Chapter4. Sampling of Continuous-Time Signals

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Presentation transcript:

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 BGL/SNU

1. Analog-to-Digital Conversion and Sampling A-to-D Conversion D-to-A Conversion Conti Disc DSP D C Sampling BGL/SNU

Ideal C/D Conversion Ideal D/C conversion BGL/SNU

Sampling <Input> <Impulse train> <Impulsed input> Sampling frequency <Impulsed input> BGL/SNU

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) BGL/SNU

Illustration of Sampling 1 t t 0 T ... t BGL/SNU

t What if Aliasing BGL/SNU

Illustration of aliasing Sampling period (note, to avoid aliasing, )  (*1000) Then the reconstructed output has 1000 component BGL/SNU

Original signal Aliased signal BGL/SNU

2. Reconstruction of Band-limited Signal (note 1) T BGL/SNU

(note 1) t T 2T BGL/SNU

3. Continuous/Discrete Frequency Characteristics vs.   C/D - (i) BGL/SNU

-(ii) BGL/SNU

(i)+(ii) - (iii) In summary, 1 normalized frequency! BGL/SNU

4. Digital Processing of Analog Signal BGL/SNU

or equivalently, take Then, BGL/SNU

5. Changing the Sampling Rate Decimation BGL/SNU