Digital Signal as a Composite Analog Signal

It should be clear that:• A digital signal, with all its sudden changes, is actually a composite

signal having an infinite number of

frequencies. • In other words, the bandwidth of a digital signal is infinite.

Digital Transmission A digital signal theoretically

needs a bandwidth between 0 and infinity. The lower limit (0) is fixed; the upper limit (infinity) can be decreased if we accept a limited number of harmonics. This means a bandwidth between 0 and f for a low-pass signal.

TRANSMISSION IMPAIRMENT• Signals travel through transmission

media, which are not perfect. • The imperfections cause impairment in

the signal. • So the signals at the beginning and end

of the medium are not the same. What is sent is not what is received.

• Three types of impairment may occur: attenuation, distortion, and noise (see Fig.)

Attenuation Attenuation means loss of energy.

•When a signal, travels through a medium, it loses some of its energy to overcome the resistance of the medium.

•That is why a wire carrying electrical signals gets warm, after a while.

•Some of the electrical energy in the signal is converted to heat.

•Amplifiers compensate this loss

•Next Fig shows the effect of attenuation and amplification.

Distortion• The signal changes its form or shape. • Distortion occurs in a composite

signal. • Each signal component has its own

propagation speed through a medium and, therefore, its own delay in arriving at the destination.

• Figure shows the effect of distortion on a composite signal.

Noise may corrupt the signal• Types: • Thermal noise: Random motion of

electrons in a wire which creates an extra signal not originally sent by the transmitter.

• Induced noise comes from sources such as motors and appliances. These devices act as a sending antenna and the transmission medium acts as the receiving antenna.

Crosstalk • The effect of one wire on the other. • One wire acts as a sending antenna

and the other as the receiving antenna.

• Impulse noise is a spike (a signal with high energy in a very short period of time) that comes from power lines, lightning, and so on.

• Fig shows the effect of noise on a signal.

ANALOG/ DIGITAL TRANSMISSION Transmission of information may be

in• 1- Analog form• 2- Digital form• Analog signal is highly affected by noise • so digital is better• Need to convert analog into Digital

STEPS REQUIRED:• A- SAMPLING (i) Measuring amplitude of analog signal at equal intervals of time and (ii) Holding the taken sample for some time• B- Produce a PULSE corresponding to each sample• C- QUANTIZATION Assign a +Ve/ -Ve value to each sampled amplitude

• D- BINARY ENCODING Convert each value into 8 bit binary data 7 bits for magnitude, 8th bit for sign• E- LINE CODING Convert binary data into a digital signal suitable for transmission• NOTE 1: STEPS A to B give rise to a process called PULSE AMPLITUDE MODULATION or PAM• NOTE 2: STEPS A to E give rise to a process called PULSE CODE MODULATION or PCM

NYQUIST THEOREMHow many samples for digital reproduction

of an analog signal ?According to Nyquist theorem, for accurate reproduction of analog signal using PAM, sampling rate must be twice the highestfrequency contained in original signalE.g. Telephone voice has max frequency of 4KHz. We need sampling rate of 8KHz.

HOW MANY BITS TO ENCODE A SAMPLE ?More bits more precise value of sampled amplitude. For voice, 8bits are used for

each sampleFor telephone voice, Bit rate = Sampling rate X No. of bits/

sample = 8000 x 8 = 64Kbps

PCM - Pulse Code PCM - Pulse Code ModulationModulation

local loop

phone switch(DIGITAL)

Central Office(Telco)

Analog transmission

To other switches

trunk

Digital transmission

convert analog signals to digital data using PCM (similar to PAM)• 8000 samples per second and 8 bits

per sample (7 bits for sample+ 1 bit for control)

64 Kb/s (DS-0 rate)

• DS-0: • Basic digital

communications unit used by phone network• Corresponds to 1

digital voice signal