PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

568 Practical MATLAB® Applications for Engineers

For example, the LP-to-HP transformation means that the s’s in the transfer func-

tion H(s) of the LP normalized fi lter are replaced by wc/s and in terms of circuit ele-

ments that translates that the inductor Ln be replaced by a capacitor

C

wLc

1

()* n

R.6.35 The designing specs of a fi lter can best be visualized by a sketch in which the bands
of frequencies that are highly attenuated or blocked within certain limits as well as
the band of frequencies that pass with little or no attenuation are indicated within
limits.
Analytically, this translates into a set of parameters that specify a fi lter given by
a. The deviation parameters δp and δs
b. The frequencies wp and ws and transition width ws − wp
c. The fi lter’s order given by n

R.6.36 The number of poles of the fi lter’s transfer function H(s), given by its denominator,
defi nes the fi lter’s order n.

TABLE 6.1

Frequency Transformations

• LP-to-HP s ⇒ wo/s


• LP-to-BP s ⇒ (s

(^2) + wo (^2) )
_____(s

• BW)

• LP-to-BR s ⇒ _____(s^ * BW)
  (s^2 + wo^2 )

Note: BW = wu−wl (bandwidth) and wo = (^) √ w___u – w (^) e , where wo denotes the
fi lter’s center frequency and represents the geometric mean of wu (upper
cutoff) and we (lower cutoff).
TABLE 6.2
Element Transformation
Normalized Elements HPF Elements BPF Elements BRF Elements
Ln
woLn BW
BW
wo^2 Ln
BWLn
cn
BWCn
1
woCn
1
1
1
wo^2
BWCn
Ln
BW
Cn
BW
wo^2 Cn
BWLn
wo^2
Note: Ln and Cn are normalized LPF prototypes.