Digital Signal Processing Reference
In-Depth Information
575
120
(
b
)
(
a
)
100
475
h
AP
80
h
LP
375
60
275
40
20
175
0
75
-20
-25
-40
0
50
100
0
50
100
Index, k
Index,
k
450
20
(
d
)
(
c
)
AP
0
350
-20
HP
250
-40
h
HP
-60
LP
150
-80
50
-100
-120
-50
-140
-150
-160
0
50
100
0
0.2
0.4
0.6
0.8
1
Index,
k
Normalized Frequency,
F
Normalised Frequency,
F
N
Figure 2.15
Design of a high pass filter from an all pass and low pass filter. (a) all pass (AP), (b) low
pass (LP), and (c) high pass (HP) filters. (d) Normalized FFT of (a), (b), and (c),
L
+1 = 99,
F
c
= 0.2.
frequencies forms the cut-off edge. The discrete impulse response
h
BP
(
F
c-on
,
F
c-off
)
is given by
h
=
h
(
F
)
h
(
F
)
F
>
F
(2.19)
BP
LP
c
-
off
LP
c
-
on
c
-
off
c
-
on
where (
F
c-off
-
F
c-on
) is the -6 dB bandwidth. Figure 2.16 shows the impulse
response functions of the band pass and constituent low-pass filters.
2.6.4 The Band-Stop Filter
In this case, a high-pass impulse response is first formed which is then added to a
low-pass impulse response to form band-stop characteristics between the low-pass
