Digital Signal Processing Reference
In-Depth Information
k_2
l=(4,1)
4
l=(3,1)
l=(2,1)
3
l_2
l= (4,0)
l= (3,0)
l= (2,0)
l = (1,0)
l=(1,1)
2
1,1
2,1
3,1
4,1
1
l=(0,1)
k_1
l_1
0
1
2
0,0 1.0
2,0
3,0
4,0
−
2
−
1
Fig. 4
Ordering of the upsampler's output tokens
For example, consider a source actor
S
producing (3,3) samples. It thus has a
support matrix
Q
=
(
,
)
diag
3
3
. Assume that
S
is connected to an expander with input
=
sampling matrix
V
I
I
, scanning its input in row scan order. Thus the upsampler
|
(
)
|
L
has to output
det
L
samples in a parallelogram
defined by the columns of the
matrix
L
for every input sample. Suppose
2
2
32
−
L
=
10. These samples can be ordered as follows.
The first column of
L
can be interpreted as the upsampler's
horizontal direction
,
and the second column as its
vertical direction
in a
generalized rectangle
|
det
(
L
)
|
=
L
.In
L
,
there are
L
1
=
10 samples):
The sampling rate at the output of the upsampler can be chosen to be (
L
2
,
5 groups of
L
2
=
2 samples (that is
L
1
×
L
2
=
|
det
(
L
)
|
=
L
1
), that is
L
2
rows and
L
1
columns in
natural order
. The relation between the natural ordered
samples and the samples in the generalized rectangle
L
is then
(
,
)
(
,
)(
,
)(
,
)(
,
)(
,
)(
,
)(
,
)(
,
)(
,
)(
,
)
l
1
l
2
:
0
0
1
0
2
0
3
0
4
0
0
1
1
1
2
1
3
1
4
1
(
,
)
(
,
)(
,
)(
,
)(
,
)(
,
)(
−
,
)(
−
,
)(
−
,
)(
,
)(
,
)
k
1
k
2
:
0
0
0
1
0
2
1
2
1
3
1
1
1
2
1
3
0
3
0
4
is shown at the left, and the natural ordering of samples is shown
at the right. The correspondence between samples in
L
L
and the natural ordering of
these samples is displayed at the left as well.
3.1
A Complete Example
