Digital Signal Processing Reference
In-Depth Information
2.5
Original Data
Decimated Data
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
0
50
100
150
200
250
Time
Figure 2.26
. A
×
2 decimation of a signal using the algorithm given in (2.31).
2.9 INTERPOLATION
2.9.1 Sampling Rate Increase by Integer Factor
M
Interpolation is used in situations where there is a need to increase the sampling
rate of the system. This means that the number of data points is increased for the
same time duration of the original data set. To accomplish an increase in data rate
by an integer factor
M
, we first introduce
M
-1, consecutive zeros after every data
point in the original data set. This is followed by low-pass filtering with a cut-off
Input
M
Import low-pass filter h, length
(
L+1
)
with cut-off, F
c
1/M
for
m
= 1 to
N
- (
L
+1)
y
L/
2+
m
= 0
for
k
= 1 to
L
/2
y
L/
2+
m
=
y
L/
2+
m
+
h
k
(
x
k + m
- 1
+
x
L -
k + m
+ 1
)
end
y
L/
2+
m
=
y
L/
2+
m
+
h
L/
2 +1
x
L/
2 +
m
end
for
k
= 1 to floor(
N
- (
L
+1))/
M
)
y
out, k
=
y
(
k
- 1)
M
+ 1
end
Figure 2.27
Pseudocode to implement decimation by a factor
M
, given data size
N
and filter order
L
.
The output is
y
out
.
