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3-1 ©2005 Raj JainCSE473sWashington University in St. Louis

**Data
Transmission
**

Raj Jain Professor of CSE

Washington University in Saint Louis Saint Louis, MO 63130

These slides are available on-line at: http://www.cse.wustl.edu/~jain/cse473-05/

3-2 ©2005 Raj JainCSE473sWashington University in St. Louis

**Overview
**

Time Domain and Frequency Domain

Decibels

Data vs Signal

Attenuation, Delay Distortion, Noise, Capacity

3-3 ©2005 Raj JainCSE473sWashington University in St. Louis

**Transmission Terminology
** **Guided Media**: Wire, Fiber , coax

**Unguided Media**: Air, Vacuum, sea water

**Direct Link
**

**Point to Point **vs **Point to Multipoint
**

T R

T R T

R1 R2 R3

3-4 ©2005 Raj JainCSE473sWashington University in St. Louis

**Line Duplexity
**

Simplex: Transmit or receive, e.g., Television

Half-Duplex: Transmit and receive alternately, e.g., Police Radio

Full Duplex: Transmit and receive simultaneously, e.g., Telephone

T R

T/R T/R

3-5 ©2005 Raj JainCSE473sWashington University in St. Louis

**Analog vs Digital Signals
**

**Analog:
**

**Digital:**

3-6 ©2005 Raj JainCSE473sWashington University in St. Louis

**Periodic vs Aperiodic
**

Periodic: Signal pattern repeats over time

Aperiodic: Not periodic

T

*S(t+T) = s(t) *for all t
**Period **= T

3-7 ©2005 Raj JainCSE473sWashington University in St. Louis

**Examples of Periodic Signals
**

**Sine Wave**:

**Square Wave**:

3-8 ©2005 Raj JainCSE473sWashington University in St. Louis

**Frequency, Period, and Phase
** A Sin(2πft + θ), Period T=1/f, Frequency in **Hertz**

3-9 ©2005 Raj JainCSE473sWashington University in St. Louis

**Sine Wave
**

**Peak Amplitude **(A): Maximum strength of signal in
volts

**Frequency **(f): Hertz (Hz) or cycles per second
**Period **= time for one repetition (T)

T = 1/f
**Phase **(φ): Relative position in time

3-10 ©2005 Raj JainCSE473sWashington University in St. Louis

**Wavelength
**

Distance occupied by one cycle Distance between two points of corresponding phase in two

consecutive cycles
Wavelength = λ
Assuming signal velocity *v
*

λ *= vT
* λ*f = v
* c = 3*108 m/s (speed of light in free space) = 300 m/µs

Distance Amplitude

3-11 ©2005 Raj JainCSE473sWashington University in St. Louis

**Time and Frequency Domains
**

Frequency

Amplitude

Frequency

Amplitude

Frequency

Amplitude

*f
*

*3f
*

A

A

*f 3f
*

A/3

A/3

3-12 ©2005 Raj JainCSE473sWashington University in St. Louis

**Frequency Domain Concepts
** **Fundamental Frequency**: All other frequency

components are multiple of fundamental frequency f
**Period **= 1/f
**Spectrum**: Range of frequencies
**Absolute Bandwidth**: Width of the spectrum

*Absolute Bandwidth = 3f-f = 2f
* **Effective Bandwidth: **Narrow band of frequencies

containing most of the energy
**DC Component***: *Constant or zero frequency

*A+B sin (2*π*ft+*θ*)*

3-13 ©2005 Raj JainCSE473sWashington University in St. Louis

**Signal with DC Component**

3-14 ©2005 Raj JainCSE473sWashington University in St. Louis

**Frequency Components of Square Wave
**

Freq.

Amplitude

Amplitude

Frequency

*f
*

A

*3f 5f
*

A/3 A/5

Freq.*f 3f
*

A/3

*5f
*

A/5

*7f
*

A/7

Σκ=1,3,5,… A/k sin (2πkft)

3-15 ©2005 Raj JainCSE473sWashington University in St. Louis

**Data vs Signal
**

Telephone

Modem

CODEC

Digital Transceiver

Analog

Digital

**Data Signal
**Analog

Digital

Analog

Analog

Digital

Digital

Data Signal Medium

Data

3-16 ©2005 Raj JainCSE473sWashington University in St. Louis

**Analog Data Example: Speech and Music**

3-17 ©2005 Raj JainCSE473sWashington University in St. Louis

**Analog Data Example 2: Television
**

30 Screens/sec Interlacing: Odd lines every 1/60 s and even lines every 1/60 s 483 lines/screen

3-18 ©2005 Raj JainCSE473sWashington University in St. Louis

**Video Signal
** USA - 483 lines scanned per frame at 30 frames per second

525 lines but 42 lost during vertical retrace So 525 lines x 30 scans = 15750 lines per second

63.5µs per line 11µs for retrace, so 52.5 µs per video line

Max frequency if line alternates black and white Horizontal resolution is about 450 lines giving 225 cycles of

wave in 52.5 µs Max frequency of 4.2MHz

3-19 ©2005 Raj JainCSE473sWashington University in St. Louis

**Attenuation
and Dispersion (Delay Distortion)
**

Distance

3-20 ©2005 Raj JainCSE473sWashington University in St. Louis

**Digital Transmission
** Repeaters are used to regenerate digital signal
Signal attenuation is overcome
Noise is not amplified
Low cost LSI/VLSI technology
Longer distances over lower quality lines
Capacity utilization

High bandwidth links economical High degree of multiplexing easier with digital

techniques Security & Privacy: Encryption

3-21 ©2005 Raj JainCSE473sWashington University in St. Louis

**Decibels
**

Attenuation = Log10 Pin Pout

**Example 1**: Pin = 10 mW, Pout=5 mW
Attenuation = 10 log 10 (10/5) = 10 log 10 2 = 3 dB

**Example 2**: Pin = 100mW, Pout=1 mW
Attenuation = 10 log 10 (100/1) = 10 log 10 100 = 20 dB

Bel

Pin Pout

decibel Attenuation = 10 Log10

Vin Vout

decibel Attenuation = 20 Log10

3-22 ©2005 Raj JainCSE473sWashington University in St. Louis

**Noise
**

Additional signals inserted between transmitter and receiver

**Thermal Noise**:
Due to thermal agitation of electrons
Uniformly distributed
White noise

**Intermodulation Noise**:
Signals that are the sum and difference of original

frequencies sharing a medium

3-23 ©2005 Raj JainCSE473sWashington University in St. Louis

**Noise (Cont)
**

**Crosstalk Noise**: A signal from one line is picked up
by another

**Impulse Noise**:
Irregular pulses or spikes

e.g., External electromagnetic interference Short duration High amplitude

3-24 ©2005 Raj JainCSE473sWashington University in St. Louis

**Channel Capacity
**

Capacity = Maximum data rate for a channel
**Nyquist Theorem**: Bandwidth = B

Data rate < 2 B Bi-level Encoding: Data rate = 2 × Bandwidth

0

5V

Multilevel: Data rate = 2 × Bandwidth × log 2 M

**Example**: M=4, Capacity = 4 × Bandwidth

3-25 ©2005 Raj JainCSE473sWashington University in St. Louis

**Shannon's Theorem
**

Bandwidth = B Hz Signal-to-noise ratio = S/N

Maximum number of bits/sec = B log2 (1+S/N) Example: Phone wire bandwidth = 3100 Hz

S/N = 30 dB 10 Log 10 S/N = 30

Log 10 S/N = 3 S/N = 103 = 1000

Capacity = 3100 log 2 (1+1000) = 30,894 bps