1

Chapter 3: Analog and Digital Signals

Analog vs. Digital Signals

2

Digital Encoding

Encoding 0’s

3

Manchester Encoding

Differential Manchester Encoding

4

Analog Signal Variations

From Sound to Analog Signal

5

Fourier Approximations

Fourier Series

where

are Fourier Coefficients:

6

11

Harmonics

Amplitudes of i-th harmonics are ai and biThe frequency of i-th harmonics are i/PThe frequencies of ahrmonics are multiples of the fundamental frequency f=1/P

Example 1

7

00 ≥= iforai KK

dtitdtittsdtittsbi )sin(2)sin()(2)22sin()(1

00∫∫∫ ===

−

πππ

π ππππ

π

ii

iii

iitbi π

ππππ

π )1)cos((2])0cos()cos([2])cos([2 0+−

=−

−−

=−

=

uneveniifieveniifiKKK

KKK

1)cos(1)cos(−=

=ππ

ib

b

i

i

π40

=

=

122

+==kiki

K

K K2,1,0=k

Consequently:

))12sin(()12(

4)(0

tkk

tsk

++

=∑∞

= πOR

8

π

π

π

212

122

)12(4

+

+

+

k

k

k

Analysis of Harmonics

Amplitude of 2k+1-th term

Period of 2k+1-th term

Frequency of 2k+1-th term

k=0 ??

Example-Cont.

9

Effect of Limited Bandwidth on Signal Quality

Assume bit rate b bpsTime to send 8 bits: 8/b=pFrequency of first harmonic: b/8Assume max line frequency = 3000 HzNumber of harmonics sent =

b3000*8

bf8

or in general

If b=9600 bps then 2 harmonics would be sent!

Transmitting ASCII “b” using NRZ

Fourier coefficients of “b”:

10

Effect of Limited Bandwidth

Data Rate V.S. Harmonics

11

Data via Analog Signals

Bit Rate V.S. Baud Rate

12

Effect of Noise

Analog Signal Modulation withDigital Signal

13

Using Modems

Digital Voice Transmission

14

Modulation Techniques

Frequency Shift Key

15

Amplitude Shift Key

Phase Shift Key

16

Quadrature Amplitude Modulation 1

17

Quadrature Amplitude Modulation 2

Quadrature Amplitude Modulation 3

18

Signal Constellation Idea

Signal Constellations

19

20

Effect of Noise 1

Effect of Noise 2

21

Modem Connections

22

Home Connections

Cable Modem Idea

23

Cable Connections

Digital Subscriber Line (DSL)

24

Assymetric DSL (ADSL)

Band Use in ADSL

25

Bandwidth Splitting in ADSL

ADSL Connections

26

ADSL-Lite

Hybrid Local Loop

27

Analog to Digital ConversionDigitizing analog signal , e.g. sensor readingsEquivalent to using coding tables to encode characters

Pulse Amplitude Modulation

28

Pulse Code Modulation