信号与系统期末复习

1、Review chapter 4-10Chapter 4 and chapter 8 FT and IFTX(jw)/x(t)、H(jw)/h(t)、Y(jw)/y(t) The properties of FT、partial fraction expansion4. phase、special expression(Real/imaginary signal)2. Eigenfunction and Eigenvalue3. Amplitude modulation（cos/sin/ejw0t)Some contents of chapter 1-3convolutionDetermine

2、 () ( )X jw of x tExample ( 10 points)11-1-220tx(t)Example ( 12 points)2Consider an LTI system with unit impulse responsesin th(t)=sin 2,if input x(t)=1+cos2+sin5, determine y(t)tttt Consider an LTI system with unit impulse responsesinh(t)=,if input x(t)=1+cos +sin6 , determine y(t)tdte u tttdtt Exa

3、mple (13 points)If input signal is periodic, dont forget the eigenfunction and eigenvalue(fourier series)Example (12 points)12+n=-Consider the system illustrated as below.wheresin th (t)=u(t+1)-u(t-1), h (t)=,if the input x(t)=(t-4n), determine y(t)t h1(t)h2(t)x(t)y(t)Change the order of a series sy

4、stem,the system must be LTIExample (12 points)ttt112Consider the system illustrated as below.wheresin th (t)=u (t), h (t)=,1determine the frequency response H(jw) of the system2 If the input x(t)=1+sin32cos, compute4the output y(t) of the syst 、emh1(t)h2(t)x(t)y(t)The overall response of a series sy

5、stem is the multiple of all subsystemsExample (12 points)1212Consider the system illustrated in Fig 1.wheresin4 tsin th (t)= (t)-, h (t)=sin2 tsuppose the input x(t)=, determinethe spectrum of r (t),r (t) and y(t)dtdttt h1(t)Xh2(t)x(t)Xcos4 t cos6 t y(t)r1(t)r2(t)x(t) Multiple a sinwct or coswct is

6、the shift and amplitude change of X(jw) Example (12 points)+Consider the modulation-demodulation systemillustrated in Fig 1.suppose the FT of x(t) is shownin fig.2, the carrier wave of demodulator is 2p(t)=) sketch the spectrum of z(t) andncntwa y(t)b) sketch and dimension a filter H(jw) so that v(t

7、)=x(t)XH(jw)x(t)Xcostcw tpv(t)y(t)z(t)1wMX(jw)wM0 Example (10 points) 4determine the function x, for the ZT X(Z) and its associated regions of convergence:1 X(Z)= ROC:11nZZ Notice: 9.14 9.17 9.23 9.27 9.31 9.32 9.35 10.182241tt求求的的傅傅立立叶叶变变换换 00jnwTnnwwnwe 证证明明：2sin y(t)=dtatt 计计算算 000000sin222nttx tTwnwXjwXjnwTwnwTt 已已知知当当时时，证证明明 22 59Xjww 计计算算