邬震宇-信号与系统 2.pptVIP

* * * Several important formula: Problems: 2.1 2.3 2.5 2.7 2.10 2.11 2.12 2.18 2.19 2.20 2.23 2.24 2.40 2.47 * 补充例题 * * * * * * * * * * * * * * * * * * * * * * * * UESTC 何子述 * UESTC 何子述 * * * * * * 2.3.2 The Distributive Property Discrete time: x[n]*{h1[n]+h2[n]}=x[n]*h1[n]+x[n]*h2[n] Continuous time: x(t)*{h1(t)+h2(t)}=x(t)*h1(t)+x(t)*h2(t) h1(t)+h2(t) x(t) y(t)=x(t)*{h1(t)+h2(t)} h1(t) x(t) y(t)=x(t)*h1(t)+x(t)*h2(t) h2(t) ? Example 2.10 * 2.3.3 The Associative Property Discrete time: x[n]*{h1[n]*h2[n]}={x[n]*h1[n]}*h2[n] Continuous time: x(t)*{h1(t)*h2(t)}={x(t)*h1(t)}*h2(t) h1(t)*h2(t) x(t) y(t)=x(t)*{h1(t)*h2(t)} h1(t) x(t) y(t)=x(t)*h1(t)*h2(t) h2(t) * 2.3.4 LTI system with and without Memory Memoryless system: Discrete time: y[n]=kx[n], h[n]=k?[n] Continuous time: y(t)=kx(t), h(t)=k ?(t) k ?(t) x(t) y(t)=kx(t)=x(t)*k?(t) k ?[n] x[n] y[n]=kx[n]=x[n]*k?[n] Hint that: x(t)* ?(t)=x(t) and x[n]* ?[n]=x[n] * 2.3.5 Invertibility of LTI system Original system: h(t) Inverse system: h1(t) ?(t) x(t) x(t)*?(t)=x(t) So, for the invertible system: h(t)*h1(t)=?(t) or h[n]*h1[n]=?[n] h(t) x(t) x(t) h1(t) Example 2.11 2.12 * 2.3.6 Causality for LTI system Discrete time system satisfy the condition: h[n]=0 for n0 Continuous time system satisfy the condition: h(t)=0 for t0 Conclusion: The impulse response must be causal. * 2.3.7 Stability for LTI system Definition of stability: Every bounded input produces a bounded output. Discrete time system: If |x[n]|B, the condition for |y[n]|A is * Continuous time system: If |x(t)|B, the condition for |y(t)|A is Example 2.13 * 2.3.8 The Unit Step Response of LTI system Discrete time system: h[n] ?[n] h[n] u[n] s[n]=u[n]*h[n] Continuous time system: h(t) ?(t) h(t) u(t) s(t)=u(t)*h(t) * * Example 2.3 The impulse responses are as below （1） （2） Are the systems with memory? Causal? Stab