6.02 Spring 2009 Lecture 1, Slide #1

6.02 Spring 2009Lecture #13

• Filters using zeros• Filters using poles• Notch Filter Demo

6.02 Spring 2009 Lecture 1, Slide #2

New Problem – Resource Sharing

• Frequency Division Multiplexing Strategy– Represent each channel with a different frequency

• For LTI systems, frequencies do not mix

– Now need to separate the different frequencies• Use Filters to separate Y in to different channels• LTI systems with specific frequency responses

XmitBits in

Wire+XmitBits in

XmitBits in

Rcvr

Rcvr

Rcvr

Bits out

Bits out

Bits out

6.02 Spring 2009 Lecture 1, Slide #3

Channel 5, 8 Zeros Filter

6.02 Spring 2009 Lecture 1, Slide #4

Channel 4, 8-pair Zeros Filter

6.02 Spring 2009 Lecture 1, Slide #5

High Pass Filter, Two-pair Zeros

6.02 Spring 2009 Lecture 1, Slide #6

Low Pass Filter, Two-pair Zeros

6.02 Spring 2009 Lecture 1, Slide #7

One-pair Poles Bandpass Filter r=0.9

6.02 Spring 2009 Lecture 1, Slide #8

One-pair poles Bandpass Filter r=0.98

6.02 Spring 2009 Lecture 1, Slide #9

One pole-pair, two zero pairs LPF

6.02 Spring 2009 Lecture 1, Slide #10

One zero-pair notch filter

6.02 Spring 2009 Lecture 1, Slide #11

One Zero-pair, One Pole-pair Notch

6.02 Spring 2009 Lecture 1, Slide #12

Notch Unit Sample Response