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山东大学833专业课考试大纲

山东大学833专业课考试大纲
山东大学833专业课考试大纲

833-信号与系统和数字信号处理

一、考试目的

1. 信号与系统

考查学生是否掌握信号与线性系统的基本概念、基本理论和线性时不变连续(离散)系统的时域、变换域分析方法,以及相关的分析问题、解决问题的能力。

2. 数字信号处理

考察学生是否掌握数字信号处理的基本知识以及运用理论解决实际问题的能力。

二、考试要求

1. 信号与系统

掌握信号与系统的概念、表征、分类与判断;熟悉信号的分解与基本运算,特别是卷积积分(和)的定义、性质与运算;时域法会求LTI连续(离散)系统的各种响应;掌握连续(离散)信号各种变换域(FS、FT、LT,ZT、DTFT)分析法的定义、性质、反变换;并熟练应用于LTI连续(离散)系统分析;熟悉无失真传输、理想滤波器、系统的物理可实现条件、抽样定理、调制与解调的概念,掌握它们在系统分析中的应用;熟悉系统函数的概念、零极图表示,结合收敛域会判断系统的因果性、稳定性;掌握连续(离散)系统的频率响应,能大致画出系统的幅频特性,并说明其滤波性能;掌握状态方程与输出方程的概念、建立与求解;并能判断系统的稳定性、可控性与可观性。

2. 数字信号处理

掌握离散时间信号和系统分析的基本原理和基本分析方法;理解离散傅里叶变换的基本原理,运用离散傅里叶变换快速算法解决实际问题的能力;掌握数字滤波器的基本概念及结构。

三、考试内容与比例

1. 信号与系统(占70%)

1)连续(离散)信号的描述与分类;典型信号的定义、表征与性质;信号的分解、基本运算,特别是卷积积分(和)的定义、性质与运算;系统的概念、连接与分类。

2)线性连续(离散)系统的数学模型与算子表示;时域分析法求解LTI连续(离散)系统的自由响应、受迫响应,冲激响应、阶跃响应,零输入响应、零状态响应以及全响应,了解瞬态响应与稳态响应;连续(离散)LTI系统的模拟框图、特征函数与系统特性。

3)周期信号的傅立叶级数与频谱;周期信号、非周期信号以及抽样信号的傅立叶变换与频谱;能量谱与功率谱;线性连续系统的频域分析法,频率响应;无失真传输,理想滤波器,系统的物理可实现条件,抽样定理,调制与解调。

4)拉普拉斯变换,包括其定义、性质与反变换,收敛域的概念与标示,典型信号、周期信号和抽样信号的拉普拉斯变换;线性连续系统的复频域分析法,涵盖电路的S域模型,系统响应求解,系统函数及其零极图、系统的因果性和稳定性判断;傅立叶变换与拉普拉斯变换的关系,系统幅频特性的大致画法与滤波性能。

5)Z变换的定义、典型变换对、性质与反变换;收敛域的概念与标示;线性离散系统的Z域分析法;系统函数及其零极图、系统的因果性和稳定性判断;离散时间序列傅立叶变换的定义、性质;系统频率响应,系统幅频特性的大致画法与滤波性能。

6)状态方程与输出方程的概念、建立与求解;系统的稳定性、可控性与可观性判断。

2. 数字信号处理(占30%)

1)离散时间信号与系统:时域离散时间信号的表示方法、线性时不变系统的稳定性和因果性、系统的输入输出关系、以及模拟信号的数字处理方法。

2)离散时间傅里叶变换(DTFT)及离散傅里叶变换(DFT):定义、性质、物理意义及相互转换关系,掌握圆周卷积、线性卷积及两者之间的关系,以及频域采样定理和利用DFT 进行模拟信号频谱分析中的应用。

3)快速傅里叶变换:掌握基-2FFT算法的算法原理及其在逆离散傅里叶变换、线性卷积等中的应用。

4)数字滤波器:IIR和FIR滤波器的基本概念及基本结构流图。

四、试题类型

一般为填空选择题、简答题和计算题。

五、考试形式及时间

考试形式为笔试,考试时间为3小时,满分150分。

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