6 003 Signals and Systems Lecture 1 February 2 2010 6 003 Signals and Systems 6 003 Signals and Systems Signals and Systems Today s handouts Single package containing Slides for Lecture 1 Subject Information Calendar Lecturer Denny Freeman freeman mit edu Instructors Peter Hagelstein phagelstein aol com Rahul Sarpeshkar rahuls mit edu TAs Sefa Demirtas sefa mit edu Ulric Ferner uferner mit edu Alison Laferriere alaferri mit edu Website mit edu 6 003 Text Signals and Systems Oppenheim and Willsky February 2 2010 6 003 Homework 6 003 Signals and Systems Doing the homework is essential for understanding the content Collaboration Policy where subject matter is isn t learned equivalent to practice in sports or music Discussion of concepts in homework is encouraged Sharing of homework or code is not permitted and will be reported to the COD Weekly Homework Assignments Conventional Homework Problems plus Engineering Design Problems Python Matlab Firm Deadlines Open Office Hours Stata Basement 32 044 Mondays and Tuesdays afternoons and early evenings 6 003 At A Glance Tuesday 6 003 Signals and Systems Wednesday R1 Continuous Discrete Systems Thursday Friday Feb 2 L1 Signals and Systems L2 Discrete Time Systems R2 Difference Equations Feb 9 L3 Feedback Cycles and Modes HW1 R3 Feedback due Cycles and Modes L4 CT Operator Representations R4 CT Systems Feb 16 Presidents Day Monday Schedule HW2 R5 CT Operator due Representations L5 Second Order Systems R6 Second Order Systems Feb 23 L6 Laplace and Z Transforms HW3 R7 Laplace and Z due Transforms L7 Transform Properties R8 Transform Properties Mar 2 L8 Convolution Impulse Response EX4 Exam 1 no recitation L9 Frequency Response R9 Convolution and Freq Resp Mar 9 L10 Bode Diagrams HW5 R10 Bode due Diagrams L11 DT Feedback and Control R11 Feedback and Control Mar 16 L12 CT Feedback and Control HW6 R12 CT Feedback due and Control L13 CT Feedback and Control R13 CT Feedback and Control Mar 23 spring spring spring spring Spring spring Week Mar 30 L14 CT Fourier Series HW7 R14 CT Fourier Series L15 CT Fourier Series R15 CT Fourier Series Apr 6 L16 CT Fourier Transform EX8 due Exam 2 no recitation L17 CT Fourier Transform R16 CT Fourier Transform Apr 13 L18 DT Fourier Transform HW9 R17 DT Fourier due Transform L19 DT Fourier Transform R18 DT Fourier Transform Apr 20 Patriots Day Vacation L20 Fourier Relations R20 Fourier Relations HW10 R19 Fourier Transforms Apr 27 L21 Sampling EX11 Exam 3 due no recitation L22 Sampling R21 Sampling May 4 L23 Modulation HW12 R22 Modulation due L24 Modulation R23 Modulation May 11 L25 Applications of 6 003 EX13 R24 Review Breakfast with Staff Study Period May 18 finals Homework must be submitted in recitation on due date Each student can submit one late homework assignment without penalty Grades on other late assignments will be multiplied by 0 5 unless excused by an Instructor Dean or Medical Official finals Final Examination finals Period finals 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 finals 1 6 003 Signals and Systems Lecture 1 The Signals and Systems Abstraction February 2 2010 Example Mass and Spring Describe a system physical mathematical or computational by the way it transforms an input signal into an output signal x t y t signal in signal out system x t y t mass spring system t Example Tanks t Example Cell Phone System r0 t sound out h1 t r1 t sound in h2 t r2 t r0 t sound in sound out r2 t tank system t t t cell phone system t Signals and Systems Widely Applicable Signals and Systems Modular The Signals and Systems approach has broad application electrical mechanical optical acoustic biological financial The representation does not depend upon the physical substrate x t y t mass spring system t sound out t r0 t sound in h1 t r1 t r0 t h2 t r2 t tank system t t r2 t sound in E M cell sound optic sound cell E M tower tower in phone fiber phone out sound out t cell phone system t focuses on the flow of information abstracts away everything else 2 6 003 Signals and Systems Lecture 1 February 2 2010 Signals and Systems Hierarchical Signals and Systems Representations of component systems are easily combined Signals are mathematical functions Example cascade of component systems sound in E M cell optic cell E M tower tower phone fiber phone independent variable time dependent variable voltage flow rate sound pressure sound out x t y t mass spring system t t r0 t r2 t Composite system tank system t sound in cell phone system sound out t sound in sound out cell phone system t Component and composite systems have the same form and are analyzed with same methods t Signals and Systems Signals and Systems continuous time CT and discrete time DT Sampling converting CT signals to DT x t x n x t n t 0 2 4 6 8 0 10 x n x nT 2 4 6 8 10 n t 0 0T 2T 4T 6T 8T 10T Many physical systems operate in continuous time 2 4 6 8 10 T sampling interval mass and spring leaky tank Digital computations are done in discrete time Important for computational manipulation of physical data state machines given the current input and current state what is the next output and next state Signals and Systems Signals and Systems Reconstruction converting DT signals to CT Reconstruction converting DT signals to CT zero order hold piecewise linear x t x n 2 4 6 8 10 x t x n n 0 digital representations of audio signals e g MP3 digital representations of pictures e g JPEG n t 0 0 2T 4T 6T 8T 10T T sampling interval 2 4 6 8 10 t 0 2T 4T 6T 8T 10T T sampling interval commonly used in audio output devices such as CD players commonly used in rendering images 3 6 003 Signals and Systems Lecture 1 Check Yourself February 2 2010 Check Yourself f x y y 250 0 250 Computer generated speech by Robert Donovan f t t 250 250 0 x 250 f1 x y f 2x y 250 0 250 250 0 250 0 f1 t f 2t f2 t f t f3 t f 2t f4 t 2f t x How many images match the expressions beneath them y y 250 y 250 250 Listen to the following four manipulated signals f1 t f2 t f3 t f4 t How many of the following relations are true 0 250 0 250 x f2 x y f 2x 250 y 250 The Signals and Systems Abstraction Example System Leaky Tank Describe a system physical mathematical or computational by the way it transforms an input signal into an output signal Formulate a mathematical description of this system r0 t h1 t r1 t signal in
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