Post on 06-May-2015
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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