topic01 - Topic 1. Representation of Signals 1. Shift/Flip...

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Topic 1. Representation of Signals 1. Shift/Flip a Signal (8:12) Contents: Given the signal , ) ( t x Sketch the signal using the following two sequences of operations. ) 1 ( + t x a) shift first, then flip b) flip, shift Note that order doesn’t matter. However, shifting first usually works best. 2. Shift/Flip/Scale a Signal (12:18) Contents: Given the signal , ) ( t x Sketch the signal . Solve three ways by rearranging the sequence of operations. ) 1 2 ( + t x a) shift first, then flip, then scale b) flip, shift, scale c) scale, flip, shift 3. Basics of Step Functions and Impulses (27:13) Contents: Continuous-Time a) Define u ( t ) and sketch . ) ( 0 t t u b) Motivate step function as the limit of f ( t ), i.e., u , where ) ( lim ) ( 0 t f t = ε c) Motivate the impulse (delta) function as dt t du t ) ( ) ( = δ , by sketching approximation and examining dt t df ) ( 0 lim . ) x dt t df ) ( d) Define impulse as and interpret meaning via a sketch. 0 ( ) ( ) ( x dt t t = e) Define sifting (or sampling) property of impulses as . ) ( ) ( ) ( 0 0 t x dt t t t x = Topic 1. Representation of Signals
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This note was uploaded on 04/10/2008 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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topic01 - Topic 1. Representation of Signals 1. Shift/Flip...

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