邬震宇-信号与系统 1.pptVIP

* * 3. Feedback * 4.3.1.Invertibility （可逆性）﹠Inverse Systems A system is invertible, if distinct input leads distinct outputs * For invertible system, an inverse system can be found to restore input x (t) e.g. not invertible The same! 4.3.2 Invertibility （可逆的） * 4.3.3.System with or without memory (Dynamics) If the output y (t) at t0,only depends on the input x(t) at t0 and is independent of the x (t) of other time . The system is called memoryless system. Otherwise the system is with memory. e.g. * is independent of the values of x(t) after A system is causal system, if the response e.g. 4.3.4.Causality（因果性） * A system is stable ,if finite input leads to finite output. 4.3.5.Stability * e.g. * 4.3.6.Time-Invariance System(时不变) The system is time-invariance. 延时的响应等于响应的延时 e.g. * ∵ e.g. ∵ e.g. * ∵ * 4.3.7.Linearity（线性） A system is linear, if it meets both additivity and homogeneity. 1. Additivity（可加） * 2. Homogeneity (齐次性) * Linearity = additivity + homogeneity 线性：和的响应等于响应的和 The system is linear system. 例题 * LTI system: (Linear Time-Invariant system) Systems are both linear and time-invariant. 4.3.8 LTI system * （1） Whether is it with memory? ∵ is related to ∴ It is with memory. Example 4.1 A CT system is expressed as Discuss the system properties. Solution: * （2） Causality? is only related to ﹠ ∴ Causal system. ∵ Not relevant to the future value of x(t). * （3） Invertibility? ∴ it is not invertible system 找出一个反例即可。 * （4）Stability? So, the system is stable. * （5）Time-invariance? Assume that The system is time-invariance system. * Assume that （6）Linearity? Not linear system. * Example4.3.2 The response of a DT LTI to is Determine the response to Solution： * According to linearity,(即“和的响应等于响应的和”) Or： * Example4.3.3 The response of a CT LTI system to input is plotted as below. Determine the responses to and . * * solution：since According to LTI prop