Signal Encoding Techniques

Lecture 18

Overview Where we Stand on Layers Data Representation and Signaling Used Data Encoding Reasons for Choosing Encoding Schemes Factors Involved Digital Data to Analog Signal (ASK, FSK,

PSK) Analog Data to Digital Signal

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Where We Stand @ Present

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Physical Layer

Transmission Medium

Data Link

Transmission Media

Signals and their transmission over media,

Impairments

Encoding: From data to signals

Data Link: Flow and Error control

Data Communication: Synchronization,

Error detection and correction

Improved utilization: Multiplexing

Antenna and Propagation

Data Signal Combination

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Data, Signaling and its Treatment

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What's Going Up…

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Digital Data Digital Signal

Analog SignalAnalog Data

Less complex, less expensive than digital-analog modulation equipment

Use of modern digital transmission And switching equipment

Some transmission media will onlypropagate analog signals

Efficient use of transmission channel : FDM

Data Encoding Techniques Digital Data, Analog Signals [Modem] Digital Data, Digital Signals [Wired LAN] Analog Data, Digital Signals [Codec]

Frequency Division Multiplexing (FDM) Wave Division Multiplexing (WDM) [Fiber] Time Division Multiplexing (TDM) Pulse Code Modulation (PCM) [T1] Delta Modulation

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Encoding Techniques

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Digital data as digital signal Digital data as analog signal: Converter (Modem) Analog data as digital signal: Converter (Codec) Analog data as analog signalIn general:

When the outcome is a digital signal we use an Encoding process

When the outcome is an analog signal we use a Modulation process

But we call the modulation of analog signal by digital data shift-keying

Reasons for Choosing Encoding Techniques 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

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Reasons for Choosing Encoding Techniques 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

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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

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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 position

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Factors Used to CompareEncoding Schemes 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

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Basic Encoding Techniques Digital data to analog signal

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

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Basic Encoding Techniques

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Amplitude-Shift Keying One binary digit represented by presence

of carrier, at constant amplitude Other binary digit represented by

absence of carrier

where the carrier signal is Acos(2πfct)

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Amplitude-Shift Keying Susceptible to sudden gain

changes Inefficient modulation technique On voice-grade lines, used up to

1200 bps Used to transmit digital data over

optical fiber

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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

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Binary Frequency-Shift Keying (BFSK) Less susceptible to error than ASK On voice-grade lines, used up to

1200bps Used for high-frequency (3 to 30

MHz) radio transmission Can be used at higher frequencies

on LANs that use coaxial cable

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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

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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

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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

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Multiple Frequency-Shift Keying (MFSK)

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

Uses two phases to represent binary digits

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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

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

Each element represents more than one bit

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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 element27

Performance Bandwidth of modulated signal (BT)

ASK, PSK BT=(1+r)R FSK BT=2F+(1+r)R

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

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Performance Bandwidth of modulated signal (BT)

MPSK

MFSK

L = number of bits encoded per signal element

M = number of different signal elements

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Quadrature Amplitude Modulation QAM is a combination of ASK and

PSK Two different signals sent

simultaneously on the same carrier frequency

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Quadrature Amplitude Modulation

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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

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Basic Encoding Techniques Analog data to analog signal

Amplitude modulation (AM) Angle modulation

Frequency modulation (FM) Phase modulation (PM)

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Amplitude Modulation Amplitude Modulation

cos2fct = carrier x(t) = input signal na = modulation index

Ratio of amplitude of input signal to carrier a.k.a double sideband transmitted

carrier (DSBTC)

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Spectrum of AM signal

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Amplitude Modulation Transmitted power

Pt = total transmitted power in s(t) Pc = transmitted power in carrier

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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

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Angle Modulation Angle modulation

Phase modulation Phase is proportional to

modulating signal

np = phase modulation index38

Angle Modulation Frequency modulation

Derivative of the phase is proportional to modulating signal

nf = frequency modulation index

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Angle Modulation Compared to AM, FM and PM result in

a signal whose bandwidth: is also centered at fc

but has a magnitude that is much different

Angle modulation includes cos( (t)) which produces a wide range of frequencies

Thus, FM and PM require greater bandwidth than AM

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Angle Modulation Carson’s rule

where

The formula for FM becomes

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Basic Encoding Techniques Analog data to digital signal

Pulse code modulation (PCM) Delta modulation (DM)

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Analog Data to Digital Signal Once analog data have been

converted to digital signals, the digital data: can be transmitted using NRZ-L can be encoded as a digital signal

using a code other than NRZ-L can be converted to an analog signal,

using previously discussed techniques

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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

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Pulse Code Modulation

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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

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PCM

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The most common technique to change an analog signal to digital data (digitization) is called pulse code modulation (PCM). A PCM encoder has three processes.

1. The analog signal is sampled.2. The sampled signal is quantized.3. The quantized values are encoded as streams of bits.

The analog signal is sampled every Ts, where Ts is the sample interval or period. The inverse of the sampling interval is called the sampling rate or sampling frequency and denoted by fs, where fs = 1/Ts.

PCM

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•There are three sampling methods: ideal, natural, and flat-top.•In ideal sampling, pulses from the analog signal are sampled. This is an ideal sampling method and cannot be easily implemented.• In natural sampling, a high-speed switch is turned on for only the small period of time when the sampling occurs. The result is a sequence of samples that retains the shape of the analog signal. •The most common sampling method, called sample and hold, however, creates flat-top samples by using a circuit.

Sampling Rate

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•We can sample a signal only if the signal is band-limited. In other words, a signal with an infinite bandwidth cannot be sampled. •The sampling rate must be at least 2 times the highest frequency, not the bandwidth. •If the analog signal is low-pass, the bandwidth and the highest frequency are the same value. If the analog signal is bandpass, the bandwidth value is lower than the value of the maximum frequency

PCM (Example)

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A complex low-pass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal?

SolutionThe bandwidth of a low-pass signal is between 0 and f, where f is the maximum frequency in the signal. Therefore, we can sample this signal at 2 times the highest frequency (200 kHz). The sampling rate is therefore 400,000 samples per second.

Example

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A complex bandpass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal?

SolutionWe cannot find the minimum sampling rate in this case because we do not know where the bandwidth starts or ends. We do not know the maximum frequency in the signal.

Example

PCM (Example)

PCM Quantization

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Quantization and encoding of a sampled signal

Original Signal Recovery

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The recovery of the original signal requires the PCM decoder. The decoder first uses circuitry to convert the code words into a pulse that holds the amplitude until the next pulse. After the staircase signal is completed, it is passed through a low-pass filter to smooth the staircase signal into an analog signal. The filter has the same cutoff frequency as the original signal at the sender. If the signal has been sampled at (or greater than) the Nyquist sampling rate and if there are enough quantization levels, the original signal will be recreated. Note that the maximum and minimum values of the original signal can be achieved by using amplification.

Question A PCM encoder accepts a signal with a full-scale voltage

of 10 V and generates 8-bit codes using uniform quantization. The maximum normalized quantized voltage is 1-2-8. Determine

(a) normalized step size, (b) actual step size in volts, (c) actual maximum quantized level in volts, (d) normalized resolution, (e) actual resolution,and (f) percentage resolution.

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PCMa. A total of 28 quantization levels are possible, so the normalized

step size is 2–8 = 0.003906.b. The actual step size, in volts, is: 0.003906 x 10V = 0.03906Vc. The maximum normalized quantized voltage is 1 - 2 -8 =

0.9961. Thus the actual maximum quantized voltage is: 0.9961 x 10V = 9.961V

d. The normalized step size is 2 -8. The maximum error that can occur is one-half the step size. Therefore, the normalized resolution is:

e. The actual resolution isf. The percentage resolution is

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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

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Delta Modulation

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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

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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

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Summary Layered Position Data and Signaling Encoding Schemes Reasons for Different Encoding Schemes Performance Factors Involved Digital Data to Analog Signal (ASK, FSK,

PSK) Analog Data to Digital Signal (PCM,

Delta) 62