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Signals and Systems Lecture 20
Sampling Theorem Reconstruction of a Signal
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Chapter 7 Sampling
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Continuous Signal Discrete Digital DSP
Chapter Sampling Continuous Signal Discrete sampling Code Digital DSP D/A -T T T t
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§7.1.1 Impulse-Train Sampling
Chapter Sampling §7.1 The Sampling Theorem § Impulse-Train Sampling -3T -2T -T T T 3T T t
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Chapter Sampling Sampling x(t) p(t) xp(t)
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Chapter Sampling Time domain:
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Chapter Sampling Frequency domain:
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Chapter Sampling
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Chapter Sampling Sampling Theorem: Let be a band-limited signal with then is uniquely determined by its samples if where ( Minimum distortionless sampling frequency ) ( Maximum distortionless sampled signal frequency ) Excise: 7.3, 7.4
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Chapter Sampling The reconstruction of the signal
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Chapter Sampling § Natural Sampling Difficult: 1 ILPF is unpractical; 2 narrow, large-amplitude pulses are difficult to generate and transmit.
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§7.1.3 Sampling with a Zero-Order Hold
Chapter Sampling § Sampling with a Zero-Order Hold Zero-Order Hold -3T -2T -T T T 3T T t
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Chapter Sampling Zero-Order Hold
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Chapter Sampling Reconstruction Filter Zero-Order Hold LPF Impulse-Train Sampling
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Chapter Sampling
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Chapter Sampling §7.2 Reconstruction Band-limited interpolation
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The LPF smoothes out shape and fill in the gaps
Chapter Sampling Original CT Signal After sampling After passing LPF The LPF smoothes out shape and fill in the gaps
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Chapter 7 Sampling Zero-order hold After passing zero-order hold
Original CT Signal After sampling After passing zero-order hold
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Chapter Sampling Zero-Order Hold Zero-Order Hold Recover Filter
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Chapter Sampling Excise: 7.5, 7.7
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Summary Sampling Theorem Sampling and Reconstruction of Signal
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Readlist Signals and Systems: 7.3 Question: Excise 7.8
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Chapter 6 Time and Frequency Characterization
Homework: 7.22 7.23
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