1. Chapter4. Sampling of Continuous-Time Signals
1. A/D Conversion and Sampling
2. Reconstruction of a Bandlimited Signals
3. Continuous-Discrete Frequency Characteristics
4. Digital Processing of Continuous-Time Signals
5. Changing the Sampling Rate Using Discrete-Time Processing
6. Multirate Signal Processing
7. Practical Considerations in A/D and D/A Conversions
8. Multirate Processing for A/D and D/A Conversions
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2. 1. Analog-to-Digital Conversion and Sampling
A-to-D Conversion
D-to-A Conversion
Conti
Disc
DSP D C
Sampling
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3. Ideal C/D Conversion
Ideal D/C conversion
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4. Sampling <Input> <Impulse train> <Impulsed input>
Sampling frequency
<Impulsed input>
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5. Nyquist Sampling Theorem
<output> T If
is an ideal LPF
Nyquist Sampling Theorem
When xc (t) is bandlimited s.t.
If we do sampling by taking
Then xc (t) is uniquely reconstructed from x[n]= xc (nT)
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6. Illustration of Sampling1 t t
0 T ... t
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7. t
What if
Aliasing
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8. Illustration of aliasing
Sampling period
(note, to avoid aliasing, )
 (*1000)
Then the reconstructed output has component
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9. Original signal
Aliased signal
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10. 2. Reconstruction of Band-limited Signal
(note 1) T
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11. (note 1) t T 2T
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12. 3. Continuous/Discrete Frequency Characteristics
vs.
 
C/D
- (i)
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13. -(ii)
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14. (i)+(ii)
- (iii)
In summary, 1
normalized
frequency!
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15. 4. Digital Processing of Analog Signal
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16. or equivalently, take
Then,
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17. 5. Changing the Sampling Rate
Decimation
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