2025-L17su09

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 = ) ( ) (
3 7/7/2009 10 When does H(j ω ) Exist?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online