信号与系统推理：Alan V. Oppenheim与George C. Verghese

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"Signals, Systems and Inference" 是一本由Alan V. Oppenheim和George C. Verghese合著的书籍，主要探讨信号处理和系统分析领域的高级概念，并涉及推断理论。这本书适合对信号与系统以及概率有坚实基础的读者，如MIT的6.003课程中使用的Oppenheim的"Signals and Systems"经典教材，以及6.041课程中采用的Bertsekas和Tsitsiklis的"Introduction to Probability"。本书的核心知识点包括： 1. **信号理论**：信号是数据的物理表示，可以是时间、空间或其他物理量的变化。书中会详细讲解各种类型的信号，如连续时间信号、离散时间信号、模拟信号和数字信号，以及它们的性质，如幅度、频率和相位。 2. **系统理论**：系统是对输入信号进行操作以产生输出信号的任何过程或设备。书中的系统可以是线性的、非线性的，时不变的或时变的，因果的或非因果的。线性时不变系统（LTI）是分析的重点，其特性如傅立叶变换和拉普拉斯变换会被深入讨论。 3. **滤波器设计**：滤波器是用于改变信号频谱特性的系统。书中可能涵盖低通、高通、带通和带阻滤波器的设计，以及数字滤波器与模拟滤波器的转换。 4. **信号分析**：包括时域分析和频域分析，如傅立叶分析、拉普拉斯变换和Z变换，这些工具用于理解和描述信号的频谱特性。 5. **推断理论**：这是信号处理中的一个重要方面，涉及从观测数据中提取信息和做决策。书中可能包含统计推断、贝叶斯推断和最大似然估计等概念。 6. **随机过程**：由于许多自然和工程问题涉及到随机性，随机过程在信号处理中扮演着关键角色。书中会讨论平稳过程、马尔可夫过程和高斯过程等。 7. **信号检测与估计**：这部分内容将涵盖如何在噪声中检测信号的存在，以及如何准确估计信号的参数，如均值、方差和相关性。 8. **信号恢复与压缩**：信号压缩技术，如熵编码和预测编码，以及信号恢复方法，如插值和去噪，是信号处理的重要组成部分。 9. **应用实例**：书中可能会通过具体的工程和科学问题，如通信、图像处理、生物医学信号分析等，来阐述理论知识的实际应用。 "Signals, Systems and Inference" 是一个深入研究信号处理、系统分析和推断理论的综合资源，适合希望在这些领域深化理解的读者。通过学习这本书，读者能够掌握处理复杂信号问题的关键技术和理论基础。

A01_OPPE3283_01_SE_FM March 6, 2015 12:19

The Cover

In planning the cover, we were fortunate to have the opportunity to work

closely with Krista Van Guilder, a talented graphic artist who is also man-

ager of media and design in MIT’s Research Laboratory of Electronics. The

cover design originated in our desire to suggest the book’s themes in a visu-

ally pleasing and striking way. Our explorations for the cover began with

images of sundials, clocks, and astrolabes. The astrolabe (www.astrolabes.org),

invented over two thousand years ago and used well into the 17th century,

was an important instrument for numerous astronomical calculations, such

as determining time from latitude and the positions of heavenly bodies.

Inspired by these images, Krista’s search led her to photographs of the beau-

tiful astronomical clock that has kept time over the old town square in

Prague since 1410. Time, both discrete and continuous, is of course cen-

tral to our book. This clock, the Prague Orloj, with astrolabe markings on

its face, and showing the position of the sun and moon along with many

other astronomical details, was chosen as the primary image for the front

cover.

The Prague Orloj is much photographed, but the wonderful photograph

that we selected for the cover was particularly striking to us. It was taken in

2009 by Matteo Foiadelli, a computer engi neer from Bergamo, Italy, whose

hobby is photography. He was on holiday in Prague with friends, and becom-

ing familiar with a new digital SLR camera. As he explained to us, “Ijust

wanted to get an image of the astronomical clock different than the usual frontal

view. So I tried to close up a little bit and to frame it from the side.”Wefeel

fortunate to have found his photograph, and are grateful for his permis-

sion to use it on our cover and as part of the opening art for each

chapter.

The image that adorns the back cover is from a very different type

of camera: the Hubble telescope, deployed in orbit in 1990. This image

from 2001, a striking counterpoint to the astronomical clock, is the result of

A01_OPPE3283_01_SE_FM March 6, 2015 12:19

Acknowledgments

T his text has its origins in an MIT subject that was ﬁrst planned, designed

and taught by us over twenty years ago. It has subsequently evolved to its

current form through continual experimentation and with many variations

of the material and presentation. The subject was conceived as part of the

curriculum for a ﬁve-year Master of Engineering degree program that was

being launched at that time in our Department of Electrical Engineering and

Computer Science (EECS). We are grateful to Paul Penﬁeld (as then depart-

ment head), Jeffrey Shapiro (as associate head) and William Siebert for their

part in deﬁning the curricular structure that provided the opening for such

a subject. Jeff Shapiro also worked with us on the initial deﬁnition of the

content. Continued support of the curriculum, and of revisions to it, from sub-

sequent department heads – John Guttag, Rafael Reif, Eric Grimson, Anantha

Chandrakasan – and their administrations has been important, and we thank

them for their support. More generally, we consider ourselves very fortunate

to have had our academic careers develop in this highly collegial and vibrant

department. MIT’s culture of dedication to teaching and learning informed

by research, and the Institute’s recognition and celebration of excellence in

teaching, have had a signiﬁcant inﬂuence on us.

T he stafﬁng of the course, as taught in our department, includes a faculty

member who gives two weekly lectures and has overall responsibility for run-

ning the course, as well as recitation instructors and teaching assistants who

meet regularly with smaller groups of students. Numerous faculty colleagues

in our de partment have collaborated with us over the years, as recitation

instructors or as lecturers for the subject. Many students have served as able

and enthusiastic teaching assistants. We have also beneﬁted from the help of

excellent administrative assistants. We take the opportunity in what follows

to thank all these people for their multifaceted contributions to the develop-

ment and running of the course, to the student experience in the course, and

to this text.

xvii

A01_OPPE3283_01_SE_FM March 6, 2015 12:19

xviii Acknowledgments

In addition to each of us individually and jointly lecturing and overseeing

the administration of the course many times, other colleagues who have served

in that role are Bernard Lesieutre, Charles Rohrs, Jeffrey Shapiro, Gregory

Wornell, and John Wyatt. In the process they have provided valuable feedback

on the course content and course notes, as well as bringing new insights and

developing new exam and homework problems.

Over the years, we have been privileged to work with a superbly tal-

ented and committed roster of faculty and senior graduate students serving as

recitation instructors. The recitation instructors who have participated in the

teaching of the subject are Jinane Abounadi, Elfar Adalsteinsson, Babak

Ayazifar, Duane Boning, Petros Boufounos, John Buck, Mujdat Cetin, Jorge

Goncalves, Julie Greenberg, Christoforos Hadjicostis, Peter Hagelstein,

Thomas Heldt, Steven Isabelle, Franz Kaertner, James Kirtley, Amos

Lapidoth, Bernard Lesieutre, Steve Massaquoi, Shay Maymon, Alexandre

Megretski, Jose Moura, Asuman Ozdaglar, Michael Perrott, Rajeev Ram,

Charles Rohrs, Melanie Rudoy, Jeffrey Shapiro, Ali Shoeb, William Siebert,

Vladimir Stojanovic, Collin Stultz, Russell Tedrake, Mitchell Trott, Thomas

Weiss, Alan Willsky, Gregory Wornell, John Wyatt, Laura Zager, and Lizhong

Zheng. These colleagues have helped provide a rich experience for the

students, and have made many contributions to the content of the course and

this text.

Both we and the students in the class have been the beneﬁcia-

ries of the dedication and energy of the stellar teaching assistants dur-

ing this period: Irina Abarinov, Abubakar Abid, Anthony Accardi, Chalee

Asavathiratham, Thomas Baran, Leighton Barnes, Soosan Beheshti, Ballard

Blair, Petros Boufounos, Venkat Chandrasekaran, Jon Chu, Aaron Cohen,

Roshni Cooper, Ujjaval Desai, Vijay Divi, Shihab Elborai, Baris Erkmen,

Siddhartan Govindasamy, Hanhong Gao, James Geraci, Michael Girone,

Carlos Gomez-Uribe, Christoforos Hadjicostis, Andrew Halberstadt, Nicholas

Hardy, Everest Huang, Irena Hwang, Zahi Karam, Asif Khan, Alaa

Kharbouch, Ashish Khisti, Lohith Kini, Alison Laferriere, Ryan Lang, Danial

Lashkari, Adrian Lee, Karen Lee, Durodami Lisk, Karen Livescu, Lorenzo

Lorilla, Zhipeng Li, Peter Mayer, Rebecca Mieloszyk, Jose Oscar Mur

Miranda, Kirimania Murithi, Akshay Naheta, Kenny Ng, Tri Ngo, Paul

Njoroge, Ehimwenma Nosakhare, Uzoma Orji, Tushar Parlikar, Pedro Pinto,

Victor Preciado, Andrew Russell, Navid Sabbaghi, Maya Said, Peter Sallaway,

Sridevi Sarma, Matthew Secor, Mariam Shanechi, Xiaomeng Shi, Andrew

Singer, Lakshminarayan Srinivasan, Brian Stube, Eduardo Sverdlin-Lisker,

Kazutaka Takahashi, Afsin Ustundag, Kathleen Wage, Tianyu Wang, Keyuan

Xu, HoKei Yee, and Laura Zager. Their inputs are reﬂected in myriad ways

throughout this text.

Over the many years of offering this subject, we have been guided

by the wisdom of our colleague Frederick Hennie in matters of instruc-

tional stafﬁng. Agnes Chow’s strategic yet detailed oversight of the EECS

department’s administrative and ﬁnancial operations has allowed us and

other faculty to focus on our teaching. Lisa Bella, as assistant to the depart-

ment’s education ofﬁcers, attends almost single-handedly and with incredible

A01_OPPE3283_01_SE_FM March 6, 2015 12:19

Acknowledgments xix

responsiveness and good humor to the practical administrative aspects of

supporting a hundred professors and over a hundred teaching assistants

across the department’s teaching enterprise each semester. For administra-

tive assistance with our course in its m any offerings, we would like to thank

Alecia Batson, Margaret Beucler, Dimonika Bray, Susan Davco, Angela

Glass, Vivian Mizuno, Sally Santiago, Darla Secor, Eric Strattman, and Diane

Wheeler.

As the class subject has continued to evolve over the two-decade period,

the accompanying course notes that ultimately led to this text have also grown

and changed. The students in the class have been key participants in that pro-

cess, through their questions, requests, challenges, suggestions, critiques, and

encouragement. It is a continuing privilege to work with the gifted, engaged,

thoughtful, and vocal students whom we have in our classrooms at MIT.

We have sometimes said, either ruefully or in jest, that the current text

is the fourth edition of a book whose ﬁrst three editions we never formally

published. As any textbook author knows, however, the ﬁnal phase of pro-

ducing a polished text from what initially seem to be very good course notes is

still a formidable task. Some of our teaching assistants and other students have

more recently provided substantial help and feedback in advancing our lecture

notes closer to a text. We would like to speciﬁcally acknowledge the efforts of

Leighton Barnes and Ballard Blair, as well as Manishika Agaskar, Ganesh

Ajjanagadde , Michael Mekonnen, and Guolong Su. For cheerfully, efﬁciently,

and discerningly pulling together and keeping track of all the fragments and

versions and edits as we advanced towards a text, we are enormously indebted

to Laura von Bosau.

Our department leadership has consistently encouraged us to take the

course notes beyond their role as a supplement to the classroom subject and

into a published book, so that the material would be more widely and inde-

pendently accessible. Anantha Chandrakasan’s urging in recent years was a

key catalyst in making this text happen. Also signiﬁcant, and greatly appreci-

ated, was the interest from several publishers. Tom Robbins saw the potential

early on, and regularly offered helpful advice through the ﬁrst decade of the

course, during his time at Prentice Hall. Phil Meyler generously arranged for

detailed feedback at a later stage. Our respect for the vision and integrity

of vice president a nd editorial director Marcia Horton and executive editor

Andrew Gilﬁllan at Pearson were major factors in our choice of publisher;

their patience, commitment and conﬁdence in the project meant a lot to u s.

Special thanks are due to the strong and accommodating editorial and pro-

duction staff, particularly senior managing editor Scott Disanno at Pearson

for his personal attention, and senior project manager Pavithra Jayapaul at

Jouve for her outstanding and steady marshaling of the production through its

countless details over the past year.

As described more fully on our page explaining the cover design, it was

a pleasure to work closely with Krista Van Guilder, manager of media and

design in MIT’s interdisciplinary Research Laboratory of Electronics (RLE).

RLE is the research home for both of us; the creative environment that it pro-

vides for research also impacts our teaching, including the development of this

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