Audio Effects

79Filter Design

lter, except that by inverting the magnitude response using Equation (3.19),

the resultant lter has band stop behavior.

For our rst- order lter with the gain at the upper and lower cutoff fre-

quencies given as G

c

2

= 1/2, there is no need to change the gain at the cutoff

frequency. So, starting with the prototype, we invert the magnitude response,

and then shift the cutoff frequency, as in the high- pass lter, giving

Hz

z

BzB

HP

()

(tan())tan

()

=

−

++ −

1

21

21//

(3.38)

Then we transform to a band-pass lter with bandwidth B.

Hz

zz

Bz

BS

c

c

()

cos

tan( )cos

=

−+

+

()

−+−

2

2

21

21 21

ω

ω/

ttan( )B/2

(3.39)

The pole zero plots of the band stop lters in Figu ...