Pulse Code Modulation

Lecture 5

Why a Particular Encoding Technique

Digital data, digital signal Equipment less complex and expensive than

digital-to-analog modulation equipment Analog data, digital signal

Permits use of modern digital transmission and switching equipment

Why a Particular Encoding Technique

Digital data, analog signal Some transmission media will only propagate

analog signals E.g., optical fiber and unguided media

Analog data, analog signal Analog data in electrical form can be

transmitted easily and cheaply Done with voice transmission over voice-grade

lines

Criteria For Signal Encoding What determines how successful a receiver will be

in interpreting an incoming signal? Signal-to-noise ratio Data rate Bandwidth

An increase in data rate increases bit error rate An increase in SNR decreases bit error rate An increase in bandwidth allows an increase in

data rate

Factors Used to CompareEncoding Schemes Signal spectrum

With lack of high-frequency components, less bandwidth required

With no dc component, ac coupling via transformer possible Transfer function of a channel is worse near band edges

Clocking Ease of determining beginning and end of each bit

positionSignal interference and noise immunity Performance in the presence of noise

Cost and complexity The higher the signal rate to achieve a given data rate, the

greater the cost

Reasons for Analog Modulation Modulation of digital signals

When only analog transmission facilities are available, digital to analog conversion required

Modulation of analog signals A higher frequency may be needed for effective

transmission Modulation permits frequency division

multiplexing

Basic Encoding Techniques Analog data to analog signal

Amplitude modulation (AM) Angle modulation

Frequency modulation (FM) Phase modulation (PM)

Spectrum of AM signal

Amplitude Modulation Transmitted power

Pt = total transmitted power in s(t)

Pc = transmitted power in carrier

21

2a

ct

nPP

Single Sideband (SSB) Variant of AM is single sideband (SSB)

Sends only one sideband Eliminates other sideband and carrier

Advantages Only half the bandwidth is required Less power is required

Disadvantages Suppressed carrier can’t be used for synchronization

purposes

Pulse Modulation

Analogue modulated systems are quite widely used, because of their simplicity.

An alternative to analogue modulated systems is Pulsed systems.

This system is based on digital signals or pulses.The basis of such a system is the use of a digital carrier signal, which is modulated by an analogue signal.

There are various ways in which this can be achieved, giving rise different systems.

An analogue signal is transmitted continuously in its entire form.

This need not be done provided certain conditions are satisfied.

Samples of the analogue signal may be transmitted at given intervals of time.

The original signal may then be recovered at the receiving end from the transmitted samples.

This technique is known as sampling and it underlies pulsed systems.

Sampling of signals

Consider a train of signals, with a repetition frequency f and period T where

Tf

1

If the pulse train were amplitude modulated by the analogue signal, the result will be pulses whose amplitudes are samples of the analogue signal at time intervals T.

If the amplitude modulated pulse train is then analysed, its spectrum will consist of Fourier components,

...3 ,2 , ,0 fffAt each of this there will be a set of sum and difference frequencies (lower and upper sidebands) due to each frequency component of the analogue signal.

If W and f-W do not overlap then it is possible to separate the group of frequencies at the receiving end.

This can be achieved by use of a low-pass filter with a cut-off frequency f = W.

The separated frequencies are then those of the analogue signal transmitted.

From this the following condition is derived

WWf Wf 2

This means the repetition frequency must be at least twice the highest frequency component in the analogue signal.

The minimum sampling frequency is then

Wf 2min This is also called the Nyquist rate.

If the sampling rate is less than 2W the lower sideband will overlap the baseband and it will not be possible to separate them.

This effect is known as aliasing. It can be avoided by passing the signal through a filter before sampling.

Telephone siganls range from 300 Hz to 3.4 kHz, the internationally agreed sampling frequency is 8kHz. It means there is a guard band of 1.2kHz between the lower side band and the baseband.

Comment:

It means W has an upper limit

The technique can only be used if the bandwidth can be restricted to W without destroying the essential information. To achieve this, band-limited signals are used.

Sampling Theorem

Any function of time tF whose highestfrequency is W Hz can be completelydetermined by sampled amplitudes spaced at

time intervals W2

1 apart.

If a signal f(t) is sampled at regular intervals of time and at a rate higher than twice the highest frequency, then the samples contain all of the information of the original signal. The function f(t) may be reconstructed from these samples by the use of a low pass filter.

An analogue sampler commonly known as the sample-and-hold is used in sampling the input analogue signal voltage and maintaining that voltage until the next sampling instant.

Sampler

The FET (Field Effect Transistor) acts like a simple switch.

When turned "on," it provides a low‑impedance path to deposit the analogue sample voltage on capacitor.

The time that the FET is "on" is called the aperture or acquisition time.

Essentially, the capacitor is the hold circuit. When the switch FET is "Off," the capacitor does not have a complete path to discharge through and therefore stores the sampled voltage.

The storage time of the capacitor is also called the conversion time because it is during this time that the unit converts the sample voltage to a digital code.

The acquisition time should he very short. This assures that a minimum change occurs in the analogue signal while it is being deposited across the capacitor.

If the input to the sampler is changing while it is performing the conversion, distortion results. This distortion is called aperture distortion.

Thus, by having a short aperture time and keeping the input to the constant relatively constant, the sample‑and‑hold circuit reduces aperture distortion.

If the analogue signal is sampled for a short period of time and the sample voltage is held at constant amplitude during the conversion time, this is called flat‑top sampling.

If the sample time is made longer and the analogue‑to‑digital conversion takes place with a changing analogue signal, this is called natural sampling.

Natural sampling introduces more aperture distortion than flattop sampling and requires a faster A/D converter.

Pulse Code Modulation

PCM is the most commonly used technique in digital communicationsUsed in many applications:

Telephone systemsDigital audio recordingCD laser disksvoice maildigital video etc.

They are a primary building block for advanced communication systems

Pulse Code Modulation Based on the sampling theorem Each analog sample is assigned a binary

code Analog samples are referred to as pulse

amplitude modulation (PAM) samples The digital signal consists of block of n bits,

where each n-bit number is the amplitude of a PCM pulse

Quantization Is the process of converting the

sampled signal to a binary value Each voltage level will correspond to a

different binary number The magnitude of the minimum step

size is called the resolution. The error resulting from quantizing is

called the quantization noise. Its value is 1/2 the resolution

Pulse Code Modulation

Dynamic Range

This is the ratio of the largest to smallest analogue signal that can be transmitted.

min

maxDRV

V

But Vmin is the resolution and can be written as

n

VVq

2max

min

It follows thatn

V

V2DR

min

max

If this is expressed in decibels

nnV

V n 02.62log202log20log20DR(dB)min

max

n6DR(dB)

From n2DR It can be observed that the DR is the

Maximum binary number for a system. With one code used for 0V which is not considered in calculating DR, it is observed that

12DR n

Example

Given a PCM system with the following parameters:Maximum analog input frequency 3kHzA maximum decoded voltage at the receiver of +/- 1.27VA minimum dynamic range of 35dB.

Find the minimum sample rateThe number of bits requiredThe resolutionThe quantization error

Quantization Noise

2)(

2

qerror

q

2

2

21q

q

dq

2

2

3

3

1q

qq

12

2qRoot mean square

error

The effective voltage

32

q

The noise power is

R

q

12

2

Reasons for Growth of Digital Techniques

Growth in popularity of digital techniques for sending analog data Repeaters are used instead of amplifiers

No additive noise, can be used over long distances TDM is used instead of FDM

No intermodulation noise For a given bandwidth the signal/noise ratio is

superior Conversion to digital signaling allows use of

more efficient digital switching techniques Fits in well with other digital systems

Problems

Large bandwidth required. Might consider using optical fibres

Circuits for implementation are costly

uneconomical over short distances less than 5km.

Might consider using integrated circuits to deal with last two.