ymn, where n is an odd number, from gpl. The number of additions of the second adder 500 is determined by log2 N stages, and is shown in FIGS. 4B and 4.
If N=8 as shown in C, the number of additions is 3.
steps (=log2 8). Furthermore, the second adder 50
Since multiplication by 1/2 by 0 is the same as a shift operation, the actual multiplication is performed by the one-dimensional DCT unit 400.

[0122] After performing the two-dimensional DCT as described above, the operation during inverse transformation will be observed with reference to FIGS. 5A to 5C.

In general, for all orthogonal transform fast algorithms, the inverse transform flow depends on the scale factor (sca
When the flow rate (le factor) is not taken into consideration, the flow can be calculated in the reverse order of the forward direction flow. However, if the scale factor is to be taken into consideration when performing the inverse transformation, this must be slightly modified before the inverse transformation is performed. That is, FIG. 4A-
4C, there are some nodes that do not have pairs when executing the two-dimensional DCT, so the second adder 50
It becomes impossible for 0 to form a butterfly configuration.

[0124] Therefore, when the signal flow is reversed when performing two-dimensional IDCT, the first calculation unit 350, which performs the inverse operation to that of the second adder 500, doubles the value of the corresponding node and performs the inverse operation. It is best to make sure that the value of the conversion does not change. That is, it can be seen that there is no pair between the two nodes existing on the line f50 and f70 in the second adder 500. Therefore,
In the case of two-dimensional IDCT, if the first calculation unit 350 doubles the value of the corresponding line, a correct result can be obtained. Furthermore, the one-dimensional IDCT unit 450 must multiply the 0th input by 1/2 when the scale factor is considered, but this can be solved by a shift operation. However, when executing the gpl one-dimensional IDCT from the one-dimensional IDCT unit 450, such multiplication 1/2
and the node value multiplication 2 can cancel each other out.

Here, if it is desired to maintain the scale factor of X1j in its original state, it is recommended to multiply each node value by 1/2 or divide the input ymn by N2/2. However, when considering operations with a finite number of bits, it is advantageous to multiply each node value by 1/2.

[0126] Also, when you want to implement a two-dimensional DCT into a highly integrated circuit, the most important point is that the two-dimensional DC
The goal is to reduce the number of multiplications required to perform T. The reason is that multipliers occupy a large amount of integrated circuit area. The method of performing two-dimensional DCT using the method shown in FIG. 3 requires N one-dimensional DCTs. Therefore, when implementing N×N DCT in parallel, N one-dimensional DC
It can be seen that a T structure is required.

FIGS. 7A to 7C show how the multiplexer 700 is used when implementing the N×N DCT in parallel.
and N/2 1s using the demultiplexer 800.
We present a method to perform dimensional DCT. At this time, Figure 3
In A, the first adder 300 calculates the rearranged data in each group to generate first addition data and first subtraction data, and adds one-dimensional data to the output of the first adder 300. The DCT unit 400 performs DCT operation to obtain f
Generate pl and fpl. However, as shown in Figure 6,
The one-dimensional DCT unit 400 first performs a one-dimensional DCT operation on the rearranged group data, and then the one-dimensional DCT result is processed by the first adder 300 to obtain the same fp.
Generate l and gpl.

That is, while the adders (301, 302) process the rearranged data of the R1a and R1b groups, the one-dimensional DCT (403, 404)
One-dimensional DCT processing is performed on the rearranged data of the group. After that, R1a output from the adder (301, 302)
, the first addition data and first subtraction data of the R1b group and the one-dimensional DCT data of the R3a and R3b groups output from the one-dimensional DCT (403, 403) are processed by an adder (303, 304). Even if f
pl and gpl will be the same. That is, as shown in FIG. 6, the rearrangement data of R3a and R3b groups and R7a
, R7b group, even if the first addition process and one-dimensional DCT order are changed, the generated fp
l and gpl will be the same.

Therefore, as in FIGS. 7A-7C,
The multiplexer 701 selects the rearranged data of the R3a and R3b groups while the adders (311, 315) process the rearranged data of the R1a and R1b groups,
Output to one-dimensional DCT elements (411, 412).

[0130] Furthermore, the multiplexer 702 has an adder (
313, 317) process the rearranged data of the R5a, R5b groups, the rearranged data of the R7a, R7b groups are selected and sent to the one-dimensional DCT (413, 414).

Therefore, while the rearranged data of the R1a and R1b groups and the rearranged data of the R5a and R5b groups are processed by the first adder 300, the one-dimensional DCT unit 4
00 executes one-dimensional DCT on the rearranged data of the R3a and R3b groups and the rearranged data of the R7a and R7b groups.

[0132] From now on, the multiplexers (701, 702
) are adders (311, 315) and adders (313,
The demultiplexers (801, 802) select the outputs of the one-dimensional DCTs (411, 41), respectively.
2) and one-dimensional DCT (413, 414) to adders (312, 316) and adders (314, 3), respectively.
18) Selectively output to the side. Therefore, the data of R1a, R1b group and R5a, R5b group are one-dimensional D
During one-dimensional DCT processing in the CT unit 400, R3a,
It can be seen that the data of the R3b group and the R7a, R7b groups are processed by the first adder 300. From then on,
The result is sent to a second adder 500 where log2
The sums are added by N butterfly stages and output.

[0133]

Effects of the Invention: When performing two-dimensional DCT processing on two-dimensional N×N input data as described above, by executing N one-dimensional DCTs, and performing the first and second additions in a butterfly format. By doing so, two-dimensional DCT processing can be realized. In addition, when configuring hardware in parallel using multiplexers and demultiplexers, only N/2 one-dimensional DCTs are required, which greatly reduces the number of multipliers and realizes two-dimensional DCTs at high speed. It has the advantage of being able to implement highly integrated circuits at the same time.

[Brief explanation of the drawing]

FIG. 1 is a configuration diagram of a conventional two-dimensional discrete cosine transform device.

[Figure 2A],

FIG. 2B is a configuration diagram of a two-dimensional discrete cosine transform device according to the present invention.

[Figure 3A],

3B is a rearrangement data configuration diagram for the 8×8 input data of FIG. 2; FIG.

[Figure 4A],

[Figure 4B],

FIG. 4C is a diagram of a first embodiment of a two-dimensional discrete cosine transform device for 8×8 input data.

[Figure 5A],

[Figure 5B],

FIG. 5C is a configuration diagram of an 8×8 two-dimensional inverse discrete cosine transform device.

6 is another configuration diagram of the first adder and one-dimensional discrete cosine transform section in FIG. 2. FIG.

[Figure 7A],

[Figure 7B],

FIG. 7C is a diagram of a second embodiment of a two-dimensional discrete cosine transform device for 8×8 input data.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 100... Input buffer, 200... Re-ordering part, 300... First adder, 400... One-dimensional DCT part, 500... Second adder, 600... Output buffer

Claims (2)

[Claims] Claim 1. A method of performing discrete cosine transform on N×N two-dimensional input data at high speed, wherein the N×N data is transformed into a multiplication form of a cosine function, which is the core of the two-dimensional discrete cosine transform, by adding a cosine function. In order to convert it into a form,
A step of rearranging N groups so as to be the same as the kernel of the one-dimensional discrete cosine transform of the cosine function, and rearranging data of even and odd groups in the rearranged group data, respectively. Add each to N/2
a first operation step of generating N/2 first addition data and subtracting one from the other for the remaining data groups to generate N/2 first subtraction data;
A step of performing one-dimensional discrete cosine transform on each of the first addition data and first subtraction data in the calculation step, and adding and subtracting the one-dimensional discrete cosine transform output in a log2 N-stage butterfly form, and then shifting to the result of the addition and subtraction. 1. A two-dimensional discrete cosine transform method comprising the step of generating two-dimensional discrete cosine transform data by performing processing. 2. In an apparatus for performing discrete cosine transform on N×N two-dimensional input data at high speed, the N×N two-dimensional data is transformed into a cosine function by converting the multiplication form of a cosine function, which is the core of the two-dimensional discrete cosine transform, into a cosine function. a rearranging means for rearranging the data into N groups so as to be the same as the core of the one-dimensional discrete cosine transform of the above-mentioned cosine transform in order to convert the data into an additive form; and an even number group and an odd number group of the rearranged data. of the rearranged data of N/2 first
means for generating addition data and generating N/2 first subtraction data by subtracting one data from the other data for the remaining groups; first addition data and first subtraction data; a one-dimensional DCT processing means that performs a one-dimensional discrete cosine transform on each of the above, and a one-dimensional DCT processing means that is connected to the one-dimensional DCT processing means and configured in a log2 N-stage butterfly form, and that adds and subtracts the outputs of the one-dimensional DCT processing means. A two-dimensional discrete cosine transform apparatus comprising: a two-dimensional discrete cosine transform process that generates two-dimensional discrete cosine transform data by executing a shift step of multiplying by 1/2 from .