Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 34

Anti-
image
filter

Digital signal

DAC

Hold

y ()

y ()

yt

s ()

yt

H ()

FIGURE 2.24

DSP recover system for Example 2.8.

f ¼ 3; 000 Hz; fT ¼ 3; 000 1=16; 000 ¼ 0:1785

¼ 0:9484 ¼0:46 dB

sinð0:1875pÞ
0:1875p

gain ¼

and

f ¼ 13; 000 Hz; fT ¼ 13; 000 1=16; 000 ¼ 0:8125

¼ 0:2177 z 13 dB

sinð0:8125pÞ
0:8125p

gain ¼

This gain would help the attenuation requirement.
Hence, the design requirements for the anti-image filter are
• Butterworth lowpass filter
• Maximum allowable gain variation from 0 to 3,000 Hz ¼ 20.46 ¼ 1.54 dB
•33 13 ¼ 20 dB rejection at frequency 13,000 Hz.

We set up equations using log operations of the Butterworth magnitude function as
20 logð1 þð3; 000=f c Þ 2n Þ 1=2 1:54

20 logð1 þð13; 000=f c Þ 2n Þ 1=2 20

Yf

s ()

0 2177 .

0 9484 .

f

kHz

0

3 1. 1 . 3 .

FIGURE 2.25
Spectral shaping by the sample-and-hold effect in Example 2.8.