Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 30

2.2.2 Practical Considerations for Signal Reconstruction: Anti-Image Filter
and Equalizer
The analog signal recovery for a practical DSP system is illustrated in Figure 2.19 .
As shown in Figure 2.19 , the DAC unit converts the processed digital signal yðnÞ to a sampled
signal y s ðtÞ , and then the hold circuit produces the sample-and-hold voltage y H ðtÞ . The transfer

function of the hold circuit can be derived as

1 e sT
sT

H h ðsÞ¼ (2.12)

We can obtain the frequency response of the DAC with the hold circuit by substituting s ¼ ju in
Equation (2.12) . It follows that

H h ðuÞ¼e juT= 2 sin ðuT= 2 Þ
uT= 2

(2.13)

The magnitude and phase responses are given by

¼

sin ðuT= 2 Þ
uT= 2

sin ðxÞ
x

jH h ðuÞj ¼ (2.14)

: H h ðuÞ¼uT= 2

(2.15)

where x ¼ uT= 2. In terms of Hz, we have

sin ðpfTÞ
pfT

jH h ðf Þj ¼ (2.16)

1 − e

− sT

Hs () =

h

sT

Digital Signal Anti-

image
filter

Hold
Circuit

DAC

Equalizer

y () y ()

yt

s ()

yt

H ()

y () y s ( t ) y H ( t ) y ( t )

n t t

t

T T

(a) (b) (c) (d)

FIGURE 2.19

Signal notations at the practical reconstruction stage. (a) Processed digital signal. (b) Recovered ideal sampled
signal. (c) Recovered sample-and-hold voltage. (d) Recovered analog signal.