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北京邮电大学《通信原理》模拟试题2

北京邮电大学《通信原理》模拟试题2
北京邮电大学《通信原理》模拟试题2

试题二

PART I 填空题

1.某分组码的最小码距是6,若该码用于纠错,可保证纠正 位错。若用于检错,可保证检出 位错。

2.在多径时变信道中,当多径时延差远远小于符号间隔时 ,当多径时延差同符号间隔可比拟时 。(选择下面所列添入空中,每空只能选一项)

a. 不发生衰落; b 发生阴影衰落;c 发生瑞利衰落;d. 发生频率选择性衰落;

e. 发生非线性失真。

3.某m 序列由n 级移存器组成。将此m 序列延迟一位后同原序列模2相加,所得序列的周期是 ,一个周期中0的个数减1的个数等于 。

4.某信源的速率是1kbps ,用2PSK 调制,其主瓣带宽是 。若将信源序列同一个速率为10k 的m 序列异或后再进行2PSK 调制,则主瓣带宽是 。

PART II 计算题

一、已知(7,3)分组码的生成矩阵为

??????????=001110101001111001110G (1)写出所有许用码组,并求出监督矩阵。

(2)该码的编码效率为多少?

(3)若译码器输入的码组为l001001,请计算其校正子,并指出此接收码组中是否包

含错误。

二、已知某(n ,k )循环码的编码率是2/3,生成多项式是,问

)1)(1()(+++=x x x x g 4

(1)n =? k =?

(2)请写出该编码器的非全0编码结果中次数最低的码多项式()x a 。

(3)已知前问中的所代表的码字a 是非全0码以外的所有编码结果中码重最小

的,问这个循环码的最小码距是多少?

()x a (4)如果该循环码用于检错目的,问错误图样多项式()x e 具有何种特点时不能被收

端检出?

(5)证明该循环码可以检出n 个比特全都发生错误的错误图样()111321++=+++++=???x x x x x x x e n n n n Λ。(提示:设法验证的因式

中只有一个是)

1+n x 1+x (6)请写出信息码组为(1010110110)的编码输出(要求用系统码)。

三、已知某m 序列的特征多项式为35

()1f x x x =++,请:

(1)画出相应的线性反馈移位寄存器序列发生器的结构图。

(2)此m 序列的周期是多少?

(3)若是此m 序列对应的双极性NRZ 信号,请画出()t s ()t s 的自相关函数。 四、某卷积编码器码的结构如下,输出时21,c c 交替输出。

(1)写出该码的生成多项式;

(2)画出该卷积码的格图;

(3)求输入为1100101的输出。

五、某信源的信息速率为9600bit/s ,信源输出通过一个1/2率的卷积编码器后用BPSK 方式传送,BPSK 采用了滚降系数为1的频谱成形。问

(1)BPSK 的符号速率是多少?

(2)BPSK 信号的带宽是多少?

六、请

(1)写出码长为16的Hadamard 矩阵

(2)请验证此矩阵的第9行和第13行是正交的。

试题二参考答案

PART I 填空题

1.某分组码的最小码距是6,若该码用于纠错,可保证纠正 2 位错。若用于检错,可保证检出 5 位错。

2.在多径时变信道中,当多径时延差远远小于符号间隔时 c ,当多径时延差同可比拟时 d 。

a. 不发生衰落; b 发生阴影衰落;c 发生瑞利衰落;d. 发生频率选择性衰落;

e. 发生非线性失真。

3.某m 序列由n 级移存器组成。将此m 序列延迟一位后同原序列模2相加,所得序列的周期是2n ?1,一个周期中0的个数减1的个数等于 -1 。

4.某信源的速率是1kbps ,用2PSK 调制,其主瓣带宽是 2kHz 。若将信源序列同一个速率为10k 的m 序列异或后再进行2PSK 调制,则主瓣带宽是 20kHz 。 PART II 计算题

一. 解:

(1)按对所有信息比特向量u 进行计算得所有需用码字如下表

G =c u u

000 001 010 011 100 101 110 111 c 0000000 0011101 01001110111010100111010100111101001 1110100

监督矩阵为

1011000111010011000100110001H ??????=??????(2)此码的编码效率是3/7。

(3)伴随式为

101011000001110100111100010100

11000110T Hy ????????????????===????????????????s 1??????????????由于s 不是全0,表明接收码字中存在错误。

二、解:

(1)由23k n =及解得:。

5n k ?=15,10n k ==(2)()()()()45411a x g x x x x x x x ==+++=++21+

(3)a =110101,其码重为4,故该码的最小码距是4。

(4)当能被整除时,这样的错误不能被检出。

()e x ()g x (5)()1415011i i x x x =+=+×∑,()140i i x e x ==∑有15项,所以14010

i i x x ==??≠????∑,即1x =不是多项

式14

0i i x =∑的根,即()e x 不含因式1x +。因为()g x 含因式1x +,所以()e x 不可能被()g x 除尽,因此这样的错误可以被检出。

(6)用长除法,1010110110除以110101得余为10001,因此编码输出是101011011010001。

三、解:

(1)序列发生器结构图如下

(2)周期为

5213?=1(3)相关函数如下图示

四、解:

(1),

()11g x x =+()22g x x x =+(2)格图如下:

(3)输入为1100101时,考虑2bit 的尾比特,则上支路的输出是101011110,下支路的输出是010101111。变成串行后的输出是10 01 10 01 10 11 11 11 01。

五、解:

编码后的速率为19200bit/s,此即BPSK 的符号速率。BPSK 的带宽是Hz 。

()19200138400α+=六、解:

(1)码长为2的Hadarmard 矩阵为

211H ??=??11???

由递推关系

2N N N N N H H H H H ??=?????

可得

2

24221111111111111111H H H H H ??????????==???????????????

4

4844 1 1 1 1 1 1 1 11 -1 1 -1 1 -1 1 -11 1 -1 -1 1 1 -1 -11 -1 -1 1 1 -1 -1 11 1 H H H H H ??==????? 1 1 -1 -1 -1 -11 -1 1 -1 -1 1 -1 11 1 -1 -1 -1 -1 1 11 -1 -1 1 -1 1 1 -1????????????????????

8816881 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 H H H H H ??=?????

= -11 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -11 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 11 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -11 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 11 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 11 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -11 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -11 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 11 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 11 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -11 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 11 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -11 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -11 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1??????????????????????????????????????

(2)H 16的第9行为:

a =(1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1);

第13行为:

b =(1,1,1,1,-1,-1, -1,-1,-1,-1,-1,-1,1,1,1,1)

向量a 、b 之间的内积为

11111111111111110

T =+++????++++????=ab 表明这两行正交。

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