Digital Signal Processing Reference
In-Depth Information
TABLE 3.1
Comparison of Filter Performance on
Noise-Corrupted Chirp Shown in Figure 3.1
Filter
MSE
MAE
10
6
Identity
1
.
07
×
23.72
10
5
FIR
1
.
72
×
33.05
FIR-WOS
0.0989
0.2028
L
0.0205
0.1085
MAFF
0.0128
0.0862
Note:
Bold indicates best performance.
columns
3
X
1
g(n)
1
2
D f=
rows
d
j
2
g(n)
21
1
1
h(n)
D f
D f=
X
1
2
j
h
2
A f=
X
j+1
2
2
X
1
g(n)
1
2
D f=
j
v
2
h(n)
21
1
h(n)
1
2
A f=
X
j
a
2
B
: Convolve (rows or columns) with the filter B
21 : Keep one column out of two
12
: Keep one row out of two
FIGURE 3.2
The quadrature mirror filter multiresolution wavelet decomposition structure. (Reproduced from
M. Asghar and K.E. Barner,
IEEE Trans. Visualization Comput. Graphics
,7,76-93, Mar. 2001.
c
2001 IEEE. With permission.)
two-dimensional (2D) data set. If we take
X
to be a 2D data matrix, then
X
can be decomposed into its approximate and detail coefficients as follows:
=
(
↓
T
]
T
,
X
a
)
((
↓
)
)
2
Wa v
low
[
2
Wa v
low
[
X
]
(3.1)
X
h
=
(
↓
T
]
T
,
2
)
Wa v
low
[
((
↓
2
)
Wa v
high
[
X
]
)
(3.2)
v
=
(
↓
T
]
T
,
X
1
2
)
Wa v
high
[
((
↓
2
)
Wa v
low
[
X
]
)
(3.3)
X
d
=
(
↓
T
]
T
2
)
Wa v
high
[
((
↓
2
)
Wa v
high
[
X
]
)
.
(3.4)
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