Lesson+32

# Lesson+32 - 1 Lesson 32 Lesson 32 Challenge 31...

This preview shows pages 1–9. Sign up to view the full content.

Lesson 32 1

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

View Full Document
Challenge 31 Continuous-Time Fourier Transform Chap. 17 Challenge 32 (No In-Class Problem) Lesson 32 2 Lesson 32
Challenge 31 Lesson 32 3 A filter’s CTFT frequency response is shown below. - 0 0 0 |H( )| - 0 0 0 H( ) - t 0 Linear phase This is called an ideal or boxcar filter. What is h(t)? (impulse response) H( ) = |H( )| H( )=e -j t 0 1.0

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

View Full Document
Lesson 32 4 )) ( ( ) ( ) ( ( ) ( ) ( ) ( ) ( 0 0 0 0 0 0 0 sinc sin 2 1 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 t t t t t t e t t j d e d e e t h t t j t t j t j t j ω π ω π ω π ω π ω π ω ω ω ω ω ω ω ω ω ω ω ω - 0 0 0 |H( )| - 0 0 0 H( ) - t 0 Inverse CTFT Could also have used the CTFT Properties tables For – 0 0 H( ) = |H( )| H( )=e -j t 0 1 0
Challenge 31 Lesson 32 5 )) ( ( ) ( 0 0 0 sinc t t t h - 0 0 0 |H( )| - 0 0 0 H( ) - t 0 Interpretation t t 0 Group delay g = -d ( )/d = t 0 (constant delay for all ) Impulse response 1 0 Can you build this filter in hardware?

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

View Full Document
Lesson 32 6 t t e t e t d je d je t h t j t j t j t j ) ( cos 1 2 1 2 1 2 1 2 1 ) ( 0 0 0 0 0 0 0 0 0 - 0 0 0 |H( )| - 0 0 0 H( ) Suppose /2  /2 Different phase spectrum – different outcome Non-linear phase (Hilbert filter) Same magnitude response Inverse CTFT
CTFT Overview Lesson 32 7 T T j a t j a T t j at j a e dt e dt e e X 0 0 1 ) ( ) ( ) ( 0 T t x(t)=e -at , t [0,T] square integrable Causal input (1-sided Fourier transform)

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

View Full Document
Lesson 32 8 T T j a t j a T t j at j a e dt
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern