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《信号检测》09期末试题

《信号检测》09期末试题
《信号检测》09期末试题

《信号检测与估计理论》期末试题

注:试题必须和答题纸一起交。一、二、三、六题必答。是学位课的同学第四题必答,

五、七题中任选1题作答;非学位课的同学四、五、七题中任选1题作答。

姓名 学号 是否学位课 得分

一、 名词解释(每题3分,任选8题作答,共24分)

1、Bayes 估计

2、似然比

3、后验概率

4、检测概率

5、信号统计检测

6、平稳过程

7、充分统计量

8、有效估计

9、接收机工作特性 10、线性最小均方误差估计

二、填空题(每空2分,共16分)

1、在信号检测理论模型中,概率转移机构是将信源输出的假设按一定的概率关系映射到 。

2、信号统计检测的贝叶斯准则就是在假设的 已知,各种代价因子赋定的情况下,使 最小的准则。

3、对于一种假设检验,它的性能主要与 有关。

4、两个联合平稳随机过程()X t 、()Y t 如果相互正交,则它们的互相关函数12(,)XY C t t 为 。

5、序列检测的基本思想是 ,最大优点是 。

6、如果随机量θ的估计值θ∧满足[][]E E θθ∧=,则称θ∧

是θ的 估计。 三、简答题(任选4题作答,每题5分, 共20分)

1、 设()X n 是实平稳随机序列,其均值为m x ,均方值为2[()]E X n ,方差为2x σ,()

X n 的自相关序列为()x R m 。试证明: (0)x R =2

[()]E X n

2、写出课本中相关器与匹配滤波器的输入输出关系表达式,说明两者输出的关系。

3、说明对接收信号x(t)=s(t)+n(t)进行波形检测的基本思路。

4、简述含随机参量的信号的统计检测方法。

5、说明参量的线性最小均方误差估计量的特性。

6、说明参量的最小二乘估计方法的基本思路。

四(10分)、在二元数字通信系统中,假设H 1时,信源输出为常值电压A ,假设H 0时,信源输出为0;信号在通信信道传输过程中叠加了高斯噪声n (t );在接收端对接收信号x (t )进行N 次独立采样,样本为x k ,k=1,2,…,N ;如果噪声样本n k 是均

值为0、方差为σn 2的高斯随机变量。试确定似然比检验的判决规则;建立信号检测系

统的模型。

五(15分)、考虑发送周期为T=2π/ω0秒的移频键控(FSK )通信系统。在假设H 1和假设H 0下发送的信号分别为:

S 0(t )=Asin ω0 t 0≤t ≤T

S 1(t )=Asin2ω0 t 0≤t ≤T

已知A、ω0,假设H1和假设H0是等概出现的。信号在信道传输中叠加了均值为0、功率谱密度为G n(ω)=N0/2的高斯白噪声n(t)。采用最小总错误概率准则,试求:(1)设计该通信系统的一种信号波形检测系统;(8分)

(2)说明该检测系统的总错误概率计算步骤。(7分)

六(15分)、在加性噪声中对单个随机参量θ进行估计,观测方程为:x k=εθ+ n k,k=1,2,…,N

ε为常数,n K是均值为0、方差为σn2的独立同分布高斯噪声,θ也是均值为0、方差为σθ2的高斯随机参量。试求:

(1)求θ的最小均方误差估计;(8分)

(2)能否求θ的最大似然估计?如果不能,说明理由。如果能,求θ的最大似然估计,比较两种估计结果的性能。(7分)

七(15分)、二元数字通信系统中,假设H1时,信源输出为常值电压1v,假设H0时,信源输出为电压0;信号在通信信道传输过程中叠加了均值为0、方差为0. 1的高斯噪声n(t);如果假设H1和假设H0等概出现,Bayes检测时H0判为H0、H1判为H1的代价因子为0,H1判为H0、H0判为H1的代价因子为1。试求:

(1)Bayes检测的检测门限;(8分)

(2)总错误概率。(7分)

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————————————————————————————————作者:————————————————————————————————日期:

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