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2025-L17

# 2025-L17 - ECE-2025 Spring-2004 Info Web-CT Lab HW Quiz#2...

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ECE-2025 Spring-2004 Lecture 17 Continuous-Time Convolution 19-March-04 3/18/2004 ECE-2025 Spring-04 jMc 2 Info: Web-CT, Lab, HW ± Quiz #2: resolve grades by 26-Mar (Friday) ± HW #8 due next week ± Lab #8 due next week 3/18/2004 ECE-2025 Spring-04 jMc 3 cconvdemo ± Continuous-time convolution demo: Lecture 3/18/2004 ECE-2025 Spring-04 jMc 4 READING ASSIGNMENTS ± This Lecture: ± Chapter 9, Sects. 9-6, 9-7, and 9-8 ± Other Reading: ± Recitation: Ch. 9, all ± Next Lecture: Start reading Chapter 10

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3/18/2004 ECE-2025 Spring-04 jMc 5 LECTURE OBJECTIVES ± Review of C-T LTI systems ± Evaluating convolutions ± Examples ± Impulses ± LTI Systems ± Stability and causality ± Cascade and parallel connections 3/18/2004 ECE-2025 Spring-04 jMc 6 Linear and Time-Invariant (LTI) Systems ± If a continuous-time system is both linear and time-invariant, then the output y(t) is related to the input x(t) by a convolution integral convolution integral where h(t) is the impulse response of the system. = = ) ( ) ( ) ( ) ( ) ( t h t x d t h x t y τ 3/18/2004 ECE-2025 Spring-04 jMc 7 Testing for Linearity x 1 ( t ) x 2 ( t ) y 1 ( t ) y 2 ( t ) w ( t ) y ( t ) x ( t ) x 2 ( t ) x 1 ( t ) w ( t ) y ( t ) 3/18/2004 ECE-2025 Spring-04 jMc 8 Testing Time-Invariance x ( t ) x ( t t 0 ) y ( t ) w ( t ) y ( t t 0 ) t 0 w ( t ) y ( t t 0 ) t 0
3/18/2004 ECE-2025 Spring-04 jMc 9 Ideal Delay: ± Linear ± and Time-Invariant ) ( ) ( d t t x t y

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2025-L17 - ECE-2025 Spring-2004 Info Web-CT Lab HW Quiz#2...

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