
85-6 Signal Processing
In the next example, the order N of a low-pass Butterworth lter is to be determined whose cuto
fr
equency
(−
3
dB
)
is Ω
c
= 2 kHz and stopband attenuation is greater than 40 dB at Ω
s
= 6 kHz. us the
de
sired
lter
s
pecication
i
s
20 40log | ( )| ,H j
a s
Ω Ω Ω
≤ − ≥
(85.14)
or
e
quivalently,
| ( )| . ,H j
a s
Ω Ω Ω
≤ ≥0 01
(8
5
.15
)
It
f
ollows
f
rom
E
quation
8
5
.7
1
1
0 01
2
2
+
=
( )
( . )
Ω Ω
s c
/
N
(85.16)
Solving the earlier equation for N gives N = 4.19. Since N must be an integer, a h-order lter is required
for this specication.
85.3.2 Chebyshev Filters or Chebyshev I Filters
e frequency response of an Nth-order Chebyshev low-pass lter ...