6.003: Signals and SystemsSignals and SystemsSeptember 10, 20096.003: Signals and SystemsToday’s handouts: Single package containing• Subject Information & Calendar• Slides from Lecture 1• Homework Assignment 1Lecturer: Denny Freeman ([email protected])Instructors: Elfar Adalsteinsson ([email protected])Marc Baldo ([email protected])TAs: Jennifer Roberts ([email protected])Dennis Wei ([email protected])TBAWebsite: mit.edu/6.003Text: Signals and Systems – Oppenheim and Willsky6.003: HomeworkDoing the homework is essential for understanding the content.• where subject matter is/isn’t learned• equivalent to “practice” in sports or musicWeekly Homework Assignments• Conventional Homework Problems plus• Engineering Design Problems (Python/Matlab)Open Office Hours !• Stata Basement (32-044)• Mondays and Tuesdays, afternoons and early evenings6.003: Signals and SystemsCollaboration Policy•Discussion of concepts in homework is encouraged• Sharing of homework or code is not permitted and will be re-ported to the CODFirm Deadlines• Homework must be submitted in recitation on due date• Late homework will NOT be accepted unless excused by thestaff, a Dean, or Physician (except for single “extension”)Homework Extension Policy• Every student gets one extension• Can be used for any weekly homework assignment and for anyreason• Simply ask your TA for an extension before 11:59 pm on the daypreceding the due date (cannot be rescinded)6.003 At-A-GlanceSep 8Registration DayR1: Continuous &Discrete SystemsL1: Signals andSystemsR2: DifferenceEquationsSep 15L2: Discrete-TimeSystemsHW1dueR3: Discrete-TimeSystemsL3: Feedback,Cycles, and ModesR4: Feedback,Cycles, and ModesSep 22L4: Feedback andPosition ControlHW2dueR5: Feedback andPosition ControlL5: FeedbackControl SchemesR6: FeedbackControl SchemesSep 29L6: CT Systems,Differential Eqs.HW3dueR7: CT Systems,Differential Eqs.L7: Laplace and ZTransformsR8: Laplace and ZTransformsOct 6L8: CT OperatorRepresentationsEX4Exam 1no recitationL9: Second-OrderSystemsR9: CT OperatorRepresentationsOct 13Columbus Day:Monday ScheduleHW5dueR10: Second-OrderSystemsL10: Convolution;Impulse ResponseR11: Convolution;Impulse ResponseOct 20L11: FrequencyResponseHW6dueR12: FrequencyResponseL12: BodeDiagramsR13: BodeDiagramsOct 27L13: CT Feedbackand ControlEX7Exam 2no recitationL14: CT Feedbackand ControlR14: CT Feedbackand ControlNov 3L15: CT FourierSeriesHW8dueR15: CT FourierSeriesL16: CT FourierSeriesR16: CT FourierSeriesNov 10L17: CT FourierTransfm; FilteringHW9dueVeteran’s DayL18: CT FourierTransformsR17: CT FourierTransformsNov 17L19: DT FourierRepresentationsEX10Exam 3no recitationL20: DT FourierRepresentationsR18: DT FourierRepresentationsNov 24L21: SamplingHW11dueR19: Sampling Thanksgiving VacationDec 1L22: SamplingHW12dueR20: Sampling L23: Modulation R21: ModulationDec 8L24: Applicationsof 6.003EX13 R22: ReviewBreakfast withStaffStudy PeriodDec 15finals finals21/22finals finalsTuesday Wednesday Thursday FridayThanksgiving VacationFinal Examination Period6.003: Signals and SystemsWeekly meetings with class representatives• help staff understand student perspective• learn about teachingOne representative from each section (4 total)Tentatively meet on Thursday afternoonInterested? ...send email to [email protected] Signals and Systems AbstractionDescribe a system (physical, mathematical, or computational) bythe way it transforms an input signal into an output signal.systemsignalinsignaloutExample: Mass and SpringExample: Mass and Springx(t)y(t)mass &springsystemx(t) y(t)Example: Mass and Springx(t)y(t)mass &springsystemx(t) y(t)t tExample: Tanksr0(t)r1(t)r2(t)h1(t)h2(t)tanksystemr0(t)tr0(t) r2(t)Example: Tanksr0(t)r1(t)r2(t)h1(t)h2(t)tanksystemr0(t) r2(t)t tExample: Cell Phone Systemsound insound outcellphonesystemsound in sound outExample: Cell Phone Systemsound insound outcellphonesystemsound in sound outt tSignals and Systems: Widely ApplicableThe Signals and Systems approach has broad application: electrical,mechanical, optical, acoustic, biological, financial, ...mass &springsystemx(t) y (t)t tr0(t)r1(t)r2(t)h1(t)h2(t)tanksystemr0(t) r2(t)t tcellphonesystemsound in sound outt tSignals and Systems: ModularThe representation does not depend upon the physical substrate.sound insound outcellphonetower towercellphonesoundinE/MopticfiberE/Msoundoutfocuses on the flow of information, abstracts away everything elseSignals and Systems: HierarchicalRepresentations of component systems are easily combined.Example: cascade of component systemscellphonetower towercellphonesoundinE/MopticfiberE/MsoundoutComposite systemcell phone systemsoundinsoundoutComponent and composite systems have the same form, and areanalyzed with same methods.Signals and SystemsSignals are mathematical functions.• independent variable = time• dependent variable = voltage, flow rate, sound pressuremass &springsystemx(t) y(t)t ttanksystemr0(t) r2(t)t tcellphonesystemsound in sound outt tSignals and Systemscontinuous “time” (CT) and discrete “time” (DT)tx(t)0 246 8 10nx[n]0 246 8 10Many physical systems operate in continuous time.• mass and spring• leaky tankDigital computations are done in discrete time.• state machines: given the current input and current state, whatis the next output and next state.Signals and SystemsSampling: converting CT signals to DTtx(t)0T 2T 4T 6T 8T 10Tnx[n] = x(nT )0 246 8 10T = sampling intervalImportant for computational manipulation of physical data.• digital representations of audio signals (e.g., MP3)• digital representations of pictures (e.g., JPEG)Signals and SystemsReconstruction: converting DT signals to CTzero-order holdnx[n]0 246 8 10nx(t)0 246 8 10T = sampling intervalcommonly used in audio output devices such as CD playersSignals and SystemsReconstruction: converting DT signals to CTpiecewise linearnx[n]0 246 8 10nx(t)0 246 8 10T = sampling intervalcommonly used in rendering imagesCheck YourselfComputer generated speech (by Robert Donovan)tf(t)Listen to the following four manipulated signals:f1(t), f2(t), f3(t), f4(t).How many of the following relations are true?• f1(t) = f(2t)• f2(t) = −f(t)• f3(t) = f(2t)• f4(t) = 2f(t)Check YourselfComputer generated speech (by Robert Donovan)tf(t)Listen to the following four manipulated signals:f1(t), f2(t), f3(t), f4(t).How many of the following relations are true?• f1(t) = f(2t)• f2(t) = −f(t)• f3(t) = f(2t)• f4(t) = 2f(t)Check YourselfComputer
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