MIT6_01F09_lec03

MIT6_01F09_lec03 - 6.01: Introduction to EECS 1 Week 2...

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6.01: Introduction to EECS 1 6.01: Introduction to EECS I Signals and Systems Week 2 February 10, 2009 Week 2 February 10, 2009 Abstraction and Modularity Last week, we focused on programming, where abstraction and mod- ularity are key to the design and analysis of complex systems. Data Procedures Primitives: numbers strings +, *, == Combination: lists, dictionaries, objects for, if, while Abstraction: classes def This week: Signals and Systems approach to design and analysis of complex systems. Again, modularity and abstraction are key. Signals Systems Primitives: unit sample, sinusoids adder, gain, delay Combination: delay, scale, add cascade, feedback Abstraction: signal system function The Signals and Systems Abstraction Describe a system by the way it transforms inputs into outputs. system signal in signal out widely applicable, modular, hierarchical Example: Mass and Spring x ( t ) y ( t ) mass & spring system x ( t ) y ( t ) t t Example: Tanks r 0 ( t ) r 1 ( t ) r 2 ( t ) h 1 ( t ) h 2 ( t ) tank system r 0 ( t ) r 2 ( t ) t t Example: Cell Phone System sound in sound out cell phone system sound in sound out t t 1
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6.01: Introduction to EECS 1 Week 2 February 10, 2009 Signals and Systems: Widely Applicable Signals and Systems Abstraction has broad application: electrical, mechanical, optical, acoustic, biological, financial, ... mass & spring system x ( t ) y ( t ) t t r 0 ( t ) r 1 ( t ) r 2 ( t ) h 1 ( t ) h 2 ( t ) tank system r 0 ( t ) r 2 ( t ) t t sound in sound out cell phone system sound in sound out t t Signals and Systems: Modular The uniform representation allows us to combine modules built upon different physical substrates. sound in sound out cell phone tower tower cell phone sound in E/M optic fiber E/M sound out focuses on the flow of information , abstracts away everything else Signals and Systems: Hierarchical Primitive representations can be combined into new representations. Composition of cascaded systems: the output of one is the input to the next cell phone tower tower cell phone sound in E/M optic fiber E/M sound out The new representation can be treated just like primitives. cell phone system sound in sound out Signals and Systems with Robots In lab, we will use a Signals and Systems approach to design a robot ”brain” and characterize the resulting performance. brain robot sonar sensors velocity position Signals and Systems with Robots Example: wallFinder brain wallFinder robot sonar sensors velocity position Program the robot to approach a wall and stop desiredY from it. Sonar sensors report the current distance currentY from the wall. desiredY currentY What forward velocity should wallFollower generate as output?
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This note was uploaded on 11/07/2011 for the course COMPUTER 6.01 taught by Professor Staff during the Spring '09 term at MIT.

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MIT6_01F09_lec03 - 6.01: Introduction to EECS 1 Week 2...

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