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6.003: Signals and Systems Lecture 1 Introduction to Signals and Systems

6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

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Page 1: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

6.003: Signals and Systems

Lecture 1

Introduction to Signals and Systems

Page 2: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

6.003: Signals and Systems

Today’s handouts: Single package containing• Subject Information• Lecture #1 slides (for today)• Recitation #2 handout (for tomorrow)

Lecturer Denny Freeman ([email protected])

Instructors Qing Hu, Jeff Lang, Karen Livescu,Sanjoy Mahajan, Antonio Torralba

Head TA Demba Ba ([email protected])

TAs Paul Azunre, Dheera Venkatraman,Keng-Hoong Wee, Steve Zhou

Secretary Janice Balzer ([email protected])

Text Signals and Systems by Oppenheim and Willsky

Web Site mit.edu/6.003

mailto:[email protected]
mailto:[email protected]
mailto:[email protected]
http://mit.edu/6.003
Page 3: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

6.003: Signals and Systems

Homework: where subject matter is/isn’t learned.

equivalent to “practice” in sports or music.

• Weekly Homework Assignments− Conventional Homework Problems plus− Engineering Design Problems (often using Matlab, Oc-

tave, or Python)

• Homework Assignments are longer (by about 3 hours)than homework assignments in 12 unit subjects!− 15 units + 4 Engineering Design Points

• Open Office Hours!− Stata Basement (32-044)− Mondays and Tuesdays, afternoons and evenings

Page 4: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

6.003: Signals and Systems

Collaboration Policy

• Discussion of concepts in homework is encouraged• Sharing of homework or code is not permitted and will be

reported to the COD

Firm Deadlines

• Homework must be submitted in recitation on due date• Late homework will NOT be accepted unless excused by

the staff, a Dean, or Physician

Homework Extension Policy

• Every student gets one extension• Can be used for any weekly homework assignment and for

any reason• Simply ask your TA for an extension before 11:59 pm on

the day preceding the due date (cannot be rescinded)

Page 5: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

6.003 Calendar

• Basic Representations of Discrete-Time Systems (4weeks). difference equations, block diagrams, operatorexpressions, system functions, feedback and control, Ztransforms, convolution (O&W Chapters 1, 2, 10, and11).

• Basic Representations of Continuous-Time Systems

(3 weeks). differential equations, block diagrams, opera-tor expressions, system functions, feedback and control,Laplace transforms, convolution (O&W Chapters 1, 2, 9,and 11).

• Signal Processing (2 weeks). Fourier Series, FourierTransforms, Filtering (O&W Chapters 3, 4, 5, and 6).

• Sampling (2 weeks). Sampling, aliasing, DT processingof CT signals (O&W Chapter 7).

• Communications (2 weeks). modulation, AM, FM (O&WChapter 8).

Page 6: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

6.003: Signals and Systems

Weekly meetings with class representatives

• help staff understand student perspective• learn about teaching

One representative from each section (6 total)

Tentatively meet on Thursday afternoon

Interested? ...send email to [email protected]

mailto:[email protected]
Page 7: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Lecture 1: The 6.003 Abstraction

systemsignal

in

signal

out

6.003 abstraction: describe a system (physical, mathemat-ical, or computational) by the way it transforms inputs intooutputs.

Page 8: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 9: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 10: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 11: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 12: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 13: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 14: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 15: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

Page 16: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 17: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 18: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 19: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 20: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 21: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 22: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 23: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

Page 24: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 25: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 26: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 27: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 28: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 29: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 30: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 31: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Mass and Spring

x(t)

y(t)

mass &springsystem

x(t) y(t)

t t

Page 32: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 33: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 34: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 35: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 36: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 37: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 38: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 39: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 40: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 41: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 42: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 43: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 44: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 45: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 46: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 47: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 48: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 49: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 50: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 51: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t)

tr0(t) r2(t)

Page 52: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 53: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 54: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 55: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 56: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 57: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 58: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 59: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 60: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 61: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 62: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 63: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 64: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 65: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 66: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 67: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 68: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 69: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 70: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 71: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Tanks

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

Page 72: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Cell Phone System

sound in

sound out

cellphonesystem

sound in sound out

Page 73: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Cell Phone System

sound in

sound out

cellphonesystem

sound in sound out

t t

Page 74: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Signals and Systems: Uniform Representations

mass &springsystem

x(t) y(t)

t t

r0(t)

r1(t)

r2(t)

h1(t)

h2(t)

tanksystem

r0(t) r2(t)

t t

sound in

sound out

cellphonesystem

sound in sound out

t t

electrical, mechanical, chemical, optical, acoustic, biological,financial, ...

Page 75: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Signals and Systems: Uniformity → Modularity

sound in

sound out

cellphone

tower towercell

phonesound

in

E/M optic

fiber

E/M soundout

• focus on the flow of information

• abstract away everything else

Page 76: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Signals and Systems: Broad Applicability

mechanics circuits medical

vivoA

R1

R2

systemsignal

in

signal

out

Page 77: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Discrete-Time Systems

Page 78: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank account

Transactions (deposits/withdrawals) recorded daily (DT)

Deposits are an input (of money) into the system.

How are withdrawals represented in the framework

of signals and systems?

1. as an input signal

2. as an output signal

3. none of the above

Page 79: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$0.00

Page 80: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 81: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 82: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$2.00

Page 83: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$3.00

Page 84: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$5.00

Page 85: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$6.00

Page 86: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Transactions (deposits/withdrawals) recorded daily (DT)

x[n] y[n]

n n

account

$ deposited today current balance

$7.00

Page 87: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$0.00

Page 88: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 89: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$2.00

Page 90: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 91: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$3.00

Page 92: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$2.00

Page 93: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 94: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Withdrawals are negative deposits./

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 95: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.00

Page 96: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.05

Page 97: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.10

Page 98: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.16

Page 99: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.22

Page 100: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.28

Page 101: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$2.34

Page 102: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Compound interest./

x[n] y[n]

n n

account

$ deposited today current balance

$1.41

Page 103: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Example: Bank Account

Early Retirement? How soon can you retire if• living expenses: $25,000 per year• rate of savings: $10,000 per year• 5% annual interest• live off your savings till age 80?

x[n]

y[n]

n

n

save retire

Page 104: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 105: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 106: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 107: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 108: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 109: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 110: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 111: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 112: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

Page 113: 6.003: Signals and Systemsweb.mit.edu/6.003/for-posting/lectures/lec01.pdfText Signals and Systems by Oppenheim and Willsky Web Site mit.edu/6.003. 6.003: Signals and Systems Homework:

Population Growth

How does the number of pairs of rabbits grow?

1. logarithmic ( f [n] = O(log n))

2. polynomial ( f [n] = O(nk) for some k)

3. exponential ( f [n] = O(zn) for some z)


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6.003: Signals and Systemsweb.mit.edu/6.003/F09/www/handouts/lec18.pdf · Homework 10 will not collected or graded. Solutions will be posted. Closed book: 3 page of notes (81 2 ×11

6.003: Signals and Systemsweb.mit.edu/6.003/F09/www/handouts/lec18.pdf · Homework 10 will not collected or graded. Solutions will be posted. Closed book: 3 page of notes (81 2 ×11

Documents
6.003: Signals and Systems · 6.003: Signals and Systems Collaboration Policy • Discussion of concepts in homework is encouraged • Sharing of homework or code is not permitted

6.003: Signals and Systems · 6.003: Signals and Systems Collaboration Policy • Discussion of concepts in homework is encouraged • Sharing of homework or code is not permitted

Documents
6.003: Signals and Systemsdspace.mit.edu/.../lecture-notes/MIT6_003S10_lec24.pdfCommunications Systems Signals are not always well matched to the media through which we wish to transmit

6.003: Signals and Systemsdspace.mit.edu/.../lecture-notes/MIT6_003S10_lec24.pdfCommunications Systems Signals are not always well matched to the media through which we wish to transmit

Documents
Lecture 11: Continuous-time frequency response and Bode plots · 6.003: Signals and Systems CT Frequency Response and Bode Plots. October 18, 2011. 1

Lecture 11: Continuous-time frequency response and Bode plots · 6.003: Signals and Systems CT Frequency Response and Bode Plots. October 18, 2011. 1

Documents