1. Signal Encoding Techniques
Chapter 6

2. Analog Signaling

3. Digital Signaling

5. 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.

6. Introduction
What is the difference between both techniques?

7. 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

8. 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.

9. Introduction

10. 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.

11. 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.

12. 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.

13. 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 ???? .

14. 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.

15. 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

16. 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

17. 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

18. Signal Encoding Criteria
Definition
Units
Term
A single binary one or zero
Bits
Data Element
The rate at which the data elements are transmitted
Bits per second(bps)
Data rate
-Digital: a voltage pulse of constant amplitude
-Analog: a pulse of constant frequency, phase, and amplitude
Signal element
The rate at which signal elements are transmitted
Signal elements per second (baud)
Signaling rate or modulation rate

19. 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.

21. Signal Encoding Criteria
What determines how successful a receiver will be in interpreting an incoming signal?

22. 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

23. 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.

24. 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

25. Basic Encoding Techniques

26. Basic Encoding Techniques

27. 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)

28. Reminder

30. Amplitude-Shift Keying

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

34. 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

35. Binary Frequency-Shift Keying (BFSK)

36. 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.

37. 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

38. 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?

39. 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

40. 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?

41. Multiple Frequency-Shift Keying (MFSK)

42. 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

43. 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

44. Phase-Shift Keying (PSK)
Two-level PSK (BPSK)
Uses two phases to represent binary digits

45. Phase-Shift Keying (PSK)

46. Phase-Shift Keying (PSK)

47. Phase-Shift Keying (PSK)
Four-level PSK (QPSK)
Each element represents more than one bit

56. Quadrature Amplitude Modulation
QAM is a combination of ASK and PSK
Two different signals sent simultaneously on the same carrier frequency

64. 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

65. Basic Encoding Techniques
Analog data to analog signal
Amplitude modulation (AM)
Angle modulation
Frequency modulation (FM)
Phase modulation (PM)

66. 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).

67. Amplitude Modulation High frequency carrier
low frequency modulating signal
modulated signal

68. Amplitude Modulation m(t) = na x(t) the resulting modulating signal
Ac cos2fct is the High frequency carrier
x(t) = Am cos2fmt 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

70. Amplitude Modulation
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. 

72. Example
Derive an expression of s(t) if x(t) is cos2fmt and the carrier is cos2fct

74. Angle Modulation Angle modulation The modulated signal is
Frequency modulation (FM)
Phase modulation (PM)
The modulated signal is

75. Angle Modulation Phase modulation
Phase is proportional to modulating signal
np = phase modulation index

76. Angle Modulation Frequency modulation
Derivative of the phase is proportional to modulating signal
nf = frequency modulation index

77. 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).

78. 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).

79. 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

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

81. Angle modulation: Example
Derive an expression of s(t) if
Bessel’s trigonometric identities

84. Basic Encoding Techniques
Analog data to digital signal
Pulse code modulation (PCM)
Delta modulation (DM)

85. 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.

86. Pulse Code Modulation If a signal f(t) is
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

87. 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.

88. Pulse Code Modulation

89. 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?

90. Example
What should be the sampling frequency?

91. Example
Normalization: Let us normalize the amplitude levels?

92. 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??

93. Example Quantization: PCM codes
Is it possible to exactly reconstruct the original signal??

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

95. Pulse Code Modulation B
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.

97. 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

98. 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

99. 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

100. 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

101. 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

102. 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 ()

103. Delta Modulation Two important parameters
Size of step assigned to each binary digit ()
Sampling rate

104. Delta Modulation

105. 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.

106. 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

107. 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

108. END

109. 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

110. Performance Bandwidth of modulated signal (BT) MPSK MFSK
L = number of bits encoded per signal element
M = number of different signal elements

111. Angle Modulation
Carson’s rule
where
The formula for FM becomes

112. 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.

113. Factors Used to Compare Encoding 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

114. Appendix

115. 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

116. Spectrum of AM signal

117. 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

118. 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