Digital Signal Processing Reference
In-Depth Information
N=input...
('Specify the order of the filter:')
z_p_k='The zeros, poles and multiplying constant.'
[z,p,k]=buttap(N), pause
num_den='The numerator and denominator coefficients.'
[num,den]=zp2tf(z,p,k),pause
[mag,phase,w]=bode(num,den);
plot(w,mag)
title([Magnitude Bode plot ',num2str(N),...
'th order Butterworth filter'])
xlabel('omega')
ylabel('Magnitude')
■
Design of a second-order Butterworth filter
EXAMPLE 6.5
The input signal, to the filter network shown in Figure 6.14 is a rectified cosine voltage
signal with a peak amplitude of 33.94 V and a frequency of 377 rad/s. Using the results of
Example 5.18, we find the half-wave rectified cosine signal to have the frequency spectrum
v
1
(t),
V
1
(v) = 53.31
q
n=-
q
sinc(np/2)[d(v - (n + 1)377) + d(v - (n - 1)377)].
The frequency spectrum of the rectifier output signal is plotted in Figure 6.15(a). We now de-
sign a physically realizable filter to minimize all frequency components except the dc compo-
nent at The filter and load circuit shown in Figure 6.14 will be designed as a
second-order Butterworth filter with a cutoff frequency of 100 rad/s. Because we are dealing
with a filter that is implemented with a physically realizable electrical circuit, the impedance
of the filter will distort the rectified cosine signal if the filter is connected directly to the rectifier
circuit. In order to simplify the discussion that follows, we will assume that the rectified cosine
signal at the input to the filter circuit is the output of an isolation amplifier, as discussed in
Section 2.6 and shown in Figure 2.36.
A second-order Butterworth filter has a magnitude frequency response described by
v = 0.
v
2
1
ƒH(v) ƒ =
1 + (v/v
c
)
4
=
v
4
+ v
4
.
(6.3)
2
2
L
Filter
Load
v
i
(
t
)
v
o
(
t
)
C
R
L
Figure 6.14
A practical filter.
