1. What did you send me? How do we counter signal attenuation and noise?

2. [8, 5, 12, 12, 15] “HELLO”

3. [8, 5, 12, 12, 15] [2.70, 1.95, 3.70, 3.70, 4.45] “?????”

4. f(x) xy 8 5 12 12 15 f(x) 2.70 1.95 3.70 3.70 4.45

5. Receiver only sees y. If receiver knows f(x)… can the receiver figure out x ? Yes!

6. xy 8 5 12 12 15 2.70 1.95 3.70 3.70 4.45

7. How do we know f(x)? Assume f(x)=ax+b 8 5 12 12 15 f(x)=ax+b 2.70 1.95 3.70 3.70 4.45 xy Can you tell what is a and b?

8. Once we know a and b: !!

9. [4.2, 2.95, 1.45, 1.95] [1.45, 3.7, 0.95, 5.45, 5.45] a=0.25 b=0.7 f(x)=0.25x+0.7 g(y)=4y-2.8

10. [2.00, 2.50, 10.00, 3.00, 7.50 2.50] [2.00, 2.50, 9.50, 3.00, 2.00, 3.00, 5.00, 11.50, 3.00] Can we figure out what words are these? Let’s change the f(x). Now a and b are unknown again to us. And we received the following: What if we know every word is added with a prefix “CD” before it’s sent out? For example: “LIKE”  “CDLIKE”

11. Conclusion: Communication channels often distort our signals. If we know “how the channel distorts the signal”, we can attempt to recover the original signal by applying the “inverse effect” to our received signal to recover the original message. We can add extra agreement between the sender and receiver so that the receiver can estimate the channel. Add “CD”