Digital Signal Processing Reference
In-Depth Information
R
+
+
Input
C
Output
-
-
FIGURE 5.2
Analog realization of low-pass filter.
A/D
converter
Digital filter
H(e
j
ω
)
D/A
converter
Input analog
signal
Filtered analog
signal
FIGURE 5.3
Digital realization of low-pass filter.
Figure 5.3. The analog signal
x
(
t
) is converted into a discrete-time signal
x
(
n
),
which is processed by the digital filter, to yield a discrete-time output
y
(
n
)
.
Finally, the discrete-time output
y
(
n
) is converted to its analog form
y
(
t
)
.
The
cutoff frequency of digital filter
response
H
(
e
j
ω
), as shown in
Figure 5.1b
,
is
related to the
analog cutoff frequency
through the important analog-digital
frequency relation:
ω=Ω
T
(5.2)
where
(sec.) is the sampling interval of the discrete-time system.
Hence, the unit of analog frequency,
T
Ω,
is radians/sec, while the unit of
digital frequency,
is radians.
The digital filter, shown in Figure. 5.2, can be realized using a Digital Signal
Processor (DSP). The DSP can be programmed to act as any kind of filter.
This is one of the main advantages of digital systems.
ω,
5.1.2
Design Techniques for FIR and IIR Digital Filters
As with any other discrete-time system, any digital filter can be described
by the linear constant-coefficient difference equation of the form:
ayn
()
+
ayn
(
−
1
)
+ … −
a yn N
(
)
=
bxn
()
+
bxn
(
−
1
)
+ …−
bxn M
M
(
)
0
1
N
0
1
