Lecture 11, Slide #1 6.02 Spring 2010 Lecture #11 • Frequency Response and Filters. • Equations for Filter Design. • Effects of low-pass, high-pass and band-pass filters • Series and Parallel Composition.
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.
Lecture 11, Slide #2
• Continuous Time to Discrete Time Sinusoids
• Complex Exponentials
Basic Tools: DT Sinusoids and Complex Exponentials
Sample Period
Sample Rate
Lecture 11, Slide #3
• Frequency Response
Basic Tools: Frequency Response
Complex Number
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
Lecture 11, Slide #5
Low Pass Filter
Lecture 11, Slide #6
Low Pass Filter Applied to Bits
Lecture 11, Slide #7
Low Pass Filter Applied to Image
Lecture 11, Slide #8
“Wrong” High Pass Filter
Lecture 11, Slide #9
High Pass Filter
Lecture 11, Slide #10
High Pass Filter Applied to Bits
Lecture 11, Slide #11
High Pass Filter Applied to Image
Lecture 11, Slide #12
Band Pass Filter