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Introduction to Quantization in Signal Processing

In this lecture, Professor Eric Rozier discusses the concept of quantization in signal processing, emphasizing the classification and reconstruction of signals. The lecture outlines the types of functions, including surjective and injective, and highlights the impact of quantization error when sampling signals. Various quantization methods, including linear and non-linear approaches, are explored, demonstrating the differences in error introduced during signal reconstruction. Understanding quantization is essential for effective electrical and computer engineering.

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Introduction to Quantization in Signal Processing

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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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