Chap4 Student Version

7/30/2019 Chap4 Student Version

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ECM410

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Digital transmission is the transmission of digital signalsbetween two or more points in a communications system.

The original source information may be in digital form whichcould be binary or any other form of discrete-level digital pulses,or it could be analog signals that have been converted to digitalpulses prior to transmission and converted back to analogsignals in the receiver.

Digital transmission systems use both metallic and optical fibercables for their transmission medium. Digital pulses cannot bepropagated through a wireless transmission system such asEarths atmosphere or free space (vacuum).

Today, digital transmission systems are used to carry not onlydigitally encoded voice and video signals but also digital sourceinformation directly between computers and computer networks.

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1. Noise immunity

2. Inherently less susceptible to interference because it is not necessary to

evaluate the precise amplitude, frequency or phase to ascertain its logiccondition.

3. Better suited for processing and combining using a technique calledmultiplexing.

4. Digital signal processing (DSP) is the processing of analog signals usingdigital methods and includes bandlimiting the signal with filters, amplitudeequalization and phase shifting.

5. Much simpler to store and the transmission rate can be easily changed toadapt different environments and to interface with different types ofequipment.

6. More resistant to additive noise

7. They use signal regeneration rather than signal amplification.

8. Can be transported longer distances than analog signals.9. Simpler to measure and evaluate

10. Easier to compare the error performance of one digital system to anotherdigital system

11. Transmission errors can be detected and corrected more easily andmore accurate.

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1. The transmission of digitally encoded analog signals requires

significantly more bandwidth than simply transmitting theoriginal analog signal.

2. Bandwidth is one of the most important aspects of anycommunications system because it is costly and limited.

3. Analog signals must be converted to digital pulsestransmission and converted back.

4. Requires precise time synchronization between the clocks in

the transmission and receivers

5. Incompatible with older analog transmission systems

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1. Low-speed voice band data communications modems, suchas those found in most personal computers.

2. High-speed data transmission systems, such as broadbanddigital subscriber lines (DSL).

3. Digital microwave and satellite communication systems.

4. Cellular telephone Personal Communication Systems (PCS).

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Information capacity refer to Hartleys Law (Already covered in Chapter 1).

Binary digit or bits: the most basic digital symbol used to represent information.

Bit rate is simply the number of bits transmitted during one second and is

expressed in bits per second (bps).

Bit rate refers to the rate of the change of a digital information signal, which is

usually binary.

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M-ary is a term derived from the word binary.

M represents a digit that corresponds to the number of conditions, levels

and combinations possible for a given number of binary variables.

The number of bits necessary to produce a given number of conditions isexpressed mathematically as:

N = log2 M

where N = number of bits necessary

M = number of conditions, levels, or combinations possible with N bits.

Simplified: 2N = M

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Nyquist bandwidth defines as the minimum theoretical bandwidthnecessary to propagate a signal . Nyquist bandwidth also sometimes known

as minimum Nyquist frequency.

Binary digital signals can be propagated through an ideal noiseless

transmission medium at a rate equal to two times the bandwidth of the

medium.

fb = 2 B where fb = bit rate in bps,

B = ideal Nyquist bandwidth.

The actual bandwidth necessary to propagate a given bit rate depends on

several factors which is type of encoding, system noise, types of modulation

used, desired error performance and the types of filter used.

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There are several digital modulation techniques used to modulate

digital signal or data, depending on the applications, the rate oftransmission required, allocated bandwidth and cost.

By referring to the equation above, if the information signal is digitaland the amplitude (V) of the carrier is varied proportional to theinformation signal ASK is produced.

If the information signal is digital and the frequency (f) of the carrier isvaried proportional to the information signal FSK is produced.

If the information signal is digital and the phase () of the carrier isvaried proportional to the information signal PSK is produced.

If the information signal is digital and both the amplitude (V) and thephase () of the carrier is varied proportional to the information signalQAM is produced.

ASK, FSK, PSK and QAM are all forms ofdigital modulation.

)2sin()( tfVt

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The simplest digital modulation technique is amplitude shift keying

(ASK), where a binary information signal directly modulates theamplitude of an analog carrier.

In ASK, a carrier wave is switched ON and OFF by the input data orbinary signals. During a mark (binary 1), a carrier wave is

transmitted and during a space (Binary 0), the carrier issuppressed. Hence, it also known as ON- OFF keying (OOK).

Mathematically, amplitude- shift keying is

Where:

(ask)(t) = amplitude- shift keying wave

m(t) = digital information (modulating) signals (volts)

A/2 = unmodulated carrier amplitude (volts)

c = analog carrier radian frequency

)cos(

2)(1)(

)(

tA

tvtvcmask

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ASK waveform:

Applications of ASK:

It is used in multichannel telegraph system. Simple ASK is no longerused in digital communication system due to noise problems.

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Frequency shift keying (FSK) is another relatively simple, low-

performance type of digital modulation.

FSK is a form of constant-amplitude angle modulation similar to

standard frequency modulation (FM) except the modulating signal is a

binary signal that varies between two discrete voltage levels rather than

a continuously changing analog waveform.

The general expression for FSK is:

fsk(t) = ccos { 2 [ fc + m(t)f ] }

Where fsk(t) = binary FSK waveform

vc = peak analog carrier amplitude (volts)

fc = analog carrier center frequency (volts)

f = peak change (shift) in the analog carrier frequency (hertz)

m(t) = binary input (modulating) signal (volts)

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From the general equation of FSK, it can be seen that the peak shift in thecarrier frequency (f ) is proportional to the amplitude of binary input signal

Vm(t), and the direction of the shift is determined by the polarity.

The modulating signal is a normalized binary waveform where a

logic 1= +1V and logic 0 = -1V.

Hence, for logic 1 ormark input :

fsk(t) = Vccos [ 2 ( fc + f )]

For logic 0 orspace input :

fsk(t) = Vccos [ 2 ( fc - f )]

The mark frequency is the higher frequency ( fc + f) and the spacefrequency is the lower frequency ( fc - f ).

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FSK waveform:

data

carrier

Modulated

signal

Applications of FSK:

FSK signaling schemes are used mainly for low-speed digital data

transmissions.

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The simplest form of PSK is binary phase-shift keying (BPSK), where N=1 and

M=2. Binary system encodes single bits and produces two output conditions

possible. One output represents a logic 1, and the other output represents a logic 0.

As the input digital signal changes state (ie, from a 1 to a 0 or from 0 to 1), the

phase will switch normally 0 to 180.

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2N = M

If N=2, M=4 (4 possible combinations, known as Quarternary PSK (QPSK) orQuadrature PSK). Bits are combined into groups of two bits called dibits.

If N=3, M=8 (8 possible combinations, known as 8-PSK).

Bits are combined into groups of three bits called tribits.

If N=4, M=16 (16 possible combinations, known as 16-PSK).Bits are combined into groups of four bits called quadbits.


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Pulse modulation is a process of sampling analog information signalsand then converting those samples into discrete pulses and

transporting the pulses from a source to a destination over a physical

transmission medium.

Pulse modulation is divided broadly into two categories which is

Analog Pulse Modulation (APM) and Digital Pulse Modulation(DPM).

Analog information such as continuous speech or digital data can be

transmitted using pulse modulation technique. However, for a

continuous waveform, it is first converted into pulses by the process ofsampling.

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Sampling is the process of taking a periodic sample of the continuouswaveform to be transmitted. If sufficient samples are sent, the waveformcan be reconstructed at the receiver.

The Nyquist sampling theorem is used to determine minimum samplingrate for any signal so that the signal will be correctly restored at thereceiver.

Nyquist sampling theorem states that;

The original information signal can be reconstructed at the receiver withminimal distortion if the sampling rate in the pulse modulation system is equalto or greater than twice the maximum information signal frequency.

That is, sampling frequency , fs 2 fm(max)

where fs = sampling frequency

fm(max) = maximum frequency of the modulating signal

The minimum sampling frequency , fs = 2 fm(max)

Figure shows the frequency spectrum of a

modulating waveform such as a voice signal.

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The 3 basic conditions of sampling process are:

1. Sampling at fs = 2 fm(max)

- When the modulating signal is sampled at a minimum sampling frequency, the frequency spectrum is

shown as figure below.

2. Sampling at fs > 2 fm(max)

- This sampling rate creates a guard band between fm(max) and the lowest frequency component

(fs - fm(max) ) of the sampling harmonics.

3. Sampling at fs < 2 fm(max)

- When the sampling rate is less than the minimum value, distortion will occurs. This distortion is called

aliasing or folded over distortion.

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In APM, the carrier is in the form of pulse modulation and the

modulated signal is where one of the characteristics (eitheramplitude, width or position) is changed according to the modulatingsignal.

The predominant methods of APM are Pulse width modulation(PWM), Pulse position modulation (PPM) and Pulse amplitudemodulation (PAM).

1. Pulse amplitude modulation (PAM)-PAM is the simplest form of pulse modulation. It is very similar toamplitude modulation (AM).

- With PAM, the amplitude of a constant-width and constant positionpulse is varied according to the amplitude of the sample of the analog

signal.- PAM is not generally used for a complete system but is largelyemployed as an intermediate form of modulation with PSK, QAM and

PCM.

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2. Pulse width modulation (PWM)

-PWM also is called as pulse duration modulation (PDM) or pulseslength modulation (PLM). PWM refer to the technique of varying thewidth of the constant-amplitude pulse proportional to the amplitudeof the modulating signal.

- PWM gives a better signal to noise performance than PAM. PWMhas a disadvantage, when compared to PPM, that is its pulses are ofvarying width and therefore of varying power content.

3. Pulse position modulation (PPM)

-PPM is when the position of a constant-width and constant-amplitude pulse within prescribed time slot is varied according to theamplitude of the modulating signal.

-With PPM, the higher the amplitude of the sample, the farther to theright the pulse is positioned within a prescribed time slot.

- PWM and PPM are seldom used for commercial system. There are

used in special-purpose communication systems such as military

communication systems.

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Digital modulation is the process by which digital symbols aretransformed into waveforms that are compatible with the characteristicsof the channel. In digital modulation code (DPM), a code is used torepresent the amplitude of the samples that has been divided intovarious levels.

Advantages of digital system:

1. It is relatively immune to channel noise and interference.

2. Signals and messages can be coded for error detection and correction.3. It is easier and more efficient to multiplex several digital signals.

4. It can carry a combination of traffics (telephone signals, data, codedvideo) if the medium has enough capacity.

5. More economical.

Disadvantages of digital system:1. The disadvantages of digital system compared to analog system is the

large bandwidth requirement. However, it is no longer a serious problembecause of the advent of large-bandwidth fiber optic systems.

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Pulse code modulation (PCM)

-PCM is a digitally encoded modulation technique that commonly use fordigital transmission.

-With PCM, a group of coded pulses are used to represent the analogsignal. The analog signal is sampled and converted to a fixed-lengthserial binary number for transmission.

- PCM is the preferred method of communications because with PCM, itis easy to combine digitized voice and digital data into a single, highspeed digital signal and propagate it over either metallic or optical fibercables

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PCM transmission system

(i) BPF limit the freq of analog input signal to standard voice band freq (300 to 3400Hz)

(ii) Sample and hold samples the input and converts those samples to a multilevel PAM signal

(iii) ADC converts the PAM samples to parallel PCM codes which are converted to serial binary data

in the parallel to serial converter ( serial digital pulses eg 10110001010)(iv) In the Rx, the serial to parallel converter converts serial pulses received from transmission line to

parallel PCM codes. The DAC converts the parallel PCM codes to multilevel PAM signals.

(v) The hold circuit is basically a low pas filter that converts the PAM signals back to its original

analog form. -A clock ( an oscillator circuit that outputs timing Pulses) is set to the

sampling frequency

-The sample command must be accurately clocked- cant have varying

sample times. Must be controlled by a clock designed with a highly

accurate crystal oscillator.


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1 Sample-and-hold circuit;

It periodically samples the analog signal and converts those samplesto a multilevel PAM signal.

2 Analog-to-digital converter (ADC);

Convert the PAM samples parallel PCM codes which are convertedto serial binary data in the parallel-to-serial converter. After that, theoutputted onto the transmission line as serial digital pulse.

3 Repeaters; are placed at prescribed distance to regenerate the digital pulse. In

receiver a serial-to-parallel converter converts the serial pulses toparallel PCM code.

4 Digital-to-analog converter (DAC);

To converts the parallel PCM codes to multilevel PAM signals

5 The hold circuit is basically a low-pass filter that converts the PAMsignals back to the original analog form.

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Three main processes in PCM transmission are sampling, quantization

and coding.

1. Sampling

- It is a process of taking samples of information signal at a rate of

Nyquists sampling frequency.

2. Quantization

- Quantization is a process of assigning the analog signal samples to

a pre-determined discrete levels.

3. Encoding

- This is the process where each quantized sample is digitally encodedinto n-bits codeword, where;

n = log2 L where n = number of bits/sample

L = number of quantization levels

or L = 2n

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010

101

111

101

011

001

0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1

Analog input signal

Sampling pulse

Sampled waveform

Quantized signal

PCM pulses

Figure below illustrates an analog waveform signal can be coded into 3 bits

code using single mode for transmission using PCM technique.

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Sampling process- Multilevel PAM signal

Quantizing and encoding process

- Convert the PAM to parallel codes

Parallel codes is converted to serial data

in parallel to serial converter


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Function of sampling circuit in PCM transmitter is to periodically

sample the continually changing analog input voltage and convertthose samples to a series of constant-amplitude pulse that can

more easily be converted to binary PCM code.

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Quantization is a process of assigning the analog samples to a pre-

determined discrete levels.

It also a process of rounding off the amplitude of flat-top samples to amanageable number of level.

The number of quantization level, L, depends on the number of bits persample, n, used to code the signal where;

L = 2n

The magnitude of the minimum stepsize of the quantization levels iscalled resolution, V. It is equal in magnitude to the voltage of the leastsignificant bit or the magnitude of the minimum stepsize of the digital toanalog converter (DAC).

The resolution, V depends on the maximum and minimum voltage ofthe information signal, where;

V =

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Quantization errororquantization noise is the distortion introducedduring the quantization process when the modulating signal is not an

exact value of the quantized level.

Maximum quantization errorQe(max) = +

Quantization error can be reduced by increasing the number ofquantization levels, but this will increase the bandwidth required.

Quantization interval or quantum is the magnitude difference betweenadjacent step.The smaller the magnitude of a quantum, the better(smaller) the resolution and the more accurately the quantized signalwill resemble the original analog sample.

- the magnitude of a quantum is also called resolution.

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Transmission bit rate, R

- is the rate of information transmission (bit/s). It is depends on the

sampling frequency and the number of bit per sample used to encode

the signal.

Transmission bandwidth (TB) is equal to the transmission bit rate, but

the unit is hertz.

sec/bitsfnR s

HzfnTB s

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PCM Line Speed

Line speed is a data rate at which serial PCM bits are clockedout of the PCM encoder into a transmission line.

Where,

Line speed = the transmission rate in bits per second

Samples/second = sample rate (fs)

Bit/sample = number of bits in the compressed PCM code.

Example 3 For a single channel PCM system with a sample rate fs= 6000

samples per second and a seven bit compressed of PCM code,determine the line speed.

Solution

sample

bits

ond

samplesspeedline

sec

bps

sample

bits

ond

samplesspeedline

00042

7

sec

6000

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A PCM transmitter system is transmitting a 6kHz audio signal. Thesampling frequency used is 10% higher than the minimum sampling

rate for the guard-band purpose and the quantization level used is256.Determine:

i) the number of bits for every sample,ii) the sampling frequency rate and

iii) the transmission bit rate (bps).

If the maximum quantization error is 0.01V , what is the resolutionstep of the quantization level . Hence determine the peak-to-peakamplitude of the information signal.


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Example 2

An information signal in a form Vm(t) = 20 cos(60 x 103t)V to be transmitted through

a binary PCM modulation. The signal is sampled at a rate of 15% higher than the

minimum sampling frequency and the quantization level used is 512. Calculate :

i) The sampling frequency that can be used,

ii) The number of bit per sample,

iii) The transmission bandwidth,

iv) The resolution step and,

v) The quantization error.

If the maximum quantization error is 0.02V, determine the resolution step of the

quantization level and peak to peak amplitude of the information signal.


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Test 2 Oct 2010

Figure Q1e shows the analog waveform to be transmitted using 3 bit PCM

system. Using the ANSWER SHEET Q1e in appendix, shows how the analog

signal can be converted to:

i) Pulse Amplitude Modulation (PAM) signal,

ii) Quantized signal,

iii) A serial binary number (PCM code)

iv) PCM pulses.(8 marks)

t

3

2

1

-1

0

-2

V(t)

V(t)

t

Analog

signal

Sampling

Pulse

Figure Q1e

V(t)


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Serial PCM

Code

t

3

2

1

-1

0

-2

V(t)

t

3

2

1

-1

0

-2

V(t)

t

3

2

1

-1

0

-2

V(t)

t

Analogsignal

SamplingPulse

PAM

Quantizedsignal

PCM Pulses t


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