信號與系統(tǒng)Chapter 8Answers (1)

1、Chapter 99.2Solution: (a). According to eq.(9.3), we will get ROC:Res>-5 (b). , Res<-5If then its obviously that A=-1, , Res<-5.9.5 Solution: (a).1, 1it has a zero in the finite s-plane, that is And because the order of the denominator exceeds the order of the numerator by 1 X(s) has 1 zero

2、 at infinity. (b).0, 1it has no zero in the finite s-plane.And because the order of the denominator exceeds the order of the numerator by 1 X(s) has 1 zero at infinity. (c).1, 0it has a zero in the finite s-plane, that is And because the order of the denominator equals to the order of the numerator

3、X(s) has no zero at infinity.9.7 Solution:There are 4 poles in the expression, but only 3 of them have different real part.The s-plane will be divided into 4 strips which parallel to the jw-axis and have no cut-across.There are 4 signals having the same Laplace transform expression.9.8 Solution: ROC

4、: R(x)+Re2 And x(t) have three possible ROC strips: g(t) have three possible ROC strips: IF Then the ROC of is (-1,1) is two sides.9.9 Solution: It is obtained from the partial-fractional expansion:,We can get the inverse Laplace transform from given formula and linear property. 9.10Solution: (a). I

5、ts lowpass. (b).Its bandpass. (c).Its highpass.9.13Solution: ,and The Laplace transform : and , From the scale property of Laplace transform, ,So ,From given ,We can determine : 9.21Solution: (a). , (b)., (i)., (f).,9.22Solution: (a). ,(b). ,(c) From the property of shifting in the time-domain and (

6、b),we can get , So , From the property of shifting in the s-domain,we can get ,and 9.28.Solution: (a).All possible ROCs: (b).Its obviouse to see:unstable &uncausalunstable &uncausalstable &uncausalunstable &causal9.31.Solution: (a). (b).1. The system is stable.ROC:(-1,2)2. The system

7、 is causal.ROC:3. The system is neither stable nor causalROC:9.32.Solution:from (1), for all tand x(t) is a eigen functionfrom (2) when , ,9.33. Solution:9.35. Solution:According to the block-diagram, we will know (a), Res>-1 (b) Its obviouse that this system is stable.9.37. Solution: (a) 9.45. Solution: ,-1<Res<2,Res<2, Res>-19.60. Solution:(a)Res: (b),the zeros of ,If , then . But couldnt reach infinit