chap1 - Discrete-time Signals and Systems ii Discrete-time...

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Unformatted text preview: Discrete-time Signals and Systems ii Discrete-time Signals and Systems An Operator Approach Sanjoy Mahajan and Dennis Freeman Massachusetts Institute of Technology Typeset in Palatino and Euler by the authors using ConT E Xt and PDFT E X C Copyright 2009 Sanjoy Mahajan and Dennis Freeman Source revision: b19331f50bbd (2009-09-29 13:11:30 UTC) Discrete-time Signals and Systems by Sanjoy Mahajan and Dennis Freeman (authors) and ?? (publisher) is licensed under the ... license. Brief contents Preface ix 1 Difference equations 1 2 Difference equations and modularity 17 3 Block diagrams and operators: Two new representations 33 4 Modes 51 5 Repeated roots 63 Bibliography 71 Index 73 vi Contents Preface ix 1 Difference equations 1 1.1 Rabbits 2 1.2 Leaky tank 7 1.3 Fall of a fog droplet 11 1.4 Springs 14 2 Difference equations and modularity 17 2.1 Modularity: Making the input like the output 17 2.2 Endowment gift 21 2.3 Rabbits 25 3 Block diagrams and operators: Two new representations 33 3.1 Disadvantages of difference equations 34 3.2 Block diagrams to the rescue 35 3.3 The power of abstraction 40 3.4 Operations on whole signals 41 3.5 Feedback connections 45 3.6 Summary 49 4 Modes 51 4.1 Growth of the Fibonacci series 52 4.2 Taking out the big part from Fibonacci 55 4.3 Operator interpretation 57 4.4 General method: Partial fractions 59 5 Repeated roots 63 5.1 Leaky-tank background 64 5.2 Numerical computation 65 5.3 Analyzing the output signal 67 viii 5.4 Deforming the system: The continuity argument 68 5.5 Higher-order cascades 70 Bibliography 71 Index 73 Preface This book aims to introduce you to a powerful tool for analyzing and de- signing systems whether electronic, mechanical, or thermal. This book grew out of the Signals and Systems course (numbered 6.003) that we have taught on and off to MITs Electrical Engineering and Com- puter Science students. The traditional signals-and-systems course for example [16] empha- sizes the analysis of continuous-time systems, in particular analog circuits. However, most engineers will not specialize in analog circuits. Rather, dig- ital technology offers such vast computing power that analogy circuits are often designed through digital simulation. Digital simulation is an inherently discrete-time operation. Furthermore, almost all fundamental ideas of signals and systems can be taught using discrete-time systems. Modularity and multiple representations , for ex- ample, aid the design of discrete-time (or continuous-time) systems. Simi- larly, the ideas for modes, poles, control, and feedback. Furthermore, by teaching the material in a context not limited to circuits, we emphasize the generality of these tools. Feedback and simulation abound in the natural and engineered world, and we would like our students to be flexible and creative in understanding and designing these systems....
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chap1 - Discrete-time Signals and Systems ii Discrete-time...

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