Signal transformation apparatus applied hybrid architecture, signal transformation method, and recording medium
View Patent ↗A signal transformation apparatus, a signal transformation method, and a recording medium are provided. The signal transformation apparatus selects any one of DCT-II, DST-II, DFT, and HWT, and transforms and outputs the input signal according to the selected transform. Therefore, the hybrid architecture of low complexity can be attained.
1. A signal transformation apparatus applying a hybrid architecture for Discrete Cosine Transform (DCT)-II, Discrete Sine Transform (DST)-II, Discrete Fourier Transform (DFT), and Haar Wavelet Transform (HWT), comprising:
a switching part for selecting any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a transformation part for transforming and outputting an input signal according to the transform selected by the switching part,
wherein the switching part comprises:
a submatrix selector for selecting submatrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a permutation matrix selector for selecting permutation matrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT,
wherein when the switching part selects the DCT-II, the submatrix selector selects [L] N as a submatrix and the permutation matrix selector selects [D] N as a permutation matrix,
wherein the transformation part applies the DCT-II to the input signal by computing Equation (27) using the submatrix [L] N and the permutation matrix [D] N ;
[
C
]
N
=
2
N
[
P
r
]
N
[
I
N
/
2
0
0
L
N
/
2
]
[
I
2
⊗
P
r
N
/
2
]
[
I
2
⊗
[
I
N
/
4
0
0
L
N
/
4
]
]
[
I
4
⊗
P
r
N
/
4
]
[
I
4
⊗
[
I
N
/
8
0
0
L
N
/
8
]
]
…
[
I
N
/
4
⊗
P
r
4
]
[
I
N
/
4
⊗
[
I
2
0
0
L
2
]
]
[
I
N
/
2
⊗
C
2
]
[
I
N
/
4
⊗
[
I
2
0
0
D
2
]
]
[
I
N
/
4
⊗
[
I
2
I
2
I
2
-
I
2
]
]
[
I
N
/
4
⊗
P
c
4
]
…
[
I
4
⊗
[
I
N
/
8
0
0
D
N
/
8
]
]
[
I
4
⊗
[
I
N
/
8
I
N
/
8
I
N
/
8
-
I
N
/
8
]
]
[
I
4
⊗
P
c
N
/
4
]
[
I
2
⊗
[
I
N
/
4
0
0
D
N
/
4
]
]
[
I
4
⊗
[
I
N
/
4
I
N
/
4
I
N
/
4
-
I
N
/
4
]
]
[
I
2
⊗
P
c
N
/
2
]
[
I
N
/
2
0
0
D
N
/
2
]
[
I
N
/
2
I
N
/
2
I
N
/
2
-
I
N
/
2
]
[
P
c
]
N
,
(
27
)
wherein the submatrix [L] N and the permutation matrix [D] N are defined as
[
L
]
N
=
[
2
0
0
⋯
-
2
2
0
⋯
2
-
2
2
⋯
⋮
⋮
⋱
]
,
[
D
]
N
=
[
C
4
N
Φ
0
0
⋯
0
0
C
4
N
Φ
⋮
⋮
⋱
0
0
⋯
0
C
4
N
Φ
N
-
1
]
,
and
Φ
i
=
2
i
+
1
,
i
∈
{
0
,
1
,
2
,
…
,
N
-
1
}
and
[
Pr
]
2
=
[
I
]
2
and
[
Pr
]
N
=
[
1
0
0
…
0
0
⋯
0
0
0
0
⋯
1
0
⋯
0
0
1
0
0
0
⋯
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
⋱
0
0
0
0
⋱
0
0
0
0
0
0
0
0
0
1
]
,
N
≥
4
,
where
[
Pr
]
N
=
[
pr
i
,
j
]
N
,
with
{
pr
i
,
j
=
1
,
if
i
=
2
j
,
0
≤
j
≤
N
2
-
1
,
pr
i
,
j
=
1
,
if
i
=
(
2
j
+
1
)
mod
N
,
N
2
≤
j
≤
N
-
1
,
pr
i
,
j
=
0
,
others
,
where
i
,
j
∈
{
0
,
1
,
…
,
N
-
1
}
and
[
Pc
]
2
=
[
I
]
2
,
and
[
Pc
]
N
=
[
I
N
/
4
0
0
0
0
I
N
/
4
0
0
0
0
0
I
N
/
4
0
0
I
N
/
4
0
]
,
N
≥
4.
2. A signal transformation method applied to a signal transformation apparatus as claimed in claim 1 .
3. A non-transitory computer-readable recording medium containing a computer program for executing functions of a signal transformation apparatus as claimed in claim 1 .
4. A signal transformation apparatus applying a hybrid architecture for Discrete Cosine Transform (DCT)-II, Discrete Sine Transform (DST)-II, Discrete Fourier Transform (DFT), and Haar Wavelet Transform (HWT), comprising:
a switching part for selecting any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a transformation part for transforming and outputting an input signal according to the transform selected by the switching part,
wherein the switching part comprises:
a submatrix selector for selecting submatrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a permutation matrix selector for selecting permutation matrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT,
wherein when the switching part selects the DST-II, the submatrix selector selects matrix [U] N as a submatrix and the permutation matrix selector selects [D] N as a permutation matrix,
wherein the transformation part applies the DST-II to the input signal by computing Equation (45) by using the submatrix [U] N and the permutation matrix [D] N and multiplying every output by a matrix:
[
S
]
N
=
2
N
[
S
]
N
=
2
N
[
P
r
]
N
[
U
N
/
2
0
0
I
N
/
2
]
[
I
2
⊗
[
…
[
I
2
⊗
[
[
P
r
]
4
[
U
2
0
0
I
2
]
[
I
2
⊗
S
2
]
[
D
2
0
0
I
2
]
[
I
2
I
2
I
2
-
I
2
]
[
P
c
]
4
]
︸
S
4
]
…
]
︸
S
N
/
2
]
[
D
N
/
2
0
0
I
N
/
2
]
[
I
N
/
2
I
N
/
2
I
N
/
2
-
I
N
/
2
]
[
P
c
]
N
*
,
(
45
)
wherein
[
U
]
N
=
[
2
-
2
2
-
2
0
2
-
2
2
⋮
⋱
2
⋮
0
⋯
0
2
]
N
,
[
D
]
N
=
diag
[
C
4
N
Φ
0
,
…
,
C
4
N
Φ
N
-
1
]
N
Φ
i
=
2
i
+
1
,
i
=
0
,
1
,
⋯
,
N
-
1
and
[
Pr
]
2
=
[
I
]
2
and
[
Pr
]
N
=
[
1
0
0
⋯
0
0
⋯
0
0
0
0
⋯
1
0
⋯
0
0
1
0
0
0
⋯
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
⋱
0
0
0
0
⋱
0
0
0
0
0
0
0
0
0
1
]
,
N
≥
4
,
where
[
Pr
]
N
=
[
pr
i
,
j
]
N
,
with
{
pr
i
,
j
=
1
,
if
i
=
2
j
,
0
≤
j
≤
N
2
-
1
,
pr
i
,
j
=
1
,
if
i
=
(
2
j
+
1
)
mod
N
,
N
2
≤
j
≤
N
-
1
,
pr
i
,
j
=
0
,
others
,
where
i
,
j
∈
{
0
,
1
,
…
,
N
-
1
}
and
[
Pc
]
2
=
[
I
]
2
,
and
[
Pc
]
N
=
[
I
N
/
4
0
0
0
0
I
N
/
4
0
0
0
0
0
I
N
/
4
0
0
I
N
/
4
0
]
,
N
≥
4.
5. A signal transformation apparatus applying a hybrid architecture for Discrete Cosine Transform (DCT)-II, Discrete Sine Transform (DST)-II, Discrete Fourier Transform (DFT), and Haar Wavelet Transform (HWT), comprising:
a switching part for selecting any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a transformation part for transforming and outputting an input signal according to the transform selected by the switching part,
wherein the switching part comprises:
a submatrix selector for selecting submatrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a permutation matrix selector for selecting permutation matrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT,
wherein when the switching part selects the DFT, the submatrix selector selects [Pr] N as a submatrix and the permutation matrix selector selects [W] n as a permutation matrix,
wherein the transformation part applies the DFT to the input signal by computing Equation (56) by using the submatrix [Pr] N and the permutation matrix [W] n and multiplying the input signal by a first matrix during first h steps of 2h steps and multiplying the input signal by a second matrix during last h steps:
[
F
]
N
=
(
[
P
r
]
N
)
-
1
[
F
~
]
N
=
(
[
P
r
]
N
)
-
1
[
I
N
/
2
0
0
P
r
N
/
2
]
[
F
~
N
/
2
0
0
F
~
N
/
2
]
[
I
N
/
2
0
0
W
N
/
2
]
[
I
N
/
2
I
N
/
2
I
N
/
2
-
I
N
/
2
]
=
[
P
r
]
N
[
I
N
/
2
0
0
P
r
N
/
2
]
[
I
2
⊗
P
r
N
/
2
]
[
I
2
⊗
[
I
N
/
4
0
0
P
r
N
/
4
]
]
…
[
I
N
/
4
⊗
P
r
4
]
[
I
N
/
4
⊗
[
I
2
0
0
P
r
2
]
]
[
I
N
/
2
⊗
F
2
]
[
I
N
/
4
⊗
[
I
2
0
0
W
2
]
]
[
I
N
/
4
⊗
[
I
2
I
2
I
2
-
I
2
]
]
…
[
I
2
⊗
[
I
N
/
4
0
0
W
N
/
4
]
]
[
I
2
⊗
[
I
N
/
4
I
N
/
4
I
N
/
4
-
I
N
/
4
]
]
[
I
N
/
2
0
0
W
N
/
2
]
[
I
N
/
2
I
N
/
2
I
N
/
2
-
I
N
/
2
]
=
[
P
r
]
N
-
1
[
I
N
/
2
0
0
P
r
N
/
2
]
[
I
2
⊗
[
…
[
P
r
]
4
-
1
[
I
2
0
0
P
r
2
]
[
I
2
⊗
F
~
2
]
[
I
2
0
0
W
2
]
[
I
2
I
2
I
2
-
I
2
]
︸
F
~
4
…
]
︸
F
~
N
/
2
]
[
I
N
/
2
0
0
W
N
/
2
]
[
I
N
/
2
I
N
/
2
I
N
/
2
-
I
N
/
2
]
,
(
56
)
wherein
[
Pr
]
2
=
[
I
]
2
and
[
Pr
]
N
=
[
1
0
0
⋯
0
0
⋯
0
0
0
0
⋯
1
0
⋯
0
0
1
0
0
0
⋯
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
⋱
0
0
0
0
⋱
0
0
0
0
0
0
0
0
0
1
]
,
N
≥
4
,
where
[
Pr
]
N
=
[
pr
i
,
j
]
N
,
with
{
pr
i
,
j
=
1
,
if
i
=
2
j
,
0
≤
j
≤
N
2
-
1
,
pr
i
,
j
=
1
,
if
i
=
(
2
j
+
1
)
mod
N
,
N
2
≤
j
≤
N
-
1
,
pr
i
,
j
=
0
,
others
,
where
i
,
j
∈
{
0
,
1
,
…
,
N
-
1
}
,
and
[
W
]
N
=
[
W
0
0
⋯
0
0
W
1
0
⋮
⋱
⋮
0
⋯
0
W
N
-
1
]
W is a diagonal complex unit for 2N point DFT matrix.
6. A signal transformation apparatus applying a hybrid architecture for Discrete Cosine Transform (DCT)-II, Discrete Sine Transform (DST)-II, Discrete Fourier Transform (DFT), and Haar Wavelet Transform (HWT), comprising:
a switching part for selecting any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a transformation part for transforming and outputting an input signal according to the transform selected by the switching part,
wherein the switching part comprises:
a submatrix selector for selecting submatrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT; and
a permutation matrix selector for selecting permutation matrix computation for any one of the DCT-II, the DST-II, the DFT, and the HWT,
wherein when the switching part selects the HWT, the submatrix selector selects [Pa] N as a submatrix and the permutation matrix selector selects [Pb] N as a permutation matrix,
wherein the transformation part applies the HWT to the input signal by computing Equation (64) by using the submatrix [Pa] N and the permutation matrix [Pb] N and multiplying the input signal by a matrix during last h steps of 2h steps:
[
H
]
N
=
[
P
i
]
N
-
1
[
H
•
]
N
[
P
j
]
N
-
1
=
1
r
[
P
a
]
N
[
I
N
/
2
0
0
P
a
N
/
2
]
[
I
3
N
/
4
0
0
P
a
N
/
4
]
…
[
I
N
-
2
0
0
P
a
N
/
2
]
[
I
N
-
2
0
0
H
•
2
]
[
I
N
-
4
0
r
I
2
0
P
b
2
]
[
I
N
-
4
0
0
I
2
I
2
I
2
-
I
2
]
…
[
I
N
/
2
0
r
I
N
/
4
0
P
b
N
/
4
]
[
I
N
/
2
0
0
I
N
/
4
I
N
/
4
I
N
/
4
-
I
N
/
4
]
[
r
I
N
/
2
0
0
P
b
N
/
2
]
[
I
N
/
2
I
N
/
2
I
N
/
2
-
I
N
/
2
]
[
P
b
]
N
*
,
(
64
)
wherein
[
Pa
]
N
=
[
Pi
]
N
-
1
=
[
Pi
]
N
,
[
Pi
]
N
=
[
0
I
N
/
2
I
N
/
2
0
]
and
[
Pb
]
N
=
r
[
Pj
]
N
-
1
=
r
[
I
N
/
2
0
0
-
I
N
/
2
]
[
Pr
]
N
,
[
Pj
]
N
=
[
Pr
]
N
[
I
N
/
2
0
0
-
I
N
/
2
]
.