Signal Encoding Techniques

Chapter 6

Analog Signaling

Digital Signaling

Introduction For digital signaling, a data source g(t), which

may be either digital or analog, is encoded into a digital signal x(t). The actual form of x(t) depends on the encoding

technique and is chosen to optimize use of the transmission medium.

For example, the encoding may be chosen to conserve bandwidth or to minimize errors.

Introduction What is the difference between both techniques?

Introduction The basis for analog signaling is a continuous constant-

frequency signal known as the carrier signal. A carrier signal (frequency fc) performs the function of

transporting the digital data in an analog waveform. The frequency of the carrier signal is chosen to be

compatible with the transmission medium being used. This carrier wave is usually a much higher frequency than the

input signal. The purpose of the carrier is

either to transmit the information through space as an electromagnetic wave

or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing

Introduction Data may be transmitted using a carrier signal by

modulation. Modulation is the process of encoding source data onto a

carrier signal with frequency fc- All modulation techniques involve operation on one or more of

the three fundamental frequency domain parameters: amplitude, frequency, and phase.

Introduction

Introduction The input signal m(t) may be analog or digital and is called the

modulating signal or baseband signal (non modulated signal). The result of modulating the carrier signal is called the modulated

signal s(t). As Figure 6.1b indicates, s(t) is a bandlimited (bandpass) signal.

The location of the bandwidth on the spectrum is related to fc and is often centered on fc.

Signal Encoding Criteria A digital signal is a sequence of discrete, discontinuous

voltage pulses. Each pulse is a signal element. Binary data are transmitted by encoding data bits into signal element. In the simplest case, there is a one-to-one correspondence between bits

and signal elements. Example a binary 0 is represented by a higher voltage level and binary

1 by a lower voltage level.

Signal Encoding Criteria A digital bit stream can be encoded onto an

analog signal as a sequence of signal elements,

with each signal element being a pulse of constant frequency, phase, and amplitude.

Signal Encoding Criteria

The data signaling rate, or just data rate, of a signal is the rate, in bits per second, that data are transmitted.

The duration of a bit is the amount of time it takes for the transmitter to emit the bit; for a data rate R , what is the bit

duration ???? .

Signal Encoding Criteria The modulation rate, in contrast, is the rate at which the signal

level is changed. This will depend on the nature of the encoding, as explained

later. The modulation rate is expressed in baud, which means signal

elements per second.

Signal Encoding Criteria Bit rate, R, is the number of bits per second (bps). Baud rate is the number of signal elements per

second (bauds). In the analog transmission of digital data, the

signal or baud rate is less than or equal to the bit rate.

If L is the number of data bits per signal element. What is the baud rate?? S = Rx1/L bauds

Signal Encoding Criteria An analog signal carries 4 bits per signal element.

If 1000 signal elements are sent per second, find the bit rate.

Solution In this case, L = 4, S = 1000, and R is unknown. We can find the value of R from

S = R x 1/L bauds R = S x L

Signal Encoding Criteria An analog signal has a bit rate of 8000 bps and a

baud rate of 1000 baud. How many data elements are carried by each signal element? How many possible signal elements do we need?

Solution In this example, S = 1000, R = 8000, and L and M are unknown. We find first the value of L and then the value of M.

S = R x 1/L bauds 2L =M

Signal Encoding CriteriaTerm Units Definition

Data Element Bits A single binary one or zero

Data rate Bits per second(bps) The rate at which the data elements are transmitted

Signal element -Digital: a voltage pulse of constant amplitude

-Analog: a pulse of constant frequency, phase, and amplitude

Signaling rate or modulation rate

Signal elements per second (baud)

The rate at which signal elements are transmitted

Signal Encoding Criteria Interpreting digital signals at the receiver

First, the receiver must know the timing of each bit. That is, the receiver must know with some accuracy when a

bit begins and ends. Second, the receiver must determine whether the signal

level for each bit position (0) or (1). These tasks are performed by sampling each bit

position in the middle of the interval and comparing the value to a threshold.

Because of noise and other impairments, there will be errors, as shown in the upcoming figure.

Signal Encoding Criteria

What determines how successful a receiver will be in interpreting an incoming signal?

Signal Encoding Criteria 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

But Also encoding scheme

Basic Encoding Techniques Digital data to analog signal

The most familiar use of this transformation is for transmitting digital data through the public telephone network.

The telephone network was designed to receive, switch, and transmit analog signals in the voice-frequency range of about 300 to 3400 Hz.

It is not at present suitable for handling digital signals from the subscriber locations (although this is beginning to change).

Thus digital devices are attached to the network via a modem (modulator-demodulator), which converts digital data to analog signals, and vice versa.

Basic Encoding Techniques Digital data to analog signal: modulation

involves operation on one or more of the three characteristics of a carrier signal: amplitude, frequency and phase Amplitude-shift keying (ASK)

Amplitude difference of carrier frequency Frequency-shift keying (FSK)

Frequency difference near carrier frequency Phase-shift keying (PSK)

Phase of carrier signal shifted

Basic Encoding Techniques

Basic Encoding Techniques

Amplitude-Shift Keying One binary digit represented by presence of carrier, at

constant amplitude Zero binary digit represented by absence of carrier

where the carrier signal is A cos(2πfct)

ts tfA c2cos0

1binary 0binary

Reminder

)2

sin(cos

xx

Amplitude-Shift Keying

Amplitude-Shift Keying Inefficient modulation technique On voice-grade lines, used up to 1200 bps Used to transmit digital data over optical fiber

Binary Frequency-Shift Keying (BFSK)

Two binary digits represented by two different frequencies near the carrier frequency

where f1 and f2 are offset from carrier frequency fc by equal but opposite amounts

ts tfA 12cos tfA 22cos

1binary 0binary

dff

dff

c

c

2

1

Binary Frequency-Shift Keying (BFSK)

BFSK for full-duplex operation over a voice-grade line. Full duplex means that signals are transmitted in both directions at the

same time. To achieve full-duplex transmission, this bandwidth is split. In one

direction (transmit or receive), the frequencies used to represent 1 and 0 are centered on 1170 Hz, with a shift of 100 Hz on either side.

Similarly, for the other direction (receive or transmit) the modem uses frequencies shifted 100 Hz to each side of a center frequency of 2125 Hz.

Note that there is little overlap and thus little interference.

Binary Frequency-Shift Keying (BFSK) Less susceptible to error than ASK Used for high-frequency (3 to 30 MHz)

radio transmission Can be used at higher frequencies on

LANs that use coaxial cable

Multiple Frequency-Shift Keying (MFSK)

More than two frequencies are used More bandwidth efficient but more susceptible to error

f i = f c + (2i – 1 – M)f d

f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L

L = number of bits per signal element How many possible frequencies?

tfAts ii 2cos Mi 1

Multiple Frequency-Shift Keying (MFSK)

f i = f c + (2i – 1 – M)f d

f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L

L = number of bits per signal element

Knowing f c , f d and M=4, give L and different f i

tfAts ii 2cos Mi 1

Multiple Frequency-Shift Keying (MFSK)

f i = f c + (2i – 1 – M)f d f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L

L = number of bits per signal element

Find the separation between f i+1 and f I

What is the required signal bandwidth?? What is the duration of each bit, if R is the bit rate? What is the duration of each signal element?

tfAts ii 2cos Mi 1

Multiple Frequency-Shift Keying (MFSK)

Multiple Frequency-Shift Keying (MFSK)

To match data rate of input bit stream, each output signal element is held for:

Ts=LT seconds where T is the bit period (data rate

= 1/T) So, one signal element encodes L bits

Multiple Frequency-Shift Keying (MFSK)

Total bandwidth required 2Mfd

Minimum frequency separation required 2fd=1/Ts

Therefore, modulator requires a bandwidth of

Wd=2L/LT=M /Ts

Phase-Shift Keying (PSK) Two-level PSK (BPSK)

Uses two phases to represent binary digits

ts tfA c2cos tfA c2cos

1binary 0binary

tfA c2cos

tfA c2cos1binary 0binary

Phase-Shift Keying (PSK)

Phase-Shift Keying (PSK)

ts

2

32cos

tfA c

22cos

tfA c

1binary

0binary

Phase-Shift Keying (PSK) Four-level PSK (QPSK)

Each element represents more than one bit

ts

42cos

tfA c 11

4

32cos

tfA c

4

32cos

tfA c

42cos

tfA c

01

00

10

Quadrature Amplitude Modulation QAM is a combination of ASK and PSK

Two different signals sent simultaneously on the same carrier frequency

tftdtftdts cc 2sin2cos 21

Reasons for Analog Modulation Modulation of digital data

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

Modulation of analog data (Why) After all, voice signals are transmitted over telephone lines in their

original spectrum (referred to as baseband transmission). A higher frequency may be needed for effective transmission

For unguided transmission, it is impossible to transmit baseband signals; the required antennas would be many kilometers in diameter.

Modulation permits frequency division multiplexing

Basic Encoding Techniques

Analog data to analog signalAmplitude modulation (AM)Angle modulation

Frequency modulation (FM)Phase modulation (PM)

Amplitude Modulation It consists on multiplying the modulating signal

(low frequency) by a carrier of much higher frequency

In amplitude modulation, the amplitude (signal strength) of the carrier wave is varied in proportion to the waveform being transmitted (the modulating signal).

Amplitude ModulationHigh frequency carrier

low frequency modulating signal

modulated signal

Amplitude Modulation

tftxnts ca 2cos1

Ac cos2fct is the High frequency carrier

x(t) = Am cos2fmt is the input low frequency signal

na = modulation index, amplification factor of Am Ratio of amplitude of input signal to carrier

m(t) = na x(t) the resulting modulating signal The modulated signal is

Amplitude Modulation tftxnts ca 2cos1

The envelope of the resulting signal is 1+ na x(t)

as long as na < 1, the envelope is an exact reproduction of the original signal

na >=1 causes a standard AM modulator to fail, as the negative excursions of the wave envelope

cannot become less than zero, resulting in distortion of the received modulation. 

Example Derive an expression of s(t) if x(t) is cos2fmt

and the carrier is cos2fct

bababa coscos2

1coscos

tftxnts ca 2cos1

Angle Modulation Angle modulation

Frequency modulation (FM) Phase modulation (PM)

The modulated signal is

ttfAts cc 2cos

Angle Modulation

Phase modulation Phase is proportional to modulating signal

np = phase modulation index

ttfAts cc 2cos

tmnt p

Angle Modulation

Frequency modulation Derivative of the phase is proportional to modulating signal

nf = frequency modulation index tmnt f'

ttfAts cc 2cos

Angle Modulation

The phase of s(t) at any instant is just

The instantaneous phase deviation from the carrier signal is (𝜙 t).

In PM, this instantaneous phase deviation is proportional to m(t).

ttfc 2

ttfAts cc 2cos

tmnt p

Angle Modulation

The instantaneous frequency of s(t) is

The instantaneous frequency deviation from the carrier frequency is ’(𝜙 t) which in FM is proportional to m(t).

tftf

ttfdt

dtf

ci

ci

'2

1)(

2)(2

tmnt f'

ttfAts cc 2cos

Angle Modulation Compared to AM, FM and PM result in a signal whose

bandwidth: is also centered at fc

but Angle modulation includes cos(𝜙(t)) which produces a wide range

of frequencies

In essence, for a modulating sinusoid of frequency fm, s(t) will

contain components at fc + fm, fc + 2fm,… and so on.

Thus, FM and PM require greater bandwidth than AM

Angle modulation: Example

Derive an expression of s(t) if

tfnt mp 2cos

ttfAts cc 2cos

Angle modulation: Example Derive an expression of s(t) if

Bessel’s trigonometric identities

tfnt mp 2cos

222cos

2cos2cos

ntnftfnJts

tfntfts

mcpn

n

mpc

Basic Encoding Techniques

Analog data to digital signalPulse code modulation (PCM)

Delta modulation (DM)

Analog Data to Digital Signal It might be more correct to refer to this as a process of converting

analog data into digital data; this process is known as digitization. Once analog data have been converted into digital data, The digital data can be directly transmitted, we have in

fact gone directly from analog data to a digital signal. The digital data can be encoded as a digital signal .Thus

an extra step is required. (NRZ, Bipolar, Manchester) The digital data can be converted into an analog signal,

using one of the modulation techniques ASK, PSK and FSK.

Pulse Code Modulation Based on the sampling theorem

If a signal f(t) is sampled at regular intervals of time and

at a rate higher than twice the highest signal frequency,

then the samples contain all the information of the original signal

Pulse Code Modulation Example: If voice data are limited to frequencies below

4000 Hz, a conservative procedure for intelligibility, 8000 samples

per second would be sufficient to characterize the voice signal completely.

Note, however, that these are analog samples, called pulse amplitude modulation (PAM) samples.

To convert to digital, each of these analog samples must be assigned a binary code.

Pulse Code Modulation

Question

1- pulse amplitude modulation (PAM) samples, represent the signal power,

* the signal amplitude at different instants.2- In this example, if you divide your scale by the smallest value, What are the new values? normalized PAM values

3- Each normalized PAM value is approximated by a quantized code number

4- Is it possible for the receiver to exactly reconstruct the original signal?

Example What should be the sampling frequency?

Example Normalization: Let us normalize the

amplitude levels?

Example Approximation: Each normalized PAM value is

approximated by a quantized code number

1- How many quantized levels are there??

2- How many bits do we need??

Example Quantization: PCM codes

Is it possible to exactly reconstruct the original signal??

What can you propose, in order to better approach the original signal??

Pulse Code Modulation Figure 6.15 shows an example in which the original signal is

assumed to be bandlimited with a bandwidth of B. PAM samples are taken at a rate of 2B, or once every Ts =

1/2B seconds. Each PAM sample is approximated by being quantized into

one of 16 different levels. Each sample can then be represented by 4 bits. But because the quantized values are only approximations,

it is impossible to recover the original signal exactly.

B

Pulse Code Modulation By using an 8-bit sample, which allows 256

quantizing levels, the quality of the recovered voice signal is comparable with that achieved via analog transmission.

Note that this implies that a

data rate of (8000 samples per second) X (8 bits per sample) = 64 kbps is needed for a single voice signal

Pulse Code Modulation

Thus, PCM starts with a continuous-time, continuous-amplitude (analog) signal, from which a digital signal is produced.

The digital signal consists of blocks of n bits, where each n-bit number is the amplitude of a PCM pulse. On reception, the process is reversed to reproduce the analog signal

Pulse Code Modulation Thus, PCM starts with a continuous-time,

continuous-amplitude (analog) signal, from which a digital signal is produced.

The digital signal consists of blocks of n bits, where each n-bit number is the amplitude of a PCM pulse.

On reception, the process is reversed to reproduce the analog signal

Pulse Code Modulation By quantizing the PAM pulse, original signal is

only approximated Leads to quantizing noise Signal-to-noise ratio for quantizing noise

Thus, each additional bit increases SNR by 6 dB, or a factor of 4

dB 76.102.6dB 76.12log20SNR dB nn

Delta Modulation Analog input is approximated by staircase function

Moves up or down by one quantization level () at each sampling interval

The bit stream approximates derivative of analog signal (rather than amplitude) 1 is generated if function goes up 0 otherwise

The transition (up or down) that occurs at each sampling interval is chosen so that the staircase function tracks the original analog waveform as closely as possible

Delta Modulation Analog signal Sampling Rate Sampling time At each sampling time

the analog input is compared to the most recent value of the approximating staircase function.

If the value of the sampled waveform exceeds that of the staircase function, the function goes up;

otherwise, the function goes down. By how much the function goes up or down?? Size of step ()

Delta Modulation Two important parameters

Size of step assigned to each binary digit () Sampling rate

Delta Modulation

Delta Modulation At each sampling time,

the analog input is compared to the most recent value of the approximating staircase function.

If the value of the sampled waveform exceeds that of the staircase function, a 1 is generated;

otherwise, a 0 is generated.

Delta Modulation Two important parameters

Size of step assigned to each binary digit () Sampling rate

Accuracy improved by increasing sampling rate However, this increases the data rate

Advantage of DM over PCM is the simplicity of its implementation

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 TDM is used instead of FDM

No intermodulation noise Conversion to digital signaling allows use of more

efficient digital switching techniques

END

Performance

Bandwidth of modulated signal (BT) ASK, PSK BT=(1+r)R

FSK BT=2DF+(1+r)R

R = bit rate 0 < r < 1; related to how signal is filtered DF = f2-fc=fc-f1

Performance Bandwidth of modulated signal (BT)

MPSK

MFSK

L = number of bits encoded per signal element M = number of different signal elements

RM

rR

L

rBT

2log

11

R

M

MrBT

2log

1

Angle Modulation Carson’s rule

where

The formula for FM becomes

BBT 12

BFBT 22

FMfor

PMfor

2

B

An

B

F

An

mf

mp

2mf An

F

Amplitude Modulation Transmitted power

Pt = total transmitted power in s(t)

Pc = transmitted power in carrier

We would like na as large as possible so that most of the signal power is used to carry information. However, na must remain below 1.

It should be clear that s(t) contains unnecessary components, because each of the sidebands contains the complete spectrum of m(t). A popular variant of AM, known as single sideband (SSB), takes advantage of this fact by sending only one of the sidebands.

21

2a

ct

nPP

Factors Used to CompareEncoding Schemes

Signal spectrum With lack of high-frequency components, less bandwidth

required Clocking

Ease of determining beginning and end of each bit position Signal 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

Appendix

Phase-Shift Keying (PSK) Differential PSK (DPSK)

Phase shift with reference to previous bit Binary 0 – signal burst of same phase as previous signal

burst Binary 1 – signal burst of opposite phase to previous

signal burst

Spectrum of AM signal

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

Sends only one sideband Advantages

Only half the bandwidth is required Less power is required

Phase-Shift Keying (PSK) Multilevel PSK

Using multiple phase angles with each angle having more than one amplitude, multiple signals elements can be achieved

D = modulation rate, baud R = data rate, bps M = number of different signal elements = 2L

L = number of bits per signal element

M

R

L

RD

2log