Digital Signal Processing Reference
In-Depth Information
250
200
(
a
)
(
b
)
200
150
150
100
100
50
50
0
0
-50
-50
-100
0
20
40
0
20
40
Index,
k
Index,
k
0
0
-500
-100
-1000
-200
-1500
-300
-2000
-400
-2500
-500
-3000
-600
-3500
-700
(
c
)
(
d
)
-4000
-800
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
Normalised Frequency,
F
Normalized Frequency,
F
Normalised Frequency,
F
Normalized Frequency,
F
Figure 2.7
Low-pass filter using
LPCoef
with
L
+1 = 55,
F
c
= 0.4, and
A
=
100 dB. (a) linear phase
impulse response; (b) minimum phase impulse response; (c) phase response for (a); and (d) phase
response for (b). The frequency responses are identical for both (a) and (b).
There are a few points to note: (a) the transition width
F
, is the normalized
frequency width between the 10% and 90% value on the edge of the filter, (b) the
attenuation
A
is in decibels (dB) and should be greater than -150 dB, (c) the
attenuation
A
is determined by the height of the first lobe in the rejection band,
and (d) the pass band ripple is determined primarily by the attenuation in the stop
band, thus -100 dB attenuation would in principle correspond to about 2x10
-5
peak-to-peak ripple. Further details regarding (2.7) and (2.8) are given in Chapter
3.
Figure 2.6 gives a Matlab function to calculate low-pass FIR filter
coefficients using the design rules given above. Note that to implement the second
approach discussed there, we would need to calculate the filter length from (2.8)
before using the
LPFCoef
function. Other filter types will be discussed later in this
chapter where low-pass filters will be used as building blocks for them.
