6.02 Spring 2010 Lecture #11web.mit.edu/6.02/www/s2010/handouts/lectures/L11.pdf · Lecture 11,...

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

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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