信号与系统1——Signals and Systems

• 一、Introduction
• • 1. Signals and Systems信号与系统
  • • (1) Signal信号
    • (2) System系统
  • 2. Classification of Signals信号的分类
  • • (1) Continuous-time & discrete-time
    • • 1) Continuous-Time signal连续时间信号
      • 2) Discrete-Time signal离散时间信号
      • 3) Relationship关系
    • (2) Even and odd signals偶奇信号
    • • 1) Even signals (偶信号)
      • 2) Odd signals (奇信号)
      • 3) Even-odd decomposition of x(t)奇偶分量
      • 4) PRODUCT Rule
  • 3. Operation on Signals信号运算
  • • (1) In Time Domain时域
    • • 1) Time Scaling时间展缩
      • 2) Time Reflection时间反转
      • 3) Time Shifting时移
    • (2) In Amplitude幅度
    • • 1) Amplitude scaling幅度缩放
      • 2) Addition加
      • 3) Multiplication乘
      • 4) Differentiation 微分
      • 5) Integration 积分
    • (3) Precedence Rule步骤
    • • 1）f(t)$\to$f($\alpha$t+$\beta$)
      • 2）f($\alpha$t+$\beta$)$\to$f(t)
• 二、Basic Time Signals基本时间信号
• • 1. Exponential Signals指数信号
  • • (1) Continuous-time
    • (2) Discrete-time
  • 2. Sinusoidal Signals正弦信号
  • • (1) Continuous-time
    • (2) Discrete-time
    • (3) Relation Between Sinusoidal and Complex Exponential Signals
    • • 1) Complex exponential signal
      • 2) Discrete-time case
      • 3) Two-dimensional representation of the complex exponential e^jΩn^ for Ω = Π/4 and n = 0, 1...
    • (4) Exponential Damped (衰减) Sinusoidal Signals
  • 3. Step Functions阶跃信号
  • • (1) Continuous-time
    • (2) Discrete-time
    • (3) Properties
    • • 1) 相乘特性（单边特性）
      • 2) 表示作用区间
      • • a. f(t)[u(t-$t_1$)-u(t-$t_2$)]
        • b. 加减
      • 3) 积分
  • 4. Impulse Functions冲激信号
  • • (1) Discrete-time
    • (2) Continuous-time
    • (3) Properties of impulse function
    • • 1) Even function偶函数
      • 2) Sifting property时移特性
      • 3) Time-scaling property展缩特性
      • 4) Sampling property取样特性
      • 5) 相乘特性
      • 6) Derivatives
      • 7) 与u（t）的关系
• 三、Systems Classification and Properties系统分类和性质
• • 1. System Representation
  • 2. Continuous-time and Discrete-time Systems
  • • (1) Continuous-time
    • (2) Discrete-time
    • (3) Moving-average system
    • (4) Representation of discrete-time operations
  • 3. Systems with and without memory
  • • (1) without memory
    • (2) with memory
  • 4. Causal and Non-causal systems
  • • (1) Causal
    • (2) Non-causal
  • 5. Linear and Nonlinear systems
  • • (1) Linear
    • (2) Nonlinear
  • 6. Time-variant and Time-invariant Systems
  • • (1) Time-invariant
    • (2) Condition for time-invariant system
  • 7. Stable systems
  • 8. Feedback systems
  • 9. Invertibility(可逆性) systems
  • • (1) Continuous-time system
    • (2) Output of the second system
    • (3) Condition for invertible system