PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

562 Practical MATLAB® Applications for Engineers

In practice, the magnitude response characteristics in the pass and stop band(s) are not
constant and are specifi ed within some acceptable tolerances. Moreover, the ideal transi-
tion bands between the pass and stop bands is supposed to be as abrupt as possible.
Practical fi lters are approximations of ideal fi lters within acceptable tolerances. The more
closely a real fi lter resembles its ideal model, the better its design and performance.
The quality of a fi lter implementation can be evaluated in terms of the deviation from its
ideal characteristics.
Figure 6.1 illustrates the characteristics of a low-pass fi lter (LPF). The ideal case is shown
by constant values with an abrupt discontinuity, whereas the real case is shown by a con-
tinuous line.

6.2 Objectives

After completing this chapter the reader should be able to

Defi ne fi lter characteristics and specs

Understand the basic fi lter prototypes

Defi ne and describe the characteristics of the basic fi lter prototypes

Normalize and denormalized a prototype in terms of the desire magnitude and

frequency specs

Defi ne the basic fi lters in terms of equations, plots, or sketches (LP, HP, band pass

[BP], band reject [BR])

Identify and discuss fi lter terminology and specs such as cutoff frequencies, pass

band, stop band, transition band, bandwidth (BW), and ripples

Understand the characteristics of the most common fi lter prototypes used in indus-

try such as Butterworth, Chebyshev, Cauer or Elliptic, and Bessel

Understand the steps involved in the analysis and synthesis processes involving

fi lters

Know the meaning of the Q of a fi lter and how it affects its complexity

• • • • • • • • •

FIGURE 6.1
Frequency characteristics of an LPF.

1

Pass band Stop band

0 wp

H(jw)

w(rad/s)