6 003 Signals and Systems Signals and Systems September 10 2009 6 003 Signals and Systems Today s handouts Single package containing Subject Information Calendar Slides from Lecture 1 Homework Assignment 1 Lecturer Denny Freeman freeman mit edu Instructors Elfar Adalsteinsson elfar mit edu Marc Baldo baldo mit edu TAs Jennifer Roberts jenmarie mit edu Dennis Wei dwei mit edu TBA Website mit edu 6 003 Text Signals and Systems Oppenheim and Willsky 6 003 Homework Doing the homework is essential for understanding the content where subject matter is isn t learned equivalent to practice in sports or music Weekly Homework Assignments Conventional Homework Problems plus Engineering Design Problems Python Matlab Open Office Hours Stata Basement 32 044 Mondays and Tuesdays afternoons and early evenings 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 except for single extension 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and for any reason Simply ask your TA for an extension before 11 59 pm on the day preceding the due date cannot be rescinded 6 003 At A Glance Tuesday Wednesday Thursday Friday L1 Signals and Systems R2 Difference Equations HW1 R3 Discrete Time due Systems L3 Feedback Cycles and Modes R4 Feedback Cycles and Modes L4 Feedback and Position Control HW2 R5 Feedback and due Position Control L5 Feedback Control Schemes R6 Feedback Control Schemes Sep 29 L6 CT Systems Differential Eqs HW3 R7 CT Systems due Differential Eqs L7 Laplace and Z Transforms R8 Laplace and Z Transforms Oct 6 L8 CT Operator Representations EX4 L9 Second Order Systems R9 CT Operator Representations Oct 13 Columbus Day Monday Schedule HW5 R10 Second Order L10 Convolution due Systems Impulse Response R11 Convolution Impulse Response Oct 20 L11 Frequency Response HW6 R12 Frequency due Response L12 Bode Diagrams R13 Bode Diagrams Oct 27 L13 CT Feedback and Control EX7 L14 CT Feedback and Control R14 CT Feedback and Control L15 CT Fourier Series HW8 R15 CT Fourier due Series L16 CT Fourier Series R16 CT Fourier Series Nov 10 L17 CT Fourier Transfm Filtering HW9 Veteran s Day due L18 CT Fourier Transforms R17 CT Fourier Transforms Nov 17 L19 DT Fourier Representations EX10 L20 DT Fourier Representations R18 DT Fourier Representations Sep 8 Registration Day R1 Continuous Discrete Systems Sep 15 L2 Discrete Time Systems Sep 22 Nov 3 Exam 1 no recitation Exam 2 no recitation Exam 3 no recitation Nov 24 L21 Sampling HW11 R19 Sampling due Thanksgiving Vacation Thanksgiving Vacation Dec 1 L22 Sampling HW12 R20 Sampling due L23 Modulation R21 Modulation Dec 8 L24 Applications of 6 003 EX13 R22 Review Breakfast with Staff Study Period Dec 15 finals 21 22 finals Final Examination Period finals finals 6 003 Signals and Systems Weekly meetings with class representatives help staff understand student perspective learn about teaching One representative from each section 4 total Tentatively meet on Thursday afternoon Interested send email to freeman mit edu The Signals and Systems Abstraction Describe a system physical mathematical or computational by the way it transforms an input signal into an output signal signal in system signal out Example Mass and Spring Example Mass and Spring x t y t x t mass spring system y t Example Mass and Spring x t y t x t y t t mass spring system t Example Tanks r0 t h1 t r1 t h2 t r2 t r0 t r0 t tank system r2 t t Example Tanks r0 t h1 t r1 t h2 t r2 t r0 t r2 t t tank system t Example Cell Phone System sound out sound in sound in cell phone system sound out Example Cell Phone System sound out sound in sound in sound out t cell phone system t Signals and Systems Widely Applicable The Signals and Systems approach has broad application electrical mechanical optical acoustic biological financial x t y t mass spring system t t r0 t h1 t r1 t r0 t h2 t r2 t tank system t t r2 t sound in sound out t cell phone system t Signals and Systems Modular The representation does not depend upon the physical substrate sound out sound in E M cell sound optic sound cell E M tower tower in phone phone out fiber focuses on the flow of information abstracts away everything else Signals and Systems Hierarchical Representations of component systems are easily combined Example cascade of component systems sound in E M cell optic cell E M tower tower phone fiber phone sound out Composite system sound in cell phone system sound out Component and composite systems have the same form and are analyzed with same methods Signals and Systems Signals are mathematical functions independent variable time dependent variable voltage flow rate sound pressure x t y t mass spring system t r0 t t r2 t tank system t sound in t sound out t cell phone system t Signals and Systems continuous time CT and discrete time DT x t x n n t 0 2 4 6 8 10 0 2 4 6 8 10 Many physical systems operate in continuous time mass and spring leaky tank Digital computations are done in discrete time state machines given the current input and current state what is the next output and next state Signals and Systems Sampling converting CT signals to DT x t x n x nT n t 0T 2T 4T 6T 8T 10T 0 2 4 6 8 10 T sampling interval Important for computational manipulation of physical data digital representations of audio signals e g MP3 digital representations of pictures e g JPEG Signals and Systems Reconstruction converting DT signals to CT zero order hold x n x t n 0 2 4 6 8 10 n 0 2 4 6 8 10 T sampling interval commonly used in audio output devices such as CD players Signals and Systems Reconstruction converting DT signals to CT piecewise linear x n x t n 0 2 4 6 8 10 n 0 2 T sampling interval commonly used in rendering images 4 6 8 10 Check Yourself Computer generated speech by Robert Donovan f t 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 Yourself Computer generated speech by Robert Donovan f t 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 Yourself Computer generated speech by Robert Donovan f t t Listen
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