Basis for Data Communication

BYSABARATHINAM

What is Data Communications?

Communication is the process of sharing a message.

A conversation between two people is an example of communication.

Data communications refers to the sharing of a virtual message.

Signals : Analog or digital

• Analog signal has infinitely many levels of intensity (infinitely many values, continuous values) over a period of time.

• Digital signal has only a limited number of defined values(discrete values) say, 0,1.

Sine wave

Period and frequency

Time and frequency domains

Square wave

Signal corruption

Three harmonics

The Theoretical Basis for Data Communication

Information can be transmitted on wires by varying some physical property such as voltage or current.

The theoretical basis for data communication• Fourier Analysis• Bandwidth-Limited Signals• The Maximum Data Rate of a Channel

Fourier Analysis

Any reasonably behaved periodic function, g(t), with period T can be constructed by summing a (possibly infinite) number of sines and cosines:

where f=1/T is the fundamental frequency and an and bn are the sine and cosine amplitudes of the nth harmonics (terms).

1 1

1( ) sin(2 ) cos(2 )

2 n nn n

g t c a nft b nft

Fourier Analysis (cont..)We can compute :n na and b

0

0

0

2( )sin(2 )

2( )cos(2 )

2( )

T

n

T

n

T

a g t nft dtT

b g t nft dtT

c g t dtT

Fourier Analysis (cont..)

• For instance, suppose we use voltages (on/off) to represent “1”s and ”0”s, and we transmit the bit string ‘01100010’. The signal would look as follows:

0

2( )sin(2 )

T

na g t nft dtT

3 7

1 6

2[ sin(2 ) sin(2 ) ]na nft dt nft dt

T

Fourier Analysis (cont..)

Fourier Analysis (cont..)

Bandwidth-Limited SignalsThe larger n is, the higher the frequency nf of

the nth harmonic.All transmission facilities diminish different

Fourier components by different amounts, thus introducing distortion.

Usually, the amplitudes are transmitted undiminished from 0 up to some frequency fc (in Hertz, Hz) with all frequencies above this cutoff frequency strongly attenuated.

Bandwidth

Baud Rate and Bit RateThe signaling speed

the number of times per second that the signal changes its value (e.g. its voltage).

measured in baud.

A b baud line does not necessarily transmit b bits/sec each signal might convey several bits

Maximum Data Rate of a Channel

• Data rate depends on 3 factors:

– The bandwidth available– Number of levels of signals– Quality of the channel (noise level)

Noiseless Channel: Nyquist Bit rate

• b = 2 B log L (log is to base 2)

b : bit rate B : Bandwidth L : number of levels

Noisy channel : Shannon Capacity

• C = B log (1 + SNR)

C = capacity of the channel in bps B = Bandwidth

SNR = signal to noise ratio

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