6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11,...
Transcript of 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11,...
![Page 1: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/1.jpg)
Lecture 11, Slide #1
6.02 Spring 2010Lecture #11
• Frequency Response and Filters.• Equations for Filter Design.• Effects of low-pass, high-pass and band-pass filters• Series and Parallel Composition.
![Page 2: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/2.jpg)
Lecture 11, Slide #2
• Continuous Time to Discrete Time Sinusoids
• Complex Exponentials
Basic Tools: DT Sinusoids and Complex Exponentials
Sample Period
Sample Rate
![Page 3: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/3.jpg)
Lecture 11, Slide #3
• Frequency Response
Basic Tools: Frequency Response
Complex Number
![Page 4: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/4.jpg)
Lecture 11, Slide #4
Designing Filter’s Unit Sample Response • Design a Unit Sample response with L+1 nonzero
values with a given set of frequency responses.
• 2K constraints (desired frequency responses)• L+1 Unknowns (values of h to be designed)
#Eqns = # Unknowns 2K = L+1
![Page 5: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/5.jpg)
Lecture 11, Slide #5
Low Pass Filter
![Page 6: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/6.jpg)
Lecture 11, Slide #6
Low Pass Filter Applied to Bits
![Page 7: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/7.jpg)
Lecture 11, Slide #7
Low Pass Filter Applied to Image
![Page 8: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/8.jpg)
Lecture 11, Slide #8
“Wrong” High Pass Filter
![Page 9: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/9.jpg)
Lecture 11, Slide #9
High Pass Filter
![Page 10: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/10.jpg)
Lecture 11, Slide #10
High Pass Filter Applied to Bits
![Page 11: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/11.jpg)
Lecture 11, Slide #11
High Pass Filter Applied to Image
![Page 12: 6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11, Slide #1 6.02 Spring 2010. Lecture #11 • Frequency Response and Filters. • Equations](https://reader034.fdocuments.in/reader034/viewer/2022052005/6018625617333524ae104d37/html5/thumbnails/12.jpg)
Lecture 11, Slide #12
Band Pass Filter