内容信号与系统reference

1、11Reference Solutions for Chapter 3223.2 Signal xn，fundamental period N=5，non-zero FS：Try to express xn as the form of ：Sol：333.3 For periodic signal：Find the fundamental frequency and FSTherefore：T=3T=6T=6443.5 Consider：and：Find the relationship between and ; and the relationship between and .Solut

2、ion: ForSo, they have the same period, i.e., BecauseSo：553.8 Suppose we are given the following information about x(t) ：（1） real and odd;（2） is periodic, T=2，FS:（3）For（4）Specify two different signals that satisfy these conditions.Solution: For（1） Purely imaginary and odd。（2）66（3）（4） SO：773.13 LTI, f

3、requency response：For , find y(t).Solution: For T=8，so,and：then：Therefore：883.15 LTI LPF：When input x(t): FS: It is found that：For what values of k that ？Solution：When ，For ，if ，require：i.e.：So：993.20 Consider an LTI RLC circuit，x(t) is the input voltage，y(t) is the voltage across the capacitor。（a）F

4、ind the differential equation relating x(t) and y(t).（b）When input ,determine output （c）if ，find output.（a）Based on knowledge of circuit：KVL：then：10103.20 Consider an LTI RLC circuit，x(t) is the input voltage，y(t) is the voltage across the capacitor。（a）Find the differential equation relating x(t) an

5、d y(t).（b）When input ,determine output （c）if ，find output（b）Because for an LTI system, when inputThe output will be the form of Since,So,11113.20 Consider an LTI RLC circuit，x(t) is the input voltage，y(t) is the voltage across the capacitor。（a）Find the differential equation relating x(t) and y(t).（b

6、）When input ,determine output （c）if ，find output（c）Because： ，then： Since, So,12123.22 Determine the FS（a）x(t) is as in Fig.（a）133.34 An LTI system with , find the output for the following inputs:（a）（a）The frequency response is:143.34 An LTI system with , find the output for the following inputs:（a）（

7、a）since:So,153.34 An LTI system with , find the output for the following inputs:（b）（b）since:So,Then163.34 An LTI system with , find the output for the following inputs:（c）（c）since:So,173.35 LTI frequency response：Input x(t), ，FSIt is found that y(t)=x(t)。For what values of k that ？Solution: For , so

8、 Because：If , that means, If ，require 18183.40 Consider：Derive the FS of the following signals。（a）（b）19193.40 Consider：Derive the FS of the following signals。（c）（d）20203.43 （a）Consider：For every non-zero even integer k，x(t) is called odd-harmonic。（i）Show that if x(t) is odd-harmonic, then ：Proof：Sin

9、ce, So,21213.43 （a）Consider：For every non-zero even integer k，x(t) is called odd-harmonic。（ii ）If x(t) is satisfied that , then x(t) is odd-harmonic.Proof：SO, for every non-zero even integer k， 22223.43 （b）x(t) is an odd harmonic signal with T=2.Sketch x(t)Find FS.23233.43 （c）How abut an even-harmonic signal?I.e., for k is odd, then .Could T still be the fundamental period?According to (a), it is easy to obtainUnder such case，the fundamental period is T/224243.43 （d）Show that T is the fundamental period ofIf