Information Sources And Signals

Friday Group research assignment 1 Use class time to work on it

3 Review: Composite Signals Most signals are classified as composite The signal can be decomposed into a set of simple sine waves =+

4 Time and Frequency Domain Representations Time Domain RepresentationFrequency Domain Representation

Exercise Draw the frequency domain representation of the following signal: Sin(4  t) sin(8  t +  ) + 2 sin(10  t)

6 Signal Bandwidth A Measure of Signal Frequency Range The difference between the highest and the lowest frequencies contained in a signal. 5kHz – 1kHz = 4kHz

Why Should We Care about Bandwidth? We need to know the bandwidth of a signal to make sure the communication channel is wide enough to transmit it. 7

8 Exercise 1 What is the bandwidth of this signal?

Exercise 2 If a signal is decomposed into three sine waves with frequencies of 300, 700, and 1200 Hz, what is its bandwidth? 9

Exercise 3 What is the bandwidth of this signal? Sin(4  t) sin(8  t +  ) + 2 sin(10  )

Sending Digital Signals

12 Sending Digital Signals Use electrical voltage to represent digital values – A positive voltage  a logical one (1) – Zero or a negative voltage  a logical zero (0) +5 volts is usually what we use in computer hardware. – +5 or 0 -> 1 or 0 – Two levels: 1 bit

13 Digital Signal Levels Some physical mechanisms can support more than two signal levels. – For example, consider a system that uses four levels of voltage: – -5 volts, -2 volts, +2 volts, and +5 volts

Digital Signal Levels More signal levels a system has, more bits need to be sent out per unit time.

Bits and Signal Levels Often we use bits to describe signal levels How many bits can we represent using 4 levels? – -5, -2, 2, 5 15

Bits and Signal Levels Often we use bits to describe signal levels How many bits can we represent using 8 levels? 16

Bits and Signal Levels Often we use bits to describe signal levels How many levels do we need to represent n bits? 17

18 More Bits, Better? More bits a system can deliver at a given time period, more information it can transfer. Can we increase the signal levels as many as possible? – No, electronic systems cannot distinguish between signal levels (voltage levels) that differ by small amounts.

19 Speed/Capacity of Data Transmission We use bit rate (bits per second) to measure the speed/capacity of transmission. Two factors to consider: 1.The number of signal levels 2.How long does a system have to stay at a given level? Should be long enough to guarantee the signal to be received. We use Baud to measure how many times the signal can change per second

20 Bit Rate If a system with two signal levels operates at 1000 baud, how many bits the system can transfer per second?

21 Bit Rate How about a system that operates at 2000 baud and has four signal levels

22 Baud Baud rate is confined by hardware. Some numbers (theoretical) – Dial-in (v.90): 56k – ISDN: 128k – DSL: 300k – 1,500k (1.5M) – Cable: 300k – 6,000k (6M) (could go higher) – T1: 1.5M – T3: 44M – 100Base-T: 100M

Now, what happens on the road?

What’s the bandwidth of digital signals? Frequency Domain RepresentationTime Domain Representation = Fourier Analysis:

25 Bad news The bandwidth of a digital signal is infinite! – Accurate representation of a digital signal requires an infinite set of sine waves. – Transmitting/reproducing digital signals is impractical

26 Bad news The bandwidth of a digital signal is infinite! – Accurate representation of a digital signal requires an infinite set of sine waves. – Transmitting/reproducing digital signals is impractical Engineers adopt a compromise: – generate composite sine waves that closely approximate the digital signal – the quality of approximation depends on the channel bandwidth

Bandwidth-Limited Signals Having less bandwidth degrades the signal 8 sine waves 4 sine waves 2 sine waves Lost! Bandwidth Lost!