Lecture 2

Lecture 2 - ECE 3101 Signals and Systems Reading...

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Lecture 2, 1/25/11 ECE 3101, Copyright P. B. Luh 1 Reading Assignment: Sections 1.4-1.5 Problem Set 1 due next Thursday: 1.1.7, 1.2.3, 1.3.3, 1.4.4, 1.4.10, 1.5.7 Last Time: Signals and Systems 1.0 Introduction Motivating Examples Basic Classification of Signals Course Overview 1.1 Size of a Signal 1.2 Some Useful Signal Operations 1.3 Classification of Signals: Periodic and Aperiodic Signals ECE 3101 Signals and Systems
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Lecture 2, 1/25/11 ECE 3101, Copyright P. B. Luh 2 Today 1.4 Some Useful Signal Models Elementary Signals: Step, Ramp, and Sign Functions/Sequences Trigonometric Functions and Sequences Complex Functions and Sequences Unit Impulse Function and Unit Impulse Sequence 1.5 Even and Odd Functions and Sequences Next Time: 1.6-1.8 1.6 Systems 1.7 Classification of Systems 1.8 System Models
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Lecture 2, 1/25/11 ECE 3101, Copyright P. B. Luh 3 1.4 Some Useful Signal Models We shall present a few elementary signals The step, ramp, and sign functions or sequences Trigonometric functions or sequences Complex signals The impulse function and the delta sequence The unit step function and the unit step sequence ? u(t) 1 < = 0 t 0 0 t 1 ) t ( u u(t-2) ? u(2t)? u(-t) ? t 1 n u[n] 1 = otherwise 0 0 n 1 ] n [ u T Sampling at T
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Lecture 2, 1/25/11 ECE 3101, Copyright P. B. Luh 4 The sign function (or the signum function ) and the sign sequence ( or the signum sequence) sgn(t) 1 -1 < = > = 0 t 1 0 t 0 0 t 1 ) t sgn( n sgn[n] 1 < = > = 0 n 1 0 n 0 0 n 1 ] n sgn[
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Lecture 2, 1/25/11 ECE 3101, Copyright P. B. Luh 5 The unit ramp function and the unit ramp sequence r(t) = otherwise 0 0 t t ) t ( r r(t-2) ? r(2t) ? r(-t) ? 1 n r[n] = otherwise 0 0 n nT ] n [ r Replace t by nT
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6 Trigonometric Functions or Sequences Trigonometric functions: + + + = = = ! 2 ) x x ( dx ) x ( f d ) x x
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This note was uploaded on 03/29/2011 for the course ECE 3101 taught by Professor Luh during the Spring '11 term at UConn.

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Lecture 2 - ECE 3101 Signals and Systems Reading...

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