Chapter 9 The Laplace transform,9.5 The Laplace transform and LTI system,The Laplace transform and LTI system,System function,The properties of LTI systems,Memoryless systems,Invertible systems,The properties of LTI systems,Causal systems,is rational and its ROC is right-half plan;,The properties of LTI systems,Stable systems,For causal and stable system, its poles must lay on the left side of axis !,Examples for causal and stable property,9.17,Causal and stable !,Examples for causal and stable property,9.18,Stable, but not causal !,Examples for causal and stable property,9.19,Stable, but not causal !,Three possible ROC:,A: not causal, unstable;,B: not causal, stable;,C: causal, unstable;,9.20,Examples for causal and stable property,9.6 Representation of the LTI systems,Impulse response,System function,Input output relation,Differential equation,Representation of the LTI systems,Representation of the LTI systems,Pole-zero plot,Poles,Zeros,Gain,The block diagram representation,Basic devices,adder,integrator,amplifier,The block diagram representation,Basic interconnection,Parallel,Cascade(series),The block diagram representation,Basic interconnection,Feedback,The block diagram representation,Direct-form of system,The block diagram representation,Direct-form of system,The block diagram representation,Direct-form of system,The block diagram representation,Cascade form of system,The block diagram representation,Parallel form of system,The block diagram representation,Example 9.30,Direct-form,Cascade -form,Parallel -form,Figure 9.34,