Signals and Systems Lecture 20 Sampling Theorem Reconstruction of a Signal

Chapter 7 Sampling

Continuous Signal Discrete Digital DSP Chapter 7 Sampling Continuous Signal Discrete sampling Code Digital DSP D/A -T 0 T 2T t

§7.1.1 Impulse-Train Sampling Chapter 7 Sampling §7.1 The Sampling Theorem §7.1.1 Impulse-Train Sampling -3T -2T -T 0 T 2T 3T 4T t

Chapter 7 Sampling Sampling x(t) p(t) xp(t)

Chapter 7 Sampling Time domain:

Chapter 7 Sampling Frequency domain:

Chapter 7 Sampling

Chapter 7 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

Chapter 7 Sampling The reconstruction of the signal

Chapter 7 Sampling §7.1.2 Natural Sampling Difficult: 1 ILPF is unpractical; 2 narrow, large-amplitude pulses are difficult to generate and transmit.

§7.1.3 Sampling with a Zero-Order Hold Chapter 7 Sampling §7.1.3 Sampling with a Zero-Order Hold Zero-Order Hold -3T -2T -T 0 T 2T 3T 4T t

Chapter 7 Sampling Zero-Order Hold

Chapter 7 Sampling Reconstruction Filter Zero-Order Hold LPF Impulse-Train Sampling

Chapter 7 Sampling

Chapter 7 Sampling §7.2 Reconstruction Band-limited interpolation

The LPF smoothes out shape and fill in the gaps Chapter 7 Sampling Original CT Signal After sampling After passing LPF The LPF smoothes out shape and fill in the gaps

Chapter 7 Sampling Zero-order hold After passing zero-order hold Original CT Signal After sampling After passing zero-order hold

Chapter 7 Sampling Zero-Order Hold Zero-Order Hold Recover Filter

Chapter 7 Sampling Excise: 7.5, 7.7

Summary Sampling Theorem Sampling and Reconstruction of Signal

Readlist Signals and Systems: 7.3 Question: Excise 7.8

Chapter 6 Time and Frequency Characterization Homework: 7.22 7.23