Digital Signal Processing Reference
In-Depth Information
From
Table 6.2
and
Figure 6.15
, we can see that when the frequency increases, the magnitude
response increases. The DSP system actually performs digital highpass filtering.
Notice that if all the coefficients
a
i
for
i ¼
0
;
1
;/; M
in Equation
(6.1)
are zeros, Equation
(6.2)
is
reduced to
yðnÞ¼
M
i ¼
0
b
i
xðn iÞ
¼ b
0
xðnÞþb
1
xðn
1
Þþ/þ b
K
xðn MÞ
(6.25)
Notice that
b
i
is the
i
th impulse response coefficient. Also, since
M
is a finite positive integer,
b
i
in this
particular case is a finite set,
HðzÞ¼BðzÞ
; note that the denominator
AðzÞ¼
1. Such systems are
called
finite impulse response
(FIR) systems. If not all
a
i
in Equation
(6.1)
are zeros, the impulse
response
hðiÞ
would consist of an infinite number of coefficients. Such systems are called
infinite
impulse response
(IIR) systems. The z-transform of the IIR
hðiÞ
, in general, is given by
HðzÞ¼
BðzÞ
AðzÞ
where
AðzÞs
1.
6.5
BASIC TYPES OF FILTERING
The basic filter types can be classified into four categories:
lowpass, highpass, . bandpass
, and
bandstop
. Each of them finds a specific application in digital signal processing. One of the objectives in
applications may involve the design of digital filters. In general, the filter is designed based on the
specifications primarily for the passband, stopband, and transition band of the filter frequency
response. The filter passband is the frequency range with the amplitude gain of the filter response being
approximately unity. The filter stopband is defined as the frequency range over which the filter
magnitude response is attenuated to eliminate the input signal whose frequency components are within
that range. The transition band denotes the frequency range between the passband and stopband.
1
p
1.0
1-
p
Transition
Passband
Stopband
s
0
p
s
FIGURE 6.16
Magnitude response of the normalized lowpass filter.
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