DSP2-1

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2Discrete-time Signals and Systems
???????????????????????????????????

• ??.??. ?????? ?????????????
• ??????? ??????????????????????

2
????????

• ?? ???????????????????????????????????????????????
  ?????????
• ?? ??????????????????? (convolution)
• ?? ???????????????????????????

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Continuous v.s. Discrete-time Signals
????? DSP ?????????????? Signals and Systems ???
DSP ???????????????????????????????????????????
?????????????????????????????????????????????????
????
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Discrete-Time Continuous Amplitude

• ?????????? ?????????????????????????
  Discrete-Time, Continuous Amplitude ????????

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??????????????
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Discrete-Time Signal from A/D Converter

• ???????????????????????? Discrete-time ??? A/D
  Converter

A/D
?????????????
?????????????
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DSP System Block Diagram
DSP Processor
A/D
D/A
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Sampling

• ????????????? x(t) ??????????????????? x(n)
• ?????????? x(n)

???????????????
...
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Combination of Sampling

• ?????? x(n) ?????????? s(n) ??? ?????? x(t)
• S(n) ????????????????? ??? ????????

t
n
n
T
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Elements of the Sampling Signal

• S(n) ?????????????????????? ????????

n

s(n)
n


n
T
n

n
T
2T
3T
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An Impulse is Delta Function

• ???????? ??? ??????????????
  ?????? 1 ????? n0
• ??? ?????? 0 ????? n ????????????
• ?????????

1
????????
n
0
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Shifted Delta Function

• ????????????????????????? s(n) ??????????????????

1
????????????????????????????
n
0
1
?????????????????????????????? 1 ?????
n
1
0
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Summing of Shifted Delta Function
n


n



n


n
T
2T
3T
0
n
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Sampling SignalsSumming of Delta function

• ?????????????????????????????????????
  ?????????????????????????????????????????
• ???? ?????????????

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Discrete-time Signal x(n)

• x(n) ???????? ???????? x(t) ??? s(n)

n

n
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System with Delta function

• ????? x(n) ?????????????????? ???????????????????
  y(n)x(n) ????????

???????????????
????
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Sampled Signal
n0
n

n1

n



n2
n


n
n3
1
2
0
3
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System with Delayed Delta function

• ??? x(n) ??????????? ??????????????????? delay
  ????? y(n)x(n-1)

???????????????
????
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Delayed Signal
n0
n

n1

n



n2
n


n
n3
1
2
0
3
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????????? (Convolution)

• ????????????? ?????????????? ??????????????????
• ?????????????????????????????? Convolution ????
  ?????????

????
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Convolved Signal
n0
n


n1
n

n2

n


n3
n
1
2
0
3
1
2
0
3
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Convolution Effect

• ????????????????

????? h(1)
????? h(0)
?????????
???????????????????
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DSP System Block Diagram

• ???? DSP ????????????? ???????????????

DSP Processor
A/D
D/A
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A/D Part in DSP

• ???? A/D

DSP Processor
A/D
D/A
Hold
Quantizer
Sample and Hold
A/D Converter
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A/D Converter

• ???? DSP ???????????? A/D Converter

DSP Processor
Hold
Quantizer
D/A
Sample and Hold
A/D Converter
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?????????????????????????
Digital Signal Processor
A/D
DSP
D/A
????????????? ?????????????? DSP
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Discrete-Time Systems

• ??????????????????????? ????????????
• X(n) ??? ?????? ??????
• Y(n) ??? ?????? ????????
• T. ??? ???? (System) ???? ???????????????
  (processor)
• ??????? y(n) ?????????????? x(n) ??? T.
  ????????????????????? (Convolution)

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??????????????????????????
SUN
Solar Cell Panel
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Example System 1

• Example 2.2.1 from Proakiss Text
• ???? y(n) ??????

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Example System 2
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Example System 3
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Example System 4

• Accumulator

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?????????????????????????????? (Linear
Shift-invariant (LSI) Systems)

• ???????? (Linear) ??????? ??? ???? T
  ??????????????
• ????????????????????????????

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Example Linear I

• Example 2.2.5 ??????????????????????
  ?????????????????????????????

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Example Linear 2
????????
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Example Linear 3
????????
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Example Linear 4
???????????
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Example Linear 5
???????????
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Example Linear 6
???????????
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Shift-invariant 1

• ?????????????????? (Shift-invariant) ??????? ???
  y(n) ???????????? x(n)

??? x(n) ??????????? k ?? y(n) ???? y(n,k)
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Shift-invariant 2

• ????????? y(n) ?? k ????? y(n-k) ??????

• ??????????????????????????????? (Shift-invariant)

• ???????????????????????????? (Shift-varying)

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Example Shift-Invariant 1

• Example 2.2.4 ????????????????? Shift-invariant

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Example Shift-Invariant 2

• ??????????? y(n) ????????? x(n) ?? k ????????

Shift-invariant
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Example Shift-Invariant 3

• ??????????? y(n) ????????? x(n) ?? k ????????

?????????????? ??? n ?? x(n) ?????????????? n-k
Shift-varying
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Example Shift-Invariant 4

• ??????????? y(n) ????????? x(n) ?? k ????????

Shift-varying
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Example Shift-Invariant 5

• ??????????? y(n) ????????? x(n) ?? k ????????

Shift-invariant
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????????? Convolution (revisited)

• ???
• ????????? ????? k ????????? ??????????????????????
  

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?????????????? ???????????? ??? ????????????????
x(n) ?????????0 ??? 1 ??? ??????????????????????
? h(0) ??? h(1) ????????

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?????????????? (Convolution)
?????????????????????????
???????????????????????
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??????????? ?????????????????? ???
??????????????
?????????????? ?????????????????????????????????
(??????) ??????????????? ( ???? ?????
????????????????????????)
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?????????????????

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Example Convolution

• ?????????????????
• ????????????????????? n-1 ??? 3

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• ?????????????? n -1 ????? x(n)
• ????? y(n)
• n -1
• n0
• n1
• n2

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n -1
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n 0
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????? y(n)
dsp_2_4
??????????????? y(n) ????
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????? convolution ??? ???????
N0
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(No Transcript)
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?????????????????????

• Cumulative Property
• Associative property
• Distributive property

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????????? Ch.2 (Proakis)
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????????? Ch.2 (Proakis)
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????????? Ch.2 (Proakis)
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????????? Ch.2 (Proakis)
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????????? Ch.2 (Proakis)
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????????? Ch.2 (Proakis)