Signal Encoding Techniques Chapter 6. Analog Signaling.
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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
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