1. COMS 161 Introduction to Computing
Title: Digitization
Date: February 14, 2005
Lecture Number: 13

2. Announcements Exam 1 on Wednesday First research paper due ob Friday
2/16/05
First research paper due ob Friday
Due 2/18/05

3. Review Numbers Numeric representation of letters Hexadecimal
Binary to hexadecimal conversion
Hexadecimal to binary conversion
Binary Coded Decimal (BCD)

4. Outline
Digitization
Sound
Sampling
Aliasing
Quantization

5. Sampling
Creates a discrete set of numbers from an analog (continuous time) waveform
Advantageous to sample a regular (periodic) spaced intervals
amplitude
time 6

6. Sampling
amplitude
time 6

7. Sampling
amplitude
time 6

8. Sampling
amplitude
time
Twice as many samples 6

9. Sampling
amplitude
time
Half as many samples 6

10. Samples As the sampling frequency increases
So does the number of samples
Time between each sample decreases
The sampling frequency must be twice the highest frequency of interest
Otherwise
aliasing
fs = 1 / t0 6

11. Aliasing Is the sampling rate is too low
High frequencies fold on-top of the lower frequencies
Aliasing demo 6

12. Quantization Converts a continuous value into a binary number Binning
Samples are placed in the closest bin 6

13. Resolution and Dynamic Range
Directly related to the number of quantization levels
Depends on how much memory is needed to store individual sample amplitudes
Or how much fidelity is needed
8-bit sound
16-bit sound 6

14. Resolution and Dynamic Range
Maximum range of amplitudes of stored sounds
Dynamic
range 6

15. Resolution and Dynamic Range
111
110
101
100
011
010
001
000
3 bits
8 quantization levels
Resolution is 1/8 the dynamic range 6

16. Resolution and Dynamic Range
111
110
101
100
011
010
001
000
Sampling times 6

17. Resolution and Dynamic Range
111
110
101
100
011
010
001
000
Sampled and quantized signal 6

18. Resolution and Dynamic Range
Sampled and quantized signal
Significant error 6

19. Resolution and Dynamic Range
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
4 bits
16 quantization levels
Resolution is 1/16 the dynamic range 6

20. Resolution and Dynamic Range
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
Sampled and quantized signal
Still significant error 6

21. Resolution and Dynamic Range
Sampled and quantized signal

22. Resolution and Dynamic Range
Comparison of 3 and 4 bit resolution
White: 3 bit
Yellow: 4 bit

23. Resolution and Dynamic Range
11111
00000
5 bits
32 quantization levels 6

24. Resolution and Dynamic Range
Sampled and quantized signal

25. Resolution and Dynamic Range
Comparison of 3, 4, and 5 bit resolution
White: 3 bit
Yellow: 4 bit
Green: 5 bit

26. Double the Sampling Rate
11111
00000
Twice as many samples 6

27. Resolution and Dynamic Range
Twice as many samples
Twice as nice 6

28. Resolution and Dynamic Range
Comparison of sampling rates
Carolina blue: twice the number samples as green

29. Resolution and Dynamic Range
More quantization levels
Higher resolution
More accuracy of sample values
More samples
Better fidelity
Digital sounds are closer to the original analog signal 8

30. Resolution Illustrated7

31. Storing Digital Sound Sample rate and resolution -- tradeoffs
Voice and speech
8-bit resolution
5-10 KHz sample rate
CD-quality music
16-bit or higher resolution
44 KHz 8

32. Storing Digital Sound Audio file compression Sound on the Web
Downloading and playing sound files
Streaming audio 8