Real-time digital signal processing: implementations, ... changes in the input signal is limited by its internal clock rate, so that it may be slow to
Document source : notes.ump.edu.my
Passband
A
p
A
s
Stopband
1
+d
p
1
-d
p
0
w
p
w
c
w
s
d
s
H
(w)
w
p
Ideal filter
Actual filter
Transition
band
1
Figure 5.2 Magnitude response and performance measurement of a lowpass filter
As shown in Figure 5.2, the magnitude of passband defined by 0 ! !
p
approxi-
mates unity with an error of Æd
p
. That is,
1 À d
p
jH!j 1 d
p
, 0 ! !
p
:
5:1:4
The passband ripple, d
p
, is a measure of the allowed variation in magnitude response in
the passband of the filter. Note that the gain of the magnitude response is normalized to
1 (0 dB). In practical applications, it is easy to scale the filter output by multiplying the
output by a constant, which is equivalent to multiplying the whole magnitude response
by the same constant gain.
In the stopband, the magnitude approximates 0 with an error d
s
. That is,
jH!j d
s
, !
s
! p:
5:1:5
The stopband ripple (or attenuation) describes the maximum gain (or minimum
attenuation) for signal components above the !
s
.
Passband and stopband deviations may be expressed in decibels. The peak passband
ripple, d
p
, and the minimum stopband attenuation, d
s
, in decibels are given as
A
p
20 log
10
1 d
p
1 À d
p
dB
5:1:6
and
A
s
À20 log
10
d
s
dB:
5:1:7
Thus we have
186
DESIGN AND IMPLEMENTATION OF FIR FILTERS
Summary :
Passband A p A s Stopband 1 +d p 1 -d p 0 w p w c w s d s H (w) w p Ideal filter Actual filter Transition band 1 Figure 5.2 Magnitude response and performance measurement of a lowpass filter As shown in Figure 5.2, the magnitude of passband defined by 0 !
Tags :
passband,magnitude,filter,stopband,response,gain,ripple,attenuation,decibels,figure,output,log,jhj