Digital Signal Processing Reference
In-Depth Information
12.10. Using the commutative models for the polyphase interpolation and decimation filters,
a. draw the block diagram for interpolation polyphase filter implementation for the case of
L ¼
2, and
HðzÞ¼
0
:
25
þ
0
:
4
z
1
þ
0
:
5
z
2
;
b. draw the block diagram for decimation polyphase filter implementation for the case of
M ¼
2, and
HðzÞ¼
0
:
25
þ
0
:
4
z
1
þ
0
:
5
z
2
þ
0
:
6
z
3
.
12.11. a. Given an interpolator filter
¼
0
:
25
þ
0
:
4
z
1
þ
0
:
5
z
2
þ
0
:
6
z
3
þ
0
:
7
z
4
þ
0
:
6
z
5
H
z
;
draw the block diagram for interpolation polyphase filter implementation for the case of
L ¼
4.
b. Given a decimation filter
H
z
¼
0
:
25
þ
0
:
4
z
1
þ
0
:
5
z
2
þ
0
:
6
z
3
þ
0
:
5
z
3
þ
0
:
4
z
4
draw the block diagram for decimation polyphase filter implementation for the case of
M ¼
4.
12.12. Using the commutative models for the polyphase interpolation and decimation filters,
a. draw the block diagram for interpolation polyphase filter implementation for the case
of
L ¼
4, and
HðzÞ¼
0
:
25
þ
0
:
4
z
1
þ
0
:
5
z
2
þ
0
:
6
z
3
þ
0
:
7
z
4
þ
0
:
6
z
5
;
b. draw the block diagram for decimation polyphase filter implementation for the case of
M ¼
4, and
HðzÞ¼
0
:
25
þ
0
:
4
z
1
þ
0
:
5
z
2
þ
0
:
6
z
3
þ
0
:
5
z
3
þ
0
:
4
z
4
.
12.13. Consider a speech system with the following specifications:
Speech input frequency range: 0
e
4 kHz
ADC resolution
¼
16 bits
Current sampling rate
¼
8 kHz
a. Determine the oversampling rate if a 12-bit ADC chip is used to replace the speech
system.
b. Draw the block diagram.
12.14. Consider a speech system with the following specifications:
Speech input frequency range: 0
e
4 kHz
ADC resolution
¼
6 bits
Oversampling rate
¼
4 MHz
a. Draw the block diagram.
b. Determine the actual effective ADC resolution (number of bits per sample).
12.15. Consider an audio system with the following specifications:
Audio input frequency range: 0
e
15 kHz
ADC resolution
¼
16 bits
Current sampling rate
¼
30 kHz
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