What Is Digital?(Part 2)

Prof. Chung-Ta KingDepartment of Computer

ScienceNational Tsing Hua University

CS1103 電機資訊工程實習

(Contents from MIT EECS 6.01/6.02, Wikipedia, U. of Indiana K361,www.arrl.org, www.sounderpro.com.tw/Digital)

自然界的現象多為連續性的自然界的現象多為連續性的

如何將連續性的信號轉為數位信號，讓電腦可以處理？如何將連續性的信號轉為數位信號，讓電腦可以處理？

3

Outline

Continuous versus discrete Problems with “continuous” Going into discrete/digital

Building digital devices IC to digital logic to computing devices

Transforming analog inputs into digital Transforming digital to analog outputs

4

彩虹有幾種顏色？

真的只有七種顏色嗎？真的只有七種顏色嗎？

5

我們實際上是運用了 Sampling的技巧

Digital representations of analog waveforms

Continuous timeContinuous valuesContinuous time

Continuous values

Discrete timeDiscrete valuesDiscrete time

Discrete values

6

Sampling

The value of the analog signal is measured at certain intervals in time. Each measurement is referred to as a sample.

A series of “snapshots”

7

Sampling in Space

8

Terminologies in Sampling

Sampling rate: How often analog signal is measured

[samples per second, Hz], e.g. 44,100 Hz Sampling resolution:

Number of bits to represent each sample [“sample word length,” “bit depth”], e.g. 16 bit Analog

Input

4 Samples/cycle 8 Samples/cycle 16 Samples/cycle

9

Note: Sampling Used Widely

民意調查

檢查奶精產品中的三聚氰胺

全台灣的降雨量分佈

動畫 (24 格 /秒 )

CD 音效格式 (44.1 Khz)

10

Problem with Sampling

The analog signal is sampled at discrete intervals of time The digital output is an incomplete picture

of the behavior of the input There is no way of knowing, by looking at

the output, what the input was doing between one sampling instant and the next

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How Many Samples Are Enough?

Reconstruction: Is it possible to reconstruct the original waveform using only the discrete time samples?

12

Shannon-Nyquist Sampling Theorem

How many samples are necessary to preserve the information contained in the signal? If signal contains high frequency

components, need to sample at even higher rate to avoid losing information in the signal

How much faster? Sampling Theorem: A signal can be exactly

reproduced if it is sampled at a frequency that is greater than twice max. frequency in the signal

http://www2.egr.uh.edu/~glover/applets/Sampling/Sampling.htmlhttp://www2.egr.uh.edu/~glover/applets/Sampling/Sampling.html

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Sampling at Same Frequency

14

Sampling at Twice Frequency

15

Implications

人能聽取的音頻大概是 20 Hz ~ 20 KHz 我們只要用 40 kHz 以上的取樣率 (sampling

rate) 就可以完整紀錄 20 kHz 以下的訊號

人的聲音可以用 8kHz 來取樣 8kHz: telephone quality 44.1kHz: CD quality 48kHz: radio/TV broadcast, DV, DVD video

問題是，我們不一定知道類比信號的最高頻率，因此無法確定取樣頻率。而且往往高頻信號為雜訊

16

Aliasing

If sampling rate not high enough New frequencies appear in reconstructed

signals Need circuits to eliminate (anti-aliasing

filter) A high frequency signal

sampled at a lower rate

looks like …

… a lower frequency signal

17

Encoding of Discrete Signals

If we use N bits to encode the magnitude of one of the discrete-time samples, we can capture 2N possible values

18

3-bit Quantization

A 3-bit binary number has 23 = 8 values

0

1

2

3

4

5

6

7

Am

plit

ud

e

Time — measure amplitude at each tick of sample clock

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4-bit Quantization

A 4-bit binary number has 24 = 16 values

Time — measure amplitude at each tick of sample clock

0

2

4

6

8

10

12

14

Am

plit

ud

e

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The Digital Audio Stream

A series of sample numbers, to be interpreted as instantaneous amplitudes, one for every tick of the sample clock. This is what appears in a sound file, along

with a header that indicates the sampling rate, bit depth and other things.11 13 15 13 10 9 6 1 4 9 15 11 13 9

0

2

4

6

8

10

12

14

Am

plit

ude

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Audio File Size

CD characteristics… Sampling rate:

44,100 samples per second (44.1 kHz) Sample word length:

16 bits (i.e., 2 bytes) per sample Number of channels:

2 (stereo) How big is a 5-minute CD-quality sound

file?

22

Quantization Error

When we quantize the scaled sample values, we may be off by up to ±1/2 step from the true sampled values Round-off error: difference between actual

signal and quantization to integer values…

Random errors: sounds like low-amplitude noise

23

Sampling Rate and Encoding Bits

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Resolution Trade-offs

Bit Resolution

High Bit Count

Good Duplication

Slow

Low Bit Count

Poor Duplication

Fast

Sample Rate

High Sample Rate

Good Duplication

Slow

Low Sample Rate

Poor Duplication

Fast

 

25

ADC

Continuously varying electrical energy is an analog of the sound pressure wave.

Microphone converts acoustic to electrical energy. It’s a transducer.

ADC (Analog to Digital Converter) converts analog to digital electrical signal.Digital signal transmits binary numbers.

DAC (Digital to Analog Converter) converts digital signal in computer to analog for your headphones.

Analog to Digital Recording Chain

26

ADC and DAC

http://www.dspguide.com/ch3/4.htm http://www.dspguide.com/ch3/4.htm

27

ADC in Digital Camera

http://www.tasi.ac.uk/advice/creating/camera.htmlhttp://www.tasi.ac.uk/advice/creating/camera.html

28

Converting Analog into Digital

The simplest form of ADCuses a resistance ladderto switch in the appropriatenumber of resistors in seriesto create the desiredvoltage that is compared to the input(unknown) voltage

V-7

V-6

V-low

V-1

V-2

V-3

V-4

V-5

V-high

SW-8

SW-7

SW-6

SW-5

SW-4

SW-3

SW-2

SW-1

Output

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Converting Analog into Digital

The resistance ladder changes its configuration systematically and the output voltage is compared to the analog voltage in a comparator

When there is a match, the digital equivalent (switch configuration) is captured

Analog Voltage

ResistanceLadder Voltage

ComparatorOutput Higher

EqualLower

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How? Binary Search

Initial conditions Expected high 5

volts Expected low 0

volts 5 volts 256 0 volts 0

Voltage to be converted 3.42 volts Equates to 175

Analog Digital

5-volts 256

0-volts 0

2.5-volts 128

3.42-volts Unknown (175)

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What to Do with Digital Signals?

液晶面板廠，玻璃基板在輸送過程因震動導致的危機 基板破裂、液晶位移傾斜、發生面板亮點或暗點等不良或報廢品

若能防止震動過大，面板良率可由 85 ％提升至 90% 以上

32

輸送帶震動監測 方法：

將無線感測器佈建於玻璃基板上，以全程偵測玻璃基板於移動過程中所發生的震動及噪音

Gla

ss C

onve

yer

DB Server

Data Receive Server

AP Server

Glass

mote mote

mote mote

User

User

Glass

mote mote

mote mote

Glass

mote mote

mote mote

Glass Buffer

33

震動振幅範圍 : ± 2G 震動解析度 : ± 0.1G 防共振結構

震動振幅範圍 : ± 2G 震動解析度 : ± 0.05G 防共振結構

微震動無線感測平台Eco

震動無線感測平台 Eco

Eco Ethernet Base Station

無線感測平台

無線感測平台

34

The World SmallestWireless Sensing

Eco Node

Platform,

36

震動資料時域分析

如何知道有不正常的震動？如何知道有不正常的震動？

37

Summary

Digitization of analog signals by sampling Sampling rate and resolution Problems with sampling: aliasing,

quantization errors

Analog to digital conversion

Analysis of digital signals: FFT