Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 33

1.6

1.5

1.4

1.3

1.2

1.1

1

0.9

0.8

0.7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Radians

FIGURE 2.22

Ideal equalizer magnitude frequency response to overcome the distortion introduced by the sample-and-hold
process.

Digital signal Anti-

image
filter

DAC

Digital equalizer Hold

y () y ()

yn

eq ()

yt

s ()

yt

H ()

FIGURE 2.23
Possible implementation using a digital equalizer.

EXAMPLE 2.8
Determine the cutoff frequency and the order for the anti-image filter given a DSP system with a sampling rate of
16,000 Hz and specifications for the anti-image filter as shown in Figure 2.24 .
Design requirements:
• Maximum allowable gain variation from 0 to 3,000 Hz ¼ 2dB
• 33 dB rejection at a frequency of 13,000 Hz
• Butterworth filter is assumed for the anti-image filter.
Solution:
We first determine the spectral shaping effects at f ¼ 3; 000 Hz and f ¼ 13; 000 Hz; that is,