PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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:

Hjw

n

a nnB jwn

()

()!

!()

2

(^2)
where Bn(jw) is the n-order Bessel polynomial defi ned by
Bjw
njw
n ln
l
n
l
n
()

()!()

!( )!



 

21

0211

∑

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 dif-
fi 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 pro-
cesses, 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