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What did you send me?

What did you send me?. How do we counter signal attenuation and noise?. [ 8, 5, 12, 12, 15 ]. [8, 5, 12, 12, 15]. “ HELLO ”. [8, 5, 12, 12, 15]. [ 2.70, 1.95, 3.70, 3.70, 4.45 ]. “ ????? ”. f(x). x. y. 8 5 12 12 15. 2.70 1.95 3.70 3.70 4.45. f(x). Receiver only sees y .

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What did you send me?

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

  2. [8, 5, 12, 12, 15] [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) x y 8 5 12 12 15 2.70 1.95 3.70 3.70 4.45 f(x)

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

  6. x y 8 5 12 12 15 2.70 1.95 3.70 3.70 4.45

  7. Assume f(x)=ax+b How do we know f(x)? x y 8 5 12 12 15 2.70 1.95 3.70 3.70 4.45 f(x)=ax+b 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. Let’s change the f(x). Now a and b are unknown again to us. And we received the following: [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? 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”

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