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1、第 1 章习题答案11 题 11 图所示信号中，哪些是连续信号？哪些是离散信号？哪些是周期信号？哪些是非周期信号？哪些是有始信号？解：连续信号：图（a）、（c）、（d）；离散信号：图（b）；周期信号：图（d）；非周期信号：图（a）、（b）、（c）；有始信号：图（a）、（b）、（c）。12 已知某系统的输入f(t)与输出 y(t)的关系为y(t)=|f(t)|，试判定该系统是否为线性时不变系统。解：设 T 为此系统的运算子，由已知条件可知：y(t)=Tf(t)=|f(t)|，以下分别判定此系统的线性和时不变性。线性1）可加性不失一般性，设f(t)=f1(t)+f2(t)，则y1(t)=Tf1(t
2、)=|f1(t)|，y2(t)=Tf2(t)=|f2(t)|，y(t)=Tf(t)=Tf1(t)+f2(t)=|f1(t)+f2(t)|，而|f1(t)|f2(t)|f1(t)+f2(t)|即在 f1(t)y1(t)、f2(t)y2(t)前提下，不存在f1(t)f2(t)y1(t)y2(t)，因此系统不具备可加性。由此，即足以判定此系统为一非线性系统，而不需在判定系统是否具备齐次性特性。2）齐次性由已知条件，y(t)=Tf(t)=|f(t)|，则Taf(t)=|af(t)|a|f(t)|=ay(t)（其中 a 为任一常数）即在 f(t)y(t)前提下，不存在 af(t)ay(t),此系统不具备
3、齐次性，由此亦可判定此系统为一非线性系统。时不变特性由已知条件y(t)=Tf(t)=|f(t)|，则 y(t-t0)=Tf(t-t0)=|f(t-t0)|，即由 f(t)y(t)，可推出f(t-t0)y(t-t0)，因此，此系统具备时不变特性。依据上述、两点，可判定此系统为一非线性时不变系统。13 判定下列方程所表示系统的性质：)()()()()(3)(2)(2)()()2()()(3)(2)()()()()()(2 0tftytydtftyttytyctftftytytybdxxfdttdftyat解：（a）线性 1）可加性由tdxxfdttdfty0)()()(可得tttytfdxxfdt
4、tdftytytfdxxfdttdfty01122011111)()()()()()()()()()(即即则tttdxxfxftftfdtddxxfdttdfdxxfdttdftyty0212102201121)()()()()()()()()()(即在)()()()()()()()(21212211tytytftftytftytf前提下，有、，因此系统具备可加性。2）齐次性由)()(tytf即tdxxfdttdfty0)()()(，设 a为任一常数，可得)()()()()()()(000taydxxfdttdfadxxfadttdfadxxaftafdtdttt即)()(taytaf，因此，
5、此系统亦具备齐次性。由上述 1）、2）两点，可判定此系统为一线性系统。时不变性)()(tytf具体表现为：tdxxfdttdfty0)()()(将方程中得f(t)换成 f(t-t0）、y(t)换成 y(t-t0)（t0为大于 0 的常数），即tdxtxfdtttdftty0000)()()(设0tx，则ddx，因此00)()()(00tttdfdtttdftty也可写成00)()()(00tttdxxfdtttdftty，只有 f(t)在 t=0 时接入系统，才存在)()(00ttyttf，当 f(t)在 t0 时接入系统，不存在)()(00ttyttf，因此，此系统为一时变系统。依据上述、，
6、可判定此系统为一线性时变系统。（b）线性 1）可加性在由)2()()(3)(2)(tftftytyty规定的)()(tytf对应关系的前提下，可得)2()2()()()()(3)()(2)()()2()()(3)(2)()2()()(3)(2)(21212121 212222 21111 1tftftftftytytytytytytftftytytytftftytyty即由)()()()()()()()(21212211tytytftftytftytf可推出，系统满足可加性。2）齐次性由)()(tytf，即)2()()(3)(2)(tftftytyty，两边同时乘以常数a，有)2()()(3)
7、(2)()2()()(3)(2)(taftaftaytaytaytftfatytytya即)()(taytaf，因此，系统具备齐次性。由 1）、2）可判定此系统为一线性系统。时不变性分别将)()(00ttftty和（t0为大于 0 的常数）代入方程)2()()(3)(2)(tftftytyty左右两边，则左边)(3)(2)(00202ttydtttdydtttyd文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 Z
8、V10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7
9、ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7
10、 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U
11、7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2
12、U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S
13、2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10
14、S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10)(3)()(2)()()()2()(00000000ttyttyttddttyttddttddttfdtttdf右边而，)()()(000ttydtdttyttdd)()()()(022000ttydtdttyttddttdd所以，右边)(3)(2)(00202ttydtttdydtttyd左边，故系统
15、具备时不变特性。依据上述、，可判定此系统为一线性时不变系统。（c）线性 1）可加性在由式)(3)(2)(2)(tftyttyty规定的)()(tytf对应关系的前提下，可得)()(3)()(2)()(2)()()(3)(3)(2)(2)(2)(2)()()(3)(2)(2)()(3)(2)(2)(212121 21212121 2 1222 2111 1tftftytytytyttytytftftytyttyttytytytftyttytytftyttyty两式相加即在)()()()(2211tytftytf、的前提下，有式)()()()(2121tytytftf存在，即系统满足可加性。2）齐
16、次性由)()(tytf，即)(3)(2)(2)(tftyttyty，两边同时乘以常数a，有)(3)(2)(2)()(3)(2)(2)(taftaytayttaytaftaytatytay，即有)()(taytaf，因此，系统具备齐次性。依据上述1）、2），此系统为一线性系统。时不变性分别将)()(00ttftty和（t0为大于 0 的常数）代入方程)(3)(2)(2)(tftyttyty左右两边，则)(2)(2)(00022ttyttydtdtttydtd左边右边右边)(2)()(2)()(2)()()(2)()()(3000022000002020ttyttydtdttttydtdttytt
17、yttddttttyttddttf因此，系统是时变的。依据上述、，可判定此系统为一线性时变系统。（d）线性 1）可加性文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S
18、2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10
19、S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D1
20、0S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D
21、10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2
22、D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S
23、2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9
24、S2D10S2U7 ZV10X8Y7P2T10在由式)()()(2tftyty规定的)()(tytf对应关系的前提下，可得)()()()()()()()()()()()(2121222122221121tftftytytytytftytytftyty两式相加而不是：)()()()()()(2121221tftftytytyty即在)()()()(2211tytftytf、的前提下，并不存在)()()()(2121tytytftf因此系统不满足可加性，进而系统不具备线性特性。（下面的齐次性判定过程可省略）2）齐次性由)()(tytf，即)()()(2tftyty，两边同时乘以常数a，有)()()
25、(2taftaytya，即式)()()(2taftaytay不成立，不存在)()(taytaf因此，系统也不具备齐次性。单独此结论，也可判定此系统为一非线性系统。时不变性分别将)()(00ttftty和（t0为大于 0 的常数）代入方程)()()(2tftyty左右两边，则)()(020ttyttydtd左边右边右边)()()()()()(02002000ttydtttdyttyttdttdyttf即以式)()()(2tftyty规定的)()(tytf关系为前提，存在)()(00ttyttf因此，系统是非时变的。依据上述、，可判定此系统为一线性时不变系统。14 试证明方程)()()(tftay
26、ty所描述的系统为线性系统。提示：根据线性的定义，证明满足可加性和齐次性。证明：1）证明齐次性满足齐次性即即两边同乘任意常数)()()()()()()()()()()(tbytbftbftbyatbytbftaytybtftaytyb2）证明可加性满足可加性即即相加)()()()()()()()()()()()()()()()()()()()()()()()()(2121212121212211222111tytytftftftftytyatytytftftaytytaytytftaytytftaytytftayty由以上 1）、2），可知系统是线性的。文档编码:CF2M3U8L3A1 HQ9
27、S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ
28、9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 H
29、Q9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1
30、HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1
31、 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A
32、1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3
33、A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T1015 试证明题1 4 的系统满足时不变性。提示：将方程中的t 换为 t-t0,导出 f(t-t0)与 y（t-t
34、0)对应。证明：分别将)()(00ttftty和（t0为大于 0 的常数）代入方程)()()(tftayty左右两边，则)()(00ttayttydtd左边右边右边)()()()()()(000000ttaydtttdyttayttdttdyttf即以式)()()(tftayty规定的)()(tytf关系为前提，存在)()(00ttyttf因此，系统满足时不变性。16 试一般性的证明线性时不变系统具有微分特性。提示：利用时不变性和微分的定义推导。证明：设线性时不变系统的激励与响应的对应关系为)()(tytf，则（时不变性）)()(ttyttf由线性可加性可得)()()()(ttytyttftf
35、因此tttytytttftf)()()()(所以tttytytttftftt)()()()(limlim00即)()(tytf线性时不变系统具有微分特性。17 若有线性时不变系统的方程为)()()(tftayty，若在非零f(t)作用下其响应tety1)(，试求方程)()(2)()(tftftayty的响应。解：已知tetytf1)()(，由线性关系的齐次性特性，有tteetytf22)1(2)(2)(2又由线性系统的微分特性，有tteetytf)1()()(再由线性关系的可加性特性，可得ttteeetytftf222)()()(2文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 Z
36、V10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7
37、ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7
38、 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U
39、7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2
40、U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S
41、2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10文档编码:CF2M3U8L3A1 HQ9S2D10S2U7 ZV10X8Y7P2T10