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Claims  |
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What is claimed is:
1. A transform system for digital signals, comprising:
means for performing a first linear transform of N digital signals (x1, x2,
. . . , xN) each digitized and represented in an integer with integer
coefficients to obtain N integer transform signals (y1, y2, . . . , yN)
and ouputting the N integer transform signals (y1, y2, . . . , yn), N
being a positive integer;
means for dividing the N integer transform signals (y1, y2, . . . , yN) by
N quantization periods (d1, d2, . . . , dN) formed from multiples of a
transform determinant of the first linear transform to obtain N quotients
and N remainders and outputting the N quotients and the N remainders as
general situation transform signals (a1, a2, . . . , aN) and local
transform signals (r1, r2, . . . , rN), respectively:
means including a first numerical value table for deriving N local
quantization values (q1, q2, . . . , qN) from the N local transform
signals (r1, r2, . . . , rN) using said first numerical table; and
means for multiplying the N general situation transform signals (a1, a2, .
. . , aN) by N scaling multiplier factors (m1, m2, . . . , mN) and adding
the N local quantization values (q1, q2, . . . , qN) to resulting products
to obtain N quantization values (Q1, Q2, . . . , QN).
2. The transform system for digital signals according to claim 1, further
comprising an inverse transform system for the digital signals, the
inverse transform system comprising:
means for dividing the N quantization values (Q1, Q2, . . . , QN) by the N
scaling multiplier factors (m1, m2, . . . , mN) to obtain N quotients and
N remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively;
means including a second numerical value table for deriving N regeneration
local transform coefficients (r'1, r'2, . . . , r'N) from the N local
quantization values (q1, q2, . . . , qN) using said second numerical value
table;
means for multiplying the N general situation transform signals (a1, a2, .
. . , aN) by the N quantization periods (d1, d2, . . . , dN) and adding
the N regeneration local conversion signals (r'1, r'2, . . . , r'N) to
resulting products to obtain N regeneration integer conversion signals
(y'1, y'2, . . . , Y'N) ; and
means for applying an inverse transform of the first linear transform to
the N regeneration integer transform signals (y'1, y'2, . . . , y'N) to
obtain N regeneration signals (x'1, x'2, . . . , x'N).
3. The transform system as claimed in claim 2, wherein said second
numerical value table provides a complete inverse transform of said first
numerical value table.
4. The transform system for digital signals according to claim 1, further
comprising an inverse transform system for the digital signals, the
inverse transform system comprising:
means for dividing the N quantization values (Q1, Q2, . . . , QN) by the N
scaling multiplier factors (m1, m2, . . . , mN) to obtain N quotients and
N remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively;
means including a third numerical value table for deriving N local
regeneration signals (i1, i2, . . . , iN) from the N local quantization
values (q1, q2, . . . , qN) using said third numerical value table;
means for applying a second linear transform to the N general situation
transform signals (a1, a2, . . . , aN) to obtain N general situation
regeneration signals (g1, g2, . . . , gN); and
means for adding the N local regeneration signals (i1, i2, . . . , iN) and
the N general situation regeneration signals (g1, g2, . . . , gN) to
obtain N regeneration signals (x'1, x'2, . . . , x'N).
5. The transform system as claimed in claim 4, wherein the second linear
transform is equivalent to a combination wherein a diagonal matrix
transform of the N quantization periods (d1, d2, . . . , dN) and an
inverse linear transform are combined in order, wherein the inverse linear
transform means applies an inverse transform of the first linear transform
to N regeneration integer transform signals to obtain N regeneration
signals, and
wherein said third numerical value table is equivalent to another
combination wherein a second inverse transform and a first inverse linear
transform are combined in order,
wherein said first inverse linear transform includes,
means for dividing the N quantization values (Q1, Q2, . . . , QN) by the N
scaling multiplier factors (m1, m2, . . . , mN) to obtain N quotients and
N remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively,
means including a second numerical value table for deriving N regeneration
local transform coefficients (r'1, r'2, . . . , r'N) from the N local
quantization values (q1, q2, . . . , qN) using said second numerical value
table,
means for multiplying the N general situation transform signals (a1, a2, .
. . , aN) by the N quantization periods (d1, d2, . . . , dN) and adding
the N regeneration local conversion signals (r'1, r'2, . . . , r'N) to
resulting products to obtain N regeneration integer conversion signals
(y'1, y'2, . . . , Y'N), and
means for applying an inverse transform of the first linear transform to
the N regeneration integer transform signals (y'1, y'2, . . . , y'N) to
obtain N regeneration signals (x'1, x'2, . . . , x'N), and
wherein said second inverse transform comprises the first inverse transform
in which said second numerical value table provides a complete inverse
transform of said first numerical value table.
6. The transform system as claimed in claim 1, wherein said first numerical
value table uses, in place of one (ri) of the local transform signals
which are the input signals to said first numerical value table, a
quotient obtained when the signal (ri) is divided by a determinant (D) of
the transform matrix of the first linear transform.
7. A reversible transform system for digital signals, comprising:
transform means for receiving sample signals each digitized and represented
in an integer as inputs thereto, transforming the input sample signals in
accordance with a first transform method and outputting resulting
quantization values, the first transform method including
performing a first linear transform of N received sample digital signals
(x1, x2, . . . , xN) each digitized and represented in an integer with
integer coefficients to obtain N integer transform signals (y1, y2, . . .
, yN) and outputting the N integer transform signals (y1, y2, . . . , yN),
N being a positive integer,
dividing the N integer transform signals (y1, y2, . . . , yN) by N
quantization periods (d1, d2, . . . , dN) formed from multiples of a
transform determinant of the first linear transform to obtain N quotients
and N remainders and outputting the N quotients and the N remainders as
general situation transform signals (a1, a2, aN) and local transform
signals (r1, r2, . . . , rN), respectively,
using a first numerical value table for deriving N local quantization
values (q1, q2, . . . , qN) from the N local transform signals (r1, r2, .
. . , rN) using said first numerical table, and
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by N scaling multiplier factors (m1, m2, . . . , mN) and adding the N
local quantization values (q1, q2, . . . , qN) to resulting products to
obtain N quantization values (Q1, Q2, . . . , QN);
reversible coding means for reversibly coding the outputs of said transform
means;
means for receiving output signals of said reversible coding means as
inputs thereto and decoding the input signals; and
inverse transform means for inputting results of the decoding, performing
an inverse transform of the input decoding results in accordance with a
first inverse transform method to obtain regeneration signals and
outputting the regeneration signals, the first inverse transform method
including
dividing the N decoded quantization values (Q1, Q2, . . . , QN) by the N
scaling multiplier factors (m1, m2, . . . , mN) to obtain N quotients and
N remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively,
using a second numerical value table for deriving N regeneration local
transform coefficients (r'1, r'2, . . . , r'N) from the N local
quantization values (q1, q2, . . . , qN) using said second numerical value
table,
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by the N quantization periods (d1, d2, . . . , dN) and adding the N
regeneration local conversion signals (r'1, r'2, . . . , r'N) to resulting
products to obtain N regeneration integer conversion signals (y'1, y'2, .
. . , Y'N), and
applying an inverse transform to the first linear transform to the N
regeneration integer transform signals (y'1, y'2, . . . , y'N) to obtain N
regeneration signals (x'1, x'2, . . . , x'N),
wherein said second numerical value table provides a complete inverse
transform of said first numerical value table.
8. A reversible transform-system for digital signals, comprising:
transform means for receiving sample signals each digitized and represented
in an integer as inputs thereto, transforming the input sample signals in
accordance with a first transform method and outputting resulting
quantization values, the first transform method including
performing a first linear transform of N received sample digital signals
(x1, x2, . . . , xN) each digitized and represented as an integer with
integer coefficients to obtain N integer transform signals (y1, y2, . . .
, yN) and outputting the N integer transform signals (y1, y2, . . . , yN),
N being a positive integer,
dividing the N integer transform signals (y1, y2, . . . , yN) by N
quantization periods (d1, d2, . . . , dN) formed from multiples of a
transform determinant of the first linear transform to obtain N quotients
and N remainders and outputting the N quotients and the N remainders as
general situation transform signals (a1, a2, . . . , aN) and local
transform signals (r1, r2, . . . , rN), respectively,
using a first numerical value table for deriving N local quantization
values (q1, q2, . . . , qN) from the N local transform signals (r1, r2, .
. . , rN) using said first numerical table, and
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by N scaling multiplier factors (m1, m2, . . . , mN) and adding the N
local quantization values (q1, q2, . . . , qN) to resulting products to
obtain N quantization values (Q1, Q2, . . . , QN);
reversible coding means for reversibly coding the outputs of said transform
means;
means for receiving output signals of said reversible coding means as
inputs thereto and decoding the input signals; and
inverse transform means for inputting results of the decoding, performing
an inverse transform of the input decoding results to obtain regeneration
signals and outputting the regeneration signals, the inverse transform
comprising
means for dividing N decoded quantization values (Q1, Q2, . . . , QN) by N
scaling multiplier factors (m1, m2, . . . , mN) to obtain N quotients and
N remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively,
means including a third numerical value table for deriving N local
regeneration signals (i1, i2, . . . , iN) from the N local quantization
values (q1, q2, . . . , qN) using said third numerical value table,
means for applying a second linear transform to the N general situation
transform signals (a1, a2, . . . , aN) to obtain N general situation
regeneration signals (g1, g2, . . . , gN), and
means for adding the N local regeneration signals (i1, i2, . . . , iN) and
the N general situation regeneration signals (g1, g2, . . . , gN) to
obtain N regeneration signals (x'1, x'2, . . . , x'N),
wherein the second linear transform is equivalent to a combination wherein
a diagonal matrix transform of the N quantization periods (d1, d2, . . . ,
dN) and an inverse linear transform means are combined in order, wherein
the inverse linear transform means applies an inverse transform to a first
linear transform to N regeneration integer transform signals to obtain N
regeneration signals, and
wherein said third numerical value table is equivalent to another
combination wherein a second inverse transform and a first inverse linear
transform are combined in order,
wherein said first inverse linear transform includes,
means for dividing the N quantization values (Q1, Q2, . . . , QN) by the N
scaling multiplier factors (m1, m2, . . . , mN) to obtain N quotients and
N remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively,
means including a second numerical value table for deriving N regeneration
local transform coefficients (r'1, r'2, . . . , r'N) from the N local
quantization values (q1, q2, . . . , qN) using said second numerical value
table,
means for multiplying the N general situation transform signals (a1, a2, .
. . , aN) by the N quantization periods (d1, d2, . . . , dN) and adding
the N regeneration local conversion signals (r'1, r'2, . . . , r'N) to
resulting products to obtain N regeneration integer transform signals
(y'1, y'2, . . . , y'N), and
means for applying an inverse transform to the first linear transform to
the N regeneration integer transform signals (y'1, y'2, . . . , y'N) to
obtain N regeneration signals (x'1, x'2, . . . , x'N), and
wherein said second inverse transform comprises the first inverse transform
in which said second numerical value table provides a complete inverse
transform of said first numerical value table.
9. A transform system for digital signals for transforming four signals x0,
x1, x2 and x3, comprising:
means for calculating a sum x0+x3 and a difference x0-x3 of x0 and x3;
means for calculating a sum x1+x2 and a difference x2-x1 of x1 and x2;
means for deleting the least significant bits of the sums x0+x3 and x1+x2;
means for performing a transform of resulting values of the deletion (s1,
s2) with a first transform matrix of
##EQU21##
in accordance with a first transform method, the first transform method
including
performing a first linear transform, using the first transform matrix, of
the 2 digital signals (s1, s2), representative of the resulting values of
the deletion, each digitized and represented as an integer with integer
coefficients to obtain 2 integer transform signals (y1, y2) and outputting
the 2 integer transform signals (y1, y2),
dividing the 2 integer transform signals (y1, y2) by 2 quantization periods
(d1, d2) formed from multiples of a transform determinant of the first
linear transform to obtain 2 quotients and 2 remainders and outputting the
2 quotients and the 2 remainders as general situation transform signals
(a1, a2) and local transform signals (r1, r2), respectively,
using a first numerical value table for deriving 2 local quantization
values (q1, q2) from the 2 local transform signals (r1, r2) using said
first numerical table, and
multiplying the 2 general situation transform signals (a1, a2) by 2 scaling
multiplier factors (m1, m2) and adding the 2 local quantization values
(q1, q2) to resulting products to obtain 2 quantization values (Q1, Q2);
and
means for performing a transform of the differences x0-x3 and x2-x1 with a
second transform matrix, instead of the first transform matrix, of
##EQU22##
in accordance with the transform method employed in said first transform
method.
10. The transform system as claimed in claim 9, further comprising,
means for performing an inverse transform method for digital signals, the
inverse transform method comprising:
performing an inverse transform with the second transform matrix of
##EQU23##
in accordance with a first inverse transform method, wherein the first
inverse transform method includes
dividing 2 quantization values (Q1, Q2) by the 2 scaling multiplier factors
(m1, m2) to obtain 2 quotients and 2 remainders and outputting the 2
quotients and the 2 remainders as local quantization values (q1, q2) and
general situation transform values (a1, a2), respectively,
using a second numerical value table for deriving 2 regeneration local
transform coefficients (r'1, r'2) from the 2 local quantization values (q1
, q2) using said second numerical value table,
multiplying the 2 general situation transform signals (a1, a2) by the 2
quantization periods (d1 d2) and adding the 2 regeneration local
conversion signals (r'1, r'2) to resulting products to obtain 2
regeneration integer conversion signals (y'1, y'2), and
applying an inverse transform to the first linear transform, with the
second transform matrix, to the 2 regeneration integer conversion signals
(y'1, y'2) to obtain 2 regeneration signals (x'1, x2),
performing an inverse transform with the first transform matrix, instead of
the second transform matrix, of
##EQU24##
in accordance with the method employed by said means for calculating the
differences x0-x3 and x2-x1 and the first inverse transform method, and
adding the least significant bits of the differences x0-x3 and x2-x1 to
the least significant bits of a result of the inverse transform to obtain
the sums x0+x3 and x1+x2, respectively;
means for calculating the signals x0 and x3 by butterfly calculations from
the sum x0+x3 and the difference x0-x3; and
means for calculating the signals x2 and x1 by butterfly calculations from
the sum x2+x1 and the difference x2-x1.
11. A reversible transform system for digital signals, comprising:
transform means for receiving sample signals each digitized and represented
in an integer as inputs thereto, transforming the input sample signals in
accordance with a second transform method and outputting resulting
quantization values, the second transform method including
calculating a sum x0+x3 and a difference x0-x3 of x0 and x3, wherein x0,
x1, x2, and x4 are digital signals,
calculating a sum x1+x2 and a difference x2-x1 of x1 and x2,
deleting the least significant bits of the sums x0+x3 and x1+x2 and
performing a transform of resulting values of the deletion with a first
transform matrix of
##EQU25##
in accordance with a first transform method, the first transform method
including
performing a first linear transform, using the first transform matrix, of 2
digital signals (s1, s2), each digitized and represented as an integer
with integer coefficients to obtain 2 integer transform signals (y1, y2)
and outputting the 2 integer transform signals (y1, y2),
dividing the 2 integer transform signals (y1, y2) by 2 quantization periods
(d1, d2) formed from multiples of a transform determinant of the first
linear transform to obtain 2 quotients and 2 remainders and outputting the
2 quotients and the 2 remainders as general situation transform signals
(a1, a2) and local transform signals (r1, r2), respectively,
using a first numerical value table for deriving 2 local quantization
values (q1, q2) from the 2 local transform signals (r1, r2) using said
first numerical table, and
multiplying the N general situation transform signals (a1, a2) by 2 scaling
multiplier factors (m1, m2) and adding the 2 local quantization values
(q1, q2) to resulting products to obtain 2 quantization values (Q1, Q2),
and
means for performing a transform of the differences x0-x3 and -x1+x2 with a
second transform matrix, instead of the first transform matrix, of
##EQU26##
in accordance with the transform method employed in said first transform
method;
reversible coding means for reversibly coding the outputs of said transform
means;
means for receiving output signals of said reversible coding means as
inputs thereto and decoding the input signals; and
inverse transform means for inputting results of the decoding, performing
an inverse transform of the input decoding results in accordance with a
second inverse transform method to obtain regeneration signals and
outputting the regeneration signals, the second inverse transform method
including
performing an inverse transform with the second transform matrix of
##EQU27##
in accordance with a first inverse transform method, wherein the first
inverse transform method includes
dividing 2 quantization values (Q1, Q2) by the 2 scaling multiplier factors
(m1, m2) to obtain 2 quotients and 2 remainders and outputting the 2
quotients and the 2 remainders as local quantization values (q1, q2) and
general situation transform values (a1, a2), respectively,
using a second numerical value table for deriving 2 regeneration local
transform coefficients (r'1, r'2) from the 2 local quantization values
(q1, q2) using said second numerical value table,
multiplying the 2 general situation transform signals (a1, a2) by the 2
quantization periods (d1, d2) and adding the 2 regeneration local
transform coefficients (r'1, r'2) to resulting products to obtain 2
regeneration integer transform signals (y'1, y'2) and
applying an inverse transform to the first linear transform with the second
transform matrix to the 2 regeneration integer transform signals (y'1,
y'2) to obtain 2 regeneration signals (x'1, x'2),
performing an inverse transform with the first transform matrix of
##EQU28##
in accordance with the method employed by said means for calculating the
differences x0-x3 and x2-x1 and the first inverse transform method, and
adding the least significant bits of the differences x0-x3 and x2-x1 to
the least significant bits of a result of the inverse transform to obtain
the sums x0+x3 and x1+x2, respectively,
means for calculating the signals x0 and x3 by butterfly calculations from
the sum x0+x3 and the difference x0-x3, and
means for calculating the signals x2 and x1 by butterfly calculations from
the sum x2+x1 and the difference x2-x1.
12. A transform system for digital signals for eight signals x0, x1, x2,
x3, x4, x5, x6 and x7, comprising:
means for calculating a sum x0+x7 and a difference x0-x7 of x0 and x7;
means for calculating a sum x3+x4 and a difference x3-x4 of x3 and x4;
means for calculating a sum x1+x6 and a difference x1-x6 of x1 and x6;
means for calculating a sum x2+x5 and a difference x2-x5 of x2 and x5;
means for performing a transform of the differences x0-x7, x3-x4, x1-x6 and
x2-x5 with a first transform matrix of
##EQU29##
in accordance with a first transform method with N=4, the first transform
method including
performing a first linear transform, using the first transform matrix, of N
digital signals (s1, s2, . . . , sN) each digitized and represented as an
integer with integer coefficients to obtain N integer transform signals
(y1, y2, . . . , yN) and outputting the N integer transform signals (y1,
y2, . . . , yN), N being a positive integer,
dividing the N integer transform signals (y1, y2, . . . , yN) by N
quantization periods (d1, d2, . . . , dN) formed from multiples of a
transform determinant of the first linear transform to obtain N quotients
and N remainders and outputting the N quotients and the N remainders as
general situation transform signals (a1, a2, . . . , aN) and local
transform signals (r1, r2, . . . , rN), respectively,
using a first numerical value table for deriving N local quantization
values (q1, q2, . . . , qN) from the N local transform signals (r1, r2, .
. . , rN) using said first numerical table, and
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by N scaling multiplier factors (m1, m2, . . . , mN) and adding the N
local quantization values (q1, q2, . . . , qN) to resulting products to
obtain N quantization values (Q1, Q2, . . . , QN);
means for deleting the least significant bits of the sums x7+x0, x4+x3,
x6+x1 and x5+x2;
means for calculating a sum x7+x0+x4+x3 and a difference x7+x0-x4-x3 of the
sums x7+x0 and x4+x3;
means for calculating a sum x6+x1+x5+x2 and a difference x6+x1-x5-x2 of the
sums x6+x1 and x5+x2;
means for performing a transform of the differences x7+x0-x4-x3 and
x6+x1-x5-x2 with a second transform matrix, instead of the first transform
matrix, of
##EQU30##
in accordance with the first transform method and using the second
transform matrix instead of the transform matrix and with N=2; and
means for deleting the least significant bits of the sums x7+x0+x4+x3 and
x6+x1+x5+x2 and performing a Hadamard transform, instead of the first
linear transform, of the deletion in accordance with the first transform
method with N=2.
13. An inverse transform system for digital signals for inversely
transforming signals transformed in accordance with the transform method
employed in said transform system as claimed in claim 12, comprising:
means for performing an inverse transform with the first transform matrix
of
##EQU31##
in accordance with a first inverse transform method with N=4 to obtain
the differences x0-x7, x3-x4, x1-x6 and x2-x5, the first inverse transform
method including
dividing N quantization values (Q1, Q2, . . . , QN) by N scaling multiplier
factors (m1, m2, . . . , mN) to obtain N quotients and N remainders and
outputting the N quotients and the N remainders as local quantization
values (q1, q2, . . . , qN) and general situation transform values (a1,
a2, . . . , aN), respectively,
using a second numerical value table for deriving N regeneration local
transform coefficients (r'1, r'2, . . . , r'N) from the N local
quantization values (q1, q2, . . . , qN) using said second numerical value
table,
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by the N quantization periods (d1, d2, . . . , dN) and adding the N
regeneration local transform signals (r'1, r'2, . . . , r'N) to resulting
products to obtain N regeneration integer transform signals (y'1, y'2, . .
. , y'N), and
applying an inverse transform to the first linear transform to the N
regeneration integer transform signals (y'1, y'2, . . . , y'N) to obtain N
regeneration signals (x'1, x'2, . . . , x'N);
means for performing another inverse transform with the second transform
matrix, instead of the first transform matrix, of
##EQU32##
in accordance with the first inverse transform method with N=2 to obtain
the differences x7+x0-x4-x3 and x6+x1-x5-x2;
means for performing an inverse Hadamard transform, instead of the inverse
transform to the first linear transform, in accordance with the first
inverse transform method with N=2 and adding the least significant bits of
the differences x7+x0-x4-x3 and x6+x1-x5-x2 to a result of the inverse
Hadamard transform to obtain the sums x7+x0+x4+x3 and x6+x1+x5+x2,
respectively;
means for calculating a sum and a difference of the sum x7+x0+x4+x3 and the
difference x7+x0-x4-x3 using a butterfly calculation and adding the least
significant bits of the differences x0-x7 and x3-x4 to the least
significant bits of the sum and the difference to obtain the sums x7+x0
and x4+x3 respectively;
means for calculating a sum and a difference of the sum x6+x1+x5+x2 and the
difference x6+x1-x5-x2 using a butterfly calculation and adding the least
significant bits of the differences x1-x6 and x2-x5 to the least
significant bits of the sum and the difference to obtain the sums x6+x1
and x5+x2, respectively; and
means for calculating the signals x0, x1, x2, x3, x4, x5, x6 and x7 from
the sums x7+x0, x4+x3, x6+x1, x5+x2 and the differences x3-x7, x3-x4,
x1-x6 and x2-x5 using a butterfly calculation.
14. A reversible transform system for digital signals, comprising:
transform means for receiving sample signals each digitized and represented
in an integer as inputs thereto, transforming the input sample signals in
accordance with a second transform method and outputting resulting
quantization values, the second transform method including
calculating a sum x0+x7 and a difference x0-x7 of x0 and x7,
calculating a sum x3+x4 and a difference x3-x4 of x3 and x4,
calculating a sum x1+x6 and a difference x1-x6 of x1 and x6,
calculating a sum x2+x5 and a difference x2-x5 of x2 and x5,
performing a transform of the differences x0-x7, x3-x4, x1-x6 and x2-x5
with a first transform matrix of
##EQU33##
in accordance with a first transform method with N=4, the first transform
method including
performing a first linear transform, using the first transform matrix, of N
digital signals (s1, s2, . . . , sN) each digitized and represented as an
integer with integer coefficients to obtain N integer transform signals
(y1, y2, . . . , yN) and outputting the N integer transform signals (y1,
y2, . . . , yN), N being a positive integer,
dividing the N integer transform signals (y1, y2, . . . , yN) by N
quantization periods (d1, d2, . . . , dN) formed from multiples of a
transform determinant of the first linear transform to obtain N quotients
and N remainders and outputting the N quotients and the N remainders as
general situation transform signals (a1, a2, . . . , aN) and local
transform signals (r1, r2, . . . , rN), respectively,
using a first numerical value table for deriving N local quantization
values (q1, q2, . . . , qN) from the N local transform signals (r1, r2, .
. . , rN) using said first numerical table, and
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by N scaling multiplier factors (m1, m2, . . . , mN) and adding the N
local quantization values (q1, q2, . . . , qN) to resulting products to
obtain N quantization values (Q1, Q2, . . . , QN),
means for deleting the least significant bits of the sums x7+x0, x4+x3,
x6+x1 and x5+x2,
means for calculating a sum x7+x0+x4+x3 and a difference x7+x0-x4-x3 of the
sums x7+x0 and x4+x3,
means for calculating a sum x6+x1+x5+x2 and a difference x6+x1-x5-x2 of the
sums x6+x1 and x5+x2,
means for performing a transform of the differences x7+x0-x4-x3 and
x6+x1-x5-x2 with a second transform matrix, instead of the first transform
matrix, of
##EQU34##
in accordance with the first transform method with N=2, and means for
deleting the least significant bits of the sums x7+x0+x4+x3 and
x6+x1+x5+x2 and performing a Hadamard transform, instead of the first
linear transform, of a result of the deletion in accordance with the first
transform method with N=2;
reversible coding means for reversibly coding the outputs of said transform
means;
means for receiving output signals of said reversible coding means as
inputs thereto and decoding the input signals; and
inverse transform means for inputting results of the decoding, performing
an inverse transform of the input decoding results in accordance a second
inverse transform method to obtain regeneration signals and outputting the
regeneration signals, the second inverse transform method including
performing an inverse transform with the first transform matrix of
##EQU35##
in accordance with a first inverse transform method with N=4 to obtain
the differences x0-x7, x3-x4, x1-x6 and x2-x5 the first inverse transform
method including
dividing the N quantization values (Q1, Q2, . . . , QN) by the N scaling
multiplier factors (m1, m2, . . . , mN) to obtain N quotients and N
remainders and outputting the N quotients and the N remainders as local
quantization values (q1, q2, . . . , qN) and general situation transform
values (a1, a2, . . . , aN), respectively,
using a second numerical value table for deriving N regeneration local
transform coefficients (r'1, r'2, . . . , r'N) from the N local
quantization values (q1, q2, . . . , qN) using said second numerical value
table,
multiplying the N general situation transform signals (a1, a2, . . . , aN)
by the N quantization periods (d1, d2, . . . , dN) and adding the N
regeneration local transform signals (r'1, r'2, r'N) to resulting products
to obtain N regeneration integer transform signals (y'1, y'2, . . . ,
y'N), and
applying an inverse transform to the first linear transform using the first
transform matrix to the N regeneration integer transform signals (y'1,
y'2, . . . , y'N) to obtain N regeneration signals (x'1, x'2, . . . ,
x'N),
means for performing another inverse transform with the second transform
matrix, instead of the first transform matrix, of
##EQU36##
in accordance with the first inverse transform method with N=2 to obtain
the differences x7+x0-x4-x3 and x6+x1-x5-x2,
means for performing an inverse Hadamard transform in accordance with the
first inverse transform method with N=2 and adding the least significant
bits of the differences x7+x0-x4-x3 and x6+x1-x5-x2 to a result of the
inverse Hadamard transform to obtain the sums x7+x0+x4+x3 and x6+x1+x5+x2,
respectively,
means for calculating a sum and a difference of the sum x7+x0+x4+x3 and the
difference x7+x0-x4-x3 using a butterfly calculation and adding the least
significant bits of the differences x0-x7 and x3-x4 to the least
significant bits of the sum and the difference to obtain the sums x7+x0
and x4+x3, respectively,
means for calculating a sum and a difference of the sum x6+x1+x5+x2 and the
difference x6+x1-x5-x2 using a butterfly calculation and adding the least
significant bits of the differences x1-x6 and x2-x5 to the least
significant bits of the sum and the difference to obtain the sums x6+x1
and x5+x2, respectively, and
means for calculating the signals x0, x1, x2, x3, x4, x5, x6 and x7 from
the sums x7+x0, x4+x3, x6+x1, x5+x2 and the differences x3-x7, x3-x4,
x1-x6 and x2-x5 using a butterfly calculation. |
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