lecture 7: signal processing iv
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Lecture 7: Signal Processing IV
EEN 112: Introduction to Electrical and Computer Engineering
Professor Eric Rozier, 2/27/13
SCHEDULE
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
QUANTIZATION
Recall the types of functions
Surjective Injective
Classification and Reconstruction
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0.157620.2
0.3333330.447
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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
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
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
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
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
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
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
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
Quantization Error
• Sampling is error free when we follow the Nyquist
• Quantization always has some error.
Quantization Error
• Let’s look at the error of quantizing the numbers 1-100 using various numbers of bits…
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
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…
4-bit QuantizationBit vector k x
0000 0 0, 1, 5 1
0001 1 10 7.6
… … … …
99/15= 6.6
5-bit QuantizationBit vector k x
00000 0 0, 1, 1
00001 1 5 4.194
… … … …
99/31 = 3.194…
6-bit QuantizationBit vector k x
000000 0 0, 1 1
000001 1 2.571
… … … …
99/63 = 1.571…
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
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
Linear vs. Non-linear Quantization
• So far we’ve dealt with linear quantization
• There are other ways we might quantize data
Non-linear Quantization
Non-linear Quantization
Non-linear Quantization
• How should we change our classifier and our reconstruction rule?
• Hint: