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Lecture 7: Signal Processing IV

Lecture 7: Signal Processing IV. EEN 112: Introduction to Electrical and Computer Engineering. Professor Eric Rozier, 2/ 27/ 13. SCHEDULE. Schedule. QUANTIZATION. Recall the types of functions. Surjective. Injective. Classification and Reconstruction. 0 0.1 0.15762 0.2 0.333333

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Lecture 7: Signal Processing IV

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  1. Lecture 7: Signal Processing IV EEN 112: Introduction to Electrical and Computer Engineering Professor Eric Rozier, 2/27/13

  2. SCHEDULE

  3. Schedule

  4. QUANTIZATION

  5. Recall the types of functions Surjective Injective

  6. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  7. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  8. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  9. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  10. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  11. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  12. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  13. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  14. Classification and Reconstruction 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 0 0.1 0.15762 0.2 0.333333 0.447 0.666666 0.9 1.0 00 (0) 01 (1) 10 (2) 11 (3)

  15. Quantization Error • Sampling is error free when we follow the Nyquist • Quantization always has some error.

  16. Quantization Error • Let’s look at the error of quantizing the numbers 1-100 using various numbers of bits…

  17. 2-bit Quantization

  18. 3-bit Quantization 99/7 = 14.1429…

  19. 4-bit Quantization 99/15= 6.6

  20. 5-bit Quantization 99/31 = 3.194…

  21. 6-bit Quantization 99/63 = 1.571…

  22. Quantization Error • The error introduced when reconstructing a signal • Given an N-bit quantization over a range, [a,b], what is the maximum error? Hint, think in terms of

  23. Quantization Error over [1,100]

  24. Linear vs. Non-linear Quantization • So far we’ve dealt with linear quantization • There are other ways we might quantize data

  25. Non-linear Quantization

  26. Non-linear Quantization

  27. Non-linear Quantization • How should we change our classifier and our reconstruction rule? • Hint:

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