MS004103-现代数字信号处理（1）

研究生课程开设申请表

 开课院（系、所）：  信息科学与工程学院

 课程申请开设类型： 新开□     重开√    更名□（请在□内打勾，下同）

一、课程介绍（含教学目标、教学要求等）（300字以内）

    本课程主要讲授在平稳和非平稳环境下信号处理所遇到的各种问题、求解方法及具体算法。要求学生掌握随机过程、估计方法、变换、谱分析与谱估计、最优滤波和自适应滤波等现代数字信号处理理论与技术，要在原来本科数字信号处理课程的基础上进一步深化，对数字信号处理在通信、语音、雷达、声纳、多媒体等领域的应用有更深刻的理解。学习中将通过计算机作业和练习来加深有关理论的理解和掌握。该课程每周4课时，共16周。

二、教学大纲（含章节目录）：（可附页）

第一章  离散时间信号处理基础

1、数字信号与数字信号处理(DSP)概述2、滤波器－－简单的数字信号处理系统

3、信号的变换－z变换、DTFT、DFT和FFT

4、特殊的序列和对应的滤波器：全通系列、最小相位序列、线性相位、半正定序列

第二章  离散随机信号分析基础

1、随机过程2、随机过程通过滤波器3、谱因子分解4、特殊类型的随机过程

5、基本的正交变换：Hilbert空间的正交变换、K-L变换与主分量分析、离散余弦(DCT)变换

6、基本的参数估计方法：(a) 参数估计的基本性能；(b) 随机信号统计量的样本估计；(c) 最小二乘估计(LS)；(d) 线性均方估计(MMSE)；(e) 最大似然估计(ML)；(f) Bayes估计

第三章线性预测和格型滤波器

1、基本的线性预测模型和自相关算法；2、AR过程全极点建模与线性预测的等效

3、Levinson-Durbin递归算法；4、三组递归参数的等效关系；

5、Schur递归算法；6、一般的Levinson递归算法；

7、线性预测的协方差算法；8、前向和后向线性预测与格型滤波器

9、线性预测的格型模型法－Burg算法；10、线性预测的修正协方差算法

第四章随机信号的线性建模

1、随机信号的ARMA建模；2、随机信号的自回归(AR)建模；

3、随机过程的滑动平均(MA)建模；

4、应用实例：a) 功率谱估计; b) 约束格型滤波器用于估计信号频率

第五章功率谱估计

1、非参数方法；2、最小方差谱估计；

3、最大熵方法；4、谱估计的参数方法；

5、几种方法的性能比较；6、频率估计的子空间方法

第六章维纳滤波与卡尔曼滤波

1、FIR维纳滤波器：FIR维纳滤波问题；FIR维纳线性预测；基于FIR维纳滤波的噪声抑制；FIR维纳反卷积--MMSE均衡器；FIR维纳滤波器的格型表示

2、IIR维纳滤波器：非因果IIR维纳滤波；非因果IIR维纳反卷积；因果IIR维纳滤波器；因果维纳滤波应用；因果维纳线性预测应用

3、离散卡尔曼滤波器

第七章自适应滤波器

1、FIR自适应滤波的LMS类算法：

最陡下降法自适应滤波器；LMS算法；LMS算法的收敛性分析；归一化LMS算法；LMS-Newton算法；变换域LMS算法；仿射投影算法；其它的基于LMS的自适应滤波器；应用实例1――自适应噪声抑制；应用实例2――自适应信道均衡；梯度自适应格型滤波器；自适应联合过程估计子

2、递归最小二乘(RLS)算法：

指数加权RLS；增长窗RLS；滑动窗RLS算法；其它的RLS算法

3、自适应滤波的应用例子

第八章  多速率数字信号处理与滤波器组

1、数字信号的采样率变换：M倍降采样、L倍升采样、分数倍采样率变换

2、多速率处理模块的级联等效形式；3、抽取器和插值器的多级实现

4、多相分解结构：基于多相分解的FIR滤波器实现结构、升采样器和降采样器的高效实现结构

5、数字滤波器组：简单的最大均匀抽取DFT滤波器组，多子带滤波器，两通道滤波器组及其优化设计，多通道滤波器组(余弦调制滤波器组)

三、教学周历

四、主讲教师简介：

杨绿溪：1964年生，东南大学信息科学与工程学院教授，博士生导师，1993年获博士学位。近年来主要从事MIMO通信系统设计、协作通信与分集处理、多用户MIMO方案、有限反馈预编码等方面的科研工作，已申请发明专利20项，提交3GPP2 UMB国际通信标准提案3份，并在包括IEEE信号处理、通信、电路与系统会刊和中国科学E辑、F辑等国内外刊物与IEEE会议上发表和合作发表论文200多篇，SCI收录30多篇，EI收录120多篇。曾担任国家863项目负责人、国家攀登计划重大项目子课题组长、国家自然科学基金重点项目课题组长等，参加过国家自然科学基金重大项目的研究；主持过4项国家自然科学基金，和其它10多项省部级科研项目，结题评审均为“优”，其中2项被评为“特优”。曾作为主要参加者获2000年和2002年江苏省科技进步奖一等奖各1项，2001年中国高校科技奖自然科学二等奖，1998年教育部科技进步一等奖和二等奖各1项。另获2004年江苏省教学成果二等奖1项，IEEE国际会议最佳论文奖3次(IEEE APCCAS'2000、IEEE IWVDVT’2005和IEEE ICNNSP’2008)。

五、任课教师信息（包括主讲教师）：

Application Form For Opening Graduate Courses

School (Department/Institute)：School of Information Science and Engineering

Course Type: New Open □   Reopen √   Rename □（Please tick in □, the same below）

1. Course Introduction (including teaching goals and requirements) within 300 words:

This course focuses on problems, algorithms, and solutions for processing signals in stationary and non-stationary environment. It will provide students with the basics of stochastic processes, estimation, transformation, spectral analysis, optimal filtering and adaptive filtering techniques present in modern digital signal processing systems. The class is designed as an advanced statistical signal processing course in which students will build a strong foundation in approaching problems in such diverse areas as acoustic, sonar, radar, multimedia and communications signal processing. Understanding of the theoretical foundations of advanced signal processing theory will be achieved through a combination of theoretical and computer-based homework assignments. The class meets for 4 lecture hours per week for 16 weeks.

2. Teaching Syllabus (including the content of chapters and sections. A sheet can be attached):

Chapter 1  Fundamentals of Discrete-time Signal processing

1. Introduction to Digital Signals and Digital Signjal Processing (DSP)  

2. Digital Filters

3. Transforms for Digital Signals: a) z-Transform, b) DTFT, c) DFT and FFT

4. Special Sequences and Special Filters: a)All-Pass, b) Minimum Phase, c) Linear Phase, d) Positive Semi-definite

Chapter 2  Fundamentals of Stochastic Discrete-time Signal Analysis

1. Random Processes   

2. Filtering Random Processes   

3. Spectral Factorization

4. Special Types of Random Processes

5. Basic orthogonal transforms: a) Orthogonal transforms in Hilbert space, b) K-L transform and principal component analysis, c) Discrete-time Cosine transform (DCT)

6. Basic methods of parameter estimation: a) Principles of parameter estimation, b) Performance bounds, c) Sample mean and sample autocorrelation, d) Least squares (LS) estimation, e) Linear minimum mean squares estimation (LMMSE), f) Maximum likelihood (ML) estimation, g) Bayes estimation

Chapter 3Linear Prediction and Lattice Filters

1. Basic Model of Linear Prediction and the autocorrelation method

2. The equivalence between all-pole modeling of AR process and linear prediction

3. Levinson-Durbin recursion algorithm       

4. Step-up, step-down, and inverse recursion

5. Schur recursion                        

6. Levinson recursion

7. The covariance algorithm for linear prediction            

8. Forward and backward linear prediction and Lattice filters

9. The Burg recursion algorithm－linear prediction based on Lattice modeling   

10. The modified covariance algorithm for linear prediction

Chapter 4Linear Modeling of Random Sequences

1. ARMA modeling of random sequences

2. AR modeling of random sequences

3. MA modeling of random sequences

4. Applications and examples

Chapter 5Power spectrum estimation

1. Classical methods   

2. The minimum variance method   

3. The maximum entropy method

4. Parametric spectrum estimation   

5. Comparison of several methods

6. Subspace methods for frequency estimation

Chapter 6Wiener filtering and Kalman filtering

1. FIR Wiener filters: a) FIR Wiener filtering, b) FIR Wiener linear prediction, c) Noise cancelling by FIR Wiener filters, d) FIR Wiener deconvolution ---MMSE equalizer, e) FIR Wiener Lattice filters

2. IIR Wiener filters: a) Noncausal IIR Wiener filtering, b) Noncausal IIR Wiener deconvolution, c) Causal IIR Wiener filtering, d) Causal IIR Wiener linear prediction

3. Discret time Kalman filtering and Applications

Chapter 7Adaptive filtering

1. Adaptive direct-form FIR filters: a) Steepest Descent algorithm, b) Least-Mean-Square (LMS) algorithm, c) Properties of the LMS, d) Normalized and frequency-domain LMS, e) LMS-Newton algorithm, f) Transform-domain LMS algorithm, g) Affine projection algorithm, h) Gradient adaptive lattice methods, i) Adaptive joint process estimator

2. Recursive least squares adaptive algorithms: a) Three type of RLS algorithms, b) Properties of RLS

3. Applications of adaptive filtering

Chapter 8  Multi-rate Digital Signal Processing and Filter Banks

1. The sampling rate alteration: a) Factor-of-M down-sampling, b) Factor-of-L up-sampling, c) Fractional sampling rate alteration

2. Cascade equivalence of the basic sampling rate alteration devices

3. Multistage design of Decimator and Interpolator

4. The polyphase decomposition: a) The decomposition, b) FIR filter structures based on the polyphase decomposition, c) Efficient implementation of Decimator and Interpolator

5. Digital filter banks: a) Uniform DFT filter banks and their polyphase implementations, b) Lth-band filters, c) Two-channel filter banks and their optimal design, L-channel filter banks (Cosine-modulated filter banks)

3. Teaching Schedule:

Note: 1.Above one, two, and three items are used as teaching Syllabus in Chinese and announced on the Chinese website of Graduate School. The four and five items are preserved in Graduate School.

2. Course terms: Spring, Autumn , and Spring-Autumn term.  

3. The teaching languages for courses: Chinese, English or Chinese-English.

4. Applicable range of discipline: public, first-class discipline, second-class discipline, and third-class discipline.

5. Practice includes: experiment, investigation, research report, etc.

6. Teaching methods: lecture, seminar, practice, etc.

7. Examination for degree courses must be in paper.

8. Teaching material websites are those which have already been announced.

9. Brief introduction of chief lecturer should include: personal information (date of birth, gender, degree achieved, professional title), research direction, teaching and research achievements. (within 100-500 words)

4. Brief Introduction of Chief lecturer:

Luxi Yang, male, was born in 1964. Hereceived the M.S. and Ph. D. degree in electrical engineering, from the Southeast University, Nanjing, China, in 1990 and 1993, respectively. Since 1993, he has been with the Department of Radio Engineering, Southeast University, where he is currently a Professor of information systems and communications and the director of Digital Signal Processing Division, and also served as a doctoral students advisor. His current research interests include signal processing for wireless communications, MIMO communications, cooperative relaying systems, and statistical signal processing. He is the author or coauthor of two published books and more than 160 journal papers, and holds 20 patents. Prof. Yang received the first- and second-class prizes of Science and Technology Progress Awards of the State Education Ministry of China for 3 times, and the first-class prizes of Science and Technology Progress Awards of Jiang-su Province of China for 2 times. He is currently a Member of Signal Processing Committee of Chinese Institute of Electronics, Chapter Chair of Signal Processing, IEEE Nanjing Section.

5. Lecturer Information (include chief lecturer)