578
Practical MATLAB
® Applications for Engineers
R.6.64 Bessel fi lters, also known as linear-phase fi lters, present a linear-phase response in
the pass band, in addition they try to approximate the magnitude response in the
pass-band region satisfying the desired specs.
The system transfer function of an nth-order Bessel fi lter is given by the transfer
function shown as follows:
H jw
n
n B jw
a
n
n
( )
( )!
! ( )
ϭ
2
2
where B n (jw) is the n-order Bessel polynomial defi ned by
B jw
n
jw
l n
n
l
n
l
n
( )
(
)!( )
!(
)!
ϭ
Ϫ
Ϫ
Ϫ
ϭ
2
1
2
1
1
0
∑
Figure 6.17 shows the magnitude response and Figure 6.18 shows the phase
response of the Bessel fi lters for orders n = 1, 2, 3, 4, and 10.
R.6.65 It is obvious that the mathematics involved in either the analysis or synthesis of
any type of fi lter is generally a complicated and complex proposition, which is diffi cult and labor intensive. This book attempts to defi ne the fi lter types often used
in real application and provides an overview of the fi lter theory and a simple and
user friendly approach to the analysis and synthesis process. The mathematical
complexities of the power of fi lter theory, in either the synthesis or analysis processes, can be avoided by using MATLAB.
FIGURE 6.16
(See color insert following page 374.) Magnitude plots of normalized analog elliptic LPFs of orders n = 1, 2,
3, 4, and 10.
0
1
2
3
4
5
6
0
0.2
0.4
0.6
0.8
1
Normalized frequency
Gain
Elliptic LPF/order n = 1, 2, 3, 4, 10
n = 1
n = 4, 10
n = 2
n = 3
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