2025-L17su09

2025-L17su09 - ECE2025 Summer 2009 Lecture 17 Frequency...

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1 7/7/2009 1 ECE2025 Summer 2009 Lecture 17 Frequency Response of Continuous-Time Systems 08 Jul 09 7/7/2009 3 ANNOUNCEMENTS ± HW #8 due July 14 (in recitation)-15 (in lab) ± Do Lab #8 on July 8-9: ± Done entirely in lab, no report ± 50 points instead of 100 ± Quiz 3: Monday June 13 7/7/2009 4 THIRD QUIZ ± Quiz #3, in lecture, Monday, July 13 ± 10% of final grade ± You can use the full 1:20-2:30 time ± Review session Sunday July 12, 8 pm. ± Emphasis: ± HWs some of #5 through all of #7 ± Lectures #11 through #16 ± No Fourier Transforms ± Closed book, closed notes, except: ± One 8.5”X11” crib sheet allowed, handwritten , OK to write on both sides 7/7/2009 5 LECTURE OBJECTIVES ± Review of convolution ± THE THE operation for LTI LTI Systems ± Complex exponential input signals ± Frequency Response ± Cosine signals ± Real part of complex exponential ± Fourier Series thru H(j ω ) ± These are Analog Filters
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2 7/7/2009 6 LTI Systems ± Convolution defines an LTI system ± Response to a complex exponential gives frequency response H(j ω ) y ( t ) = h ( t ) x ( t ) = h ( τ ) −∞ x ( t ) d 7/7/2009 7 Thought Process #1 ± SUPERPOSITION (Linearity) ± Make x(t) a weighted sum of signals ± Then y(t) is also a sum—different weights DIFFERENT OUTPUT SIGNALS usually ± Use SINUSOIDS “SINUSOID IN GIVES SINUSOID OUT” ± Make x(t) a weighted sum of sinusoids ± Then y(t) is also a sum of sinusoids ± Different Magnitudes and Phase ± LTI SYSTEMS : Sinusoidal Response 7/7/2009 8 Thought Process #2 ± SUPERPOSITION (Linearity) ± Make x(t) a weighted sum of signals ± Use Use SINUSOIDS ± Any x(t) = weighted sum of sinusoids ± HOW? HOW? Use FOURIER ANALYSIS INTEGRAL Use FOURIER ANALYSIS INTEGRAL ± To find the weights from x(t) ± LTI SYSTEMS : ± Frequency Response changes each sinusoidal component 7/7/2009 9 Complex Exponential Input t j j t j j e Ae j H t y e Ae t x ϕ ) ( ) ( ) ( = = a = d e Ae h t y t j j ) ( ) ( ) ( Frequency Response = ωτ d e h j H j ) ( ) ( t j j j e Ae d e h t y = ) ( ) (
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3 7/7/2009 10 When does H(j ω ) Exist?
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2025-L17su09 - ECE2025 Summer 2009 Lecture 17 Frequency...

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