大二上信號(hào)與系統(tǒng)2013-chapter9ss

1、9 The Laplace Transform9.4.11 Table of LT Properties9.5 Some LT PairsRead by yourself!Read by yourself!9.6 Analysis and Characterization of LTI systemsUsing LT (including 9.4 9.7)h(t)H(s)x(t)y(t)=x(t)*h(t)X(s)Y(s)=X(s)H(s)Consider a LTI system:9 The Laplace Transform( system function )9 The Laplace

2、Transform9.6.1 Causality(1)A causal system(Res 1 . )ROC:right-half plane(2) For rational A causal systemROC:right-half planeTo the right of rightmost pole(1 )9 The Laplace Transform Example 9.1719A causal systemAn uncausal systemAn uncausal system9 The Laplace Transform9.6.2 Stability(1)A stable sys

3、tem(Res=0 . )includes -axis(2) A causal stable system with rational All poles lies in the left-half of s-planeROC:9 The Laplace Transform9 The Laplace Transform9.6.3 Pole-Zero Plot of and Evaluation of Frequency Response (9.4) 9 The Laplace TransformExample A causal systemLPF9 The Laplace TransformE

4、xample Second-Order System9 The Laplace TransformTop is flat when= 1/2 = 0.707 a LPF for ) damped.Unit-Impulse and Unit-Step Response of a Second-Order SystemRead P677681 by youeself!9 The Laplace TransformExample A causal system(All-pass system)9 The Laplace TransformRead P703706 by youeself! Examp

5、le(9.7.5) N-order Butterworth Filter9 The Laplace Transform9.6.4 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations Laplace transform:(9.131)(9.133)(rational) Usually, a practical system is causal and stable.9 The Laplace Transform ExampleSimilar to Example 9.24In anothe

6、r way9 The Laplace Transform9.6.5 Examples Relating System Behavior to the System FunctionExample 9.25IF inputoutput9 The Laplace Transform3.If1.causal,2. is rational ,has only 2 poles, at Example 9.26 Suppose a LTI system:S=-2 and s=- 4(correct it in book P703704).4.The value of the inpulse response at is 4.From 1 and 2,we can deduce From 3,9 The Laplace TransformFrom 4, has a zero at (9.138) By evaluating (9.139),we get K=4 .9 The Laplace Transform Example a real,causal and stable LTI system with and Show that Proof:atSuppose