PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

596 Practical MATLAB® Applications for Engineers

than the equivalent IIR such as adders, multipliers, and delay elements; and is

the preferred fi lter choice when the required phase response is linear.

b. IIR fi lters are recursive in nature, employing feedback loops, which makes them

highly effi cient in terms of components, but may create unstable conditions that

may result in outputs that may grow without bound (independent of its inputs).

c. Butterworth/IIR fi lters present no in-band ripple and they are the closest to

the FIR fi lters in terms of stability and phase response, with no sharp cutoff

characteristic.

d. Chebyshev/FIR fi lters present ripple either in the pass- or stop band depending

on the type (1 or 2), and generally the fi lter’s Chebyshev order is less than the

equivalent Butterworth/FIR fi lters.

e. Elliptic/FIR fi lters present ripples in the pass band as well as in the stop band

and their order is the lowest with respect to the Chebyshev and Butterworth

fi lter implementation.

R.6.143 Once the desirable transfer function is obtained, the next step in the design pro-
cess is to implement the fi lter in terms of circuit elements. Recall that this process
is referred to as synthesis. Recall that synthesis is the inverse of analysis.

R.6.144 For example, let us synthesize the following analog transfer function:

Hs

ss

ss

()





46

69

2

2

(6.1)

The steps followed in the process of synthesis is illustrated below:

Let us assume that the desired structure for H(s) is indicated in Figure 6.20.

Then

Hs

Zs

Zs Zs

()

()

() ()



2

(^12)
and
Hs Zs
Zs

() ()

()





1

(^11)
(^2)

(6.2)

FIGURE 6.19
Normalized multilevel fi lter characteristics of R.14.141.

mag

.8

.7

.5

.4

0.3 .5 .7 .9 1 f