1 Signals and Systems Lecture 14 Multiplication Property Communication System

2 Chapter 4 Fourier Transform §4.5 The Multiplication property (modulation property) （调制特性）

3 Chapter 4 Fourier Transform Example 4.23 Determine the Fourier transform of the signal

4 Chapter 4 Fourier Transform 例 某连续时间 LTI 系统的单位冲激响应为 若输入信号 ， 试求整个系统的输出。

5 Chapter 4 Fourier Transform ABC 例 如图所示系统中， 若输入信号 ，试分别 A 、 B 、 C 各点信号 的频谱。

6 Chapter 4 Fourier Transform §4.5.1 Frequency-Selective Filtering with Variable Center Frequency 中心频率可调的频率选择性滤波器

7 Chapter 8 Communication Systems Communication Channel 信道 Source Signals Modulator 调制器 Modulated Signals Be best suited for transmitting

8 Chapter 8 Communication Systems Modulation : The general process of embedding an information -bearing signal into a second signal. Extracting the information-bearing signal. Demodulation : Modulation : Amplitude Modulation (AM) Frequency Modulation (FM) Phase Modulation (PM) Modulating Signal Carrier Signal Modulated Signal Amplitude Modulation

9 Modulating system model: x(t) c(t) y(t)=x(t)c(t) x(t) --- modulating signal c(t) --- Carrier signal Chapter 8 Communication Systems §8.1 Complex Exponential and Sinusoidal Amplitude Modulation

Amplitude Modulation with Complex Exponential Carrier Exponential carrier: For convenience, let  c =0, so Output signal(modulated signal): (1) Modulation Theory Chapter 8 Communication Systems

11 Chapter 8 Communication Systems

12 (1) Implementation Chapter 8 Communication Systems

Amplitude Modulation with Sinusoidal signal For convenience, choose  c =0, so Chapter 8 Communication Systems

14 Chapter 8 Communication Systems

15 Chapter 8 Communication Systems

16 Chapter 8 Communication Systems §8.1 Complex Exponential and Sinusoidal Amplitude Modulation Envelope

Demodulation for Sinusoidal AM Synchronous demodulation (1) Demodulation process Chapter 8 Communication Systems

18 In frequency domain: In time domain: Expected signal: Chapter 8 Communication Systems

19 Chapter 8 Communication Systems

20 (2) Synchronous problem Chapter 8 Communication Systems

21 Time domain: The output of lowpass filter: Ideal output: x(t) When, it is referred to as synchronous demodulation. Chapter 8 Communication Systems

Asynchronous demodulation Amplitude-modulated signal: Chapter 8 Communication Systems

23 Chapter 8 Communication Systems

24 Chapter 8 Communication Systems 1.Suppose the modulator and demodulator are not synchronized in phase. ① Complex Exponential Carrier §8.2.1 Synchronous Demodulation Communication Channel Transmitter Modulation Receiver Synchronous Demodulation LPF 2. Suppose the modulator and demodulator are not synchronized in frequency.

25 Chapter 8 Communication Systems ② Sinusoidal Carrier Communication Channel Transmitter Modulation Receiver Synchronous Demodulation LPF 1.Suppose the modulator and demodulator are not synchronized in phase. 2. Suppose the modulator and demodulator are not synchronized in frequency.

26 §8.3 Frequency-Division Multiplexing （频分复用） Chapter 8 Communication Systems BPF

27 Chapter 8 Communication Systems Quadrature Multiplexing （正交多路复用） LPF Communication Channel

28 Chapter 8 Communication Systems §8.4 Single-Sideband Sinusoidal Amplitude Modulation （单边带） Upper sideband Upper sideband Lower sideband Double Sideband Modulation (DSB)

29 Chapter 8 Communication Systems Retain the upper sideband Upper sideband Upper sideband Lower sideband Retain the lower sideband Single Sideband Modulation (SSB)

30 Chapter 8 Communication Systems Figure 8.21 SSB system using a 90 o phase-shift network. 90 o phase-shift

31 Chapter 8 Communication Systems Lower Sideband

32 Summary Chapter 4 Fourier Transform Multiplication Property and Communication Systems AM and DSB 、 SSB System Modulation and Demodulation

33 Readlist Signals and Systems: –5.1, 5.2 Question: –DTFT

34 Chapter 8 Communication Systems Homework: