Download - Lecture 7: Signal Processing IV
![Page 1: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/1.jpg)
Lecture 7: Signal Processing IV
EEN 112: Introduction to Electrical and Computer Engineering
Professor Eric Rozier, 2/27/13
![Page 2: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/2.jpg)
SCHEDULE
![Page 3: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/3.jpg)
Schedule
Date M W
2/25 Signals Signals (Quiz)
3/4 Wrap up signals NASA Guest Speaker
3/11 Spring Break Spring Break
3/18 Computer Engineering Computer Engineering
3/25 Computer Engineering Midterm II
4/1 EE/Circuits EE/Circuits
4/8 EE/Circuits EE/Circuits
4/15 EE/Circuits EE/Circuits
4/22 Course Synthesis Course Synthesis
![Page 4: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/4.jpg)
QUANTIZATION
![Page 5: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/5.jpg)
Recall the types of functions
Surjective Injective
![Page 6: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/6.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 7: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/7.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 8: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/8.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 9: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/9.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 10: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/10.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 11: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/11.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 12: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/12.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 13: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/13.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 14: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/14.jpg)
Classification and Reconstruction
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
00 (0)01 (1)10 (2)11 (3)
00.1
0.157620.2
0.3333330.447
0.6666660.91.0
![Page 15: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/15.jpg)
Quantization Error
• Sampling is error free when we follow the Nyquist
• Quantization always has some error.
![Page 16: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/16.jpg)
Quantization Error
• Let’s look at the error of quantizing the numbers 1-100 using various numbers of bits…
![Page 17: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/17.jpg)
2-bit Quantization
Bit vector k x
00 0 0, 1, 5, 10, 29 1
01 1 35, 50, 61 34
10 2 75, 99 67
11 3 100 100
![Page 18: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/18.jpg)
3-bit QuantizationBit vector k x
000 0 0, 1, 5, 10 1
001 1 29 15.143
010 2 35 29.285
011 3 50 43.429
100 4 61 57.571
101 5 75 71.714
110 6 99 85.857
111 7 100 100
99/7 = 14.1429…
![Page 19: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/19.jpg)
4-bit QuantizationBit vector k x
0000 0 0, 1, 5 1
0001 1 10 7.6
… … … …
99/15= 6.6
![Page 20: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/20.jpg)
5-bit QuantizationBit vector k x
00000 0 0, 1, 1
00001 1 5 4.194
… … … …
99/31 = 3.194…
![Page 21: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/21.jpg)
6-bit QuantizationBit vector k x
000000 0 0, 1 1
000001 1 2.571
… … … …
99/63 = 1.571…
![Page 22: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/22.jpg)
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
![Page 23: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/23.jpg)
Quantization Error over [1,100]
Number of bits Maximum quantization error
2 <33
3 <14.14
4 <6.6
5 <1.597
6 <1.572
7 0.78
8 0.388
16 0.00152
32 0.0000000230
64 0.00000000000000000536
![Page 24: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/24.jpg)
Linear vs. Non-linear Quantization
• So far we’ve dealt with linear quantization
• There are other ways we might quantize data
![Page 25: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/25.jpg)
Non-linear Quantization
![Page 26: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/26.jpg)
Non-linear Quantization
![Page 27: Lecture 7: Signal Processing IV](https://reader036.vdocuments.net/reader036/viewer/2022062222/56816718550346895ddb89c0/html5/thumbnails/27.jpg)
Non-linear Quantization
• How should we change our classifier and our reconstruction rule?
• Hint: