1. Signal Encoding Techniques
Chapter 6

2. Digital Vs Analog
Analog data take on continuous values in some intervals. Digital data take on discrete values. An analog signal is a continuously varying electromagnetic wave that may be propagated.
A sequence of voltage pulses that may be transmitted over a copper wire medium.
Either form of data could be encoded into either form of signals. A data source is encoded into a digital signal. The actual form of x(t) depends on the encoding techniques , optimized the use of transmission medium. Conserve bandwidth.
Carrier signal. 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. Amplitude, phase, frequency. Bandlimited

3. 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

4. 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
Converted into analog signals for wireless transmission. Typically, a baseband analog signal, such as voice or video, must be modulated onto a higher-frequency carrier for transmission
Digitize voice signals before transmission over either guided or unguided media to improve the quality and to take advantage of TDM schemes.

5. Terms Data element, bits, a signal binary 0 or 1
Data rate, bits per second, the rate at which data elements are transmitted.
Signal elements,
Signal rate or modulation rate, signal elements per second (baud), the rate at which signal elements are transmitted.
A digital signal is a sequence of discrete, discontinuous voltage pulses. Each pulse is a signal element. Binary data are transmitted by encoding each data bit into signal elements. One-to-one correspondence between data bit and signal elements. Similarly, a digital bit stream can be encoded onto an analog signal as a sequence of signal elements. Each signal element is pulse of constant frequency, phase and amplitude.
The duration of a bit is the amount of time it takes for the transmitter to emit the bit. At which the signal level is changed.

6. 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
The receiver must know the timing of each bit. That is, the receiver must know with some accuracy when a bit begins and ends. Determine whether the signal level for each bit position is high or low. Errors.
There is another factor that can be used to improve performance, and that is the encoding scheme. The encoding scheme is the mapping from data bits to signal elements.

7. Factors Used to Compare Encoding 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
Used to evaluate and compare these schemes. Lack of dc component is also desirable. With dc, there must be direct physical attachment of transmission components. alternating current coupling via transformer is possible, this provides excellent electrical isolation, reducing interference. Therefore, a good signal design should concentrate the transmitted power in the middle of the transmitted bandwidth. In such case, less distortion. Shape the signal spectrum.
The receiver must determine when each bit begins and stops. One expensive approach is to provide a separate clock channel to synchronize the transmitter and receiver.
The alternative is to provide some sychronization methods that is based on the transmitted signal.

8. Factors Used to Compare Encoding 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
Certain codes

9. 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
The case of transmitting digital data using analog signals. Public telephone network is designed to receive, switch and transmit analog signal in the voice-frequency range Hz. Some digital devices attached to the telephone network via a modem (modulator-demodulator), which converts digital data to analog signals, vice verse.
Three encoding or modulation techniques.

10. Basic Encoding Techniques

11. 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)
In ASK, the two binary values are represented by two different amplitudes of the carrier frequency. Commonly one of the amplitudes is zero,

12. 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
Laser transmitters emit a low light level. A higher-amplitude lightwave represents another signal element.

13. 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

14. 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 even higher frequencies on LANs that use coaxial cable
Duplex both direction at the same time. The bandwidth is split. In one direction, the frequencies used to represent 1 and 0 are centered at 1170 hz., with a shift of 100Hz on either side. 2125Hz. Interference.

15. 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
Each signal element represents more than one bit. The transmitted MFSK signal for one signal element time can be defined as follows.

16. 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
To match the data rate of the input bit stream, each output signal element is held for a period of Ts=LT second,where T is the bit period (data rate=1/T)

17. 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

18. Multiple Frequency-Shift Keying (MFSK)
Example of MFSK with M=4. an input bit stream of 20 bits is encoded 2 bit at a time, with each of the four possible 2-bit combinations transmitted as a different frequency. The frequency transmitted as a function of time. Each column represents a time unit Ts in which a single 2-bit signal elemtns is transmitted. The shaded rectangle in the column indicates the frequency transmitted during that time unit.
With fc=250khz, fd=25khz, and M=8, we have the following frequency assignments for each of the 8 possible 3 bit combination
This scheme can support a data rate?

19. Phase-Shift Keying (PSK)
Two-level PSK (BPSK)
Uses two phases to represent binary digits
The resulting transmitted signal for one bit time is as follows. Because a phase shift of pi is equivalent to flipping the sine wave or multiplying it by -1.

20. 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
An alternative form of two level PSK is differential PSK. Is represented By sending.
The information to be transmitted is represented in terms of the changes between successive data symbols rather than the signal elements themselves. The preceding phase is received correctly, the reference is accurate.

21. Phase-Shift Keying (PSK)
Four-level PSK (QPSK)
Each element represents more than one bit
More efficient use of bandwidth can be achieved if each signal element represents more than one bit. Uses phase shift separated by multiples of one half PI

22. 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
The use of multiple levels can be extended. It is possible to transmit three bits at a time using eight different phase angles. Further each phase angle can have more than one amplitude. For example, the standard 9600 bps modem uses 12 different phase angles, four of them have two amplitudes. A total of 16 different signal elements.
Data rate R modulation rate Tb
Higher bit rate can be achieved by employing more complex modulation schemes.

23. 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
Measure their performance. The bandwidth of the modulated signal. This depends on many factors. Filtering. Bandpass:A range of wavelengths within which a component operates. The transmission bandwidth Bt for ASK. r is related to the techniques by which the signal is filtered to establish a bandwidth for transmission. Under certain assumption for FSK.

24. Performance Bandwidth of modulated signal (BT) MPSK MFSK
L = number of bits encoded per signal element
M = number of different signal elements
With multiple PSK, significant improvements in bandwidth can be achieved. For MFSK.

25. Performance
Bandwidth efficiency ― The ratio of data rate to transmission bandwidth (R/BT)
For MFSK, with the increase of M, the bandwidth efficiency is decreased.
For MPSK, with the increase of M, the bandwidth efficiency is increased.
This parameter is used to measure the efficiency with which bandwidth can be used to transmit data. You may note from this table, For MFSK, with the increase of M, the bandwidth efficiency is decreased. For MPSK, with the increase of M, the bandwidth efficiency is increased. We don’t consider about the noise.

26. Performance
Bit error rate is a decreasing function of the ratio Eb/N0.DPSK and BPSK are about 3 db superior to ASK and BFSK

27. Performance
For MFSK, the error probability for a given value Eb/No decreases as M increases.
the efficient bandwidth decreases as M increases.
For MPSK, the error probability for a given value Eb/No increases as M increases.
the efficient bandwidth increases as M increases.

28. Performance
Tradeoff between bandwidth efficiency and error performances: an increase in bandwidth efficiency results in an increase in error probability.
What is the bandwidth efficiency for FSK, ASK, PSK and QPSK for a bit error rate of on a channel with an SNR of 12db?
(Eb/N0)=(S/R)/(N/Bt)

29. Minimum shift keying
Can be considered as a form of BFSK modulation that is found in some mobile communications systems. It provides superior bandwidth efficiency to BFSK with only a modest decrease in error performance. For MSK, the two frequencies satisfy the following equation.
F1=fc+1/4Tb F2=fc-1/4Tb. The spacing between these two frequencies is the minimum that can be used and permit successful detection of the signal at the receiver. Miminum in MSK.
Where Eb is the transmitted signal energy per bit, and Tb is the bit duration, the phase (0) denotes the value of the phase at time t=0.

30. Quadrature Amplitude Modulation
QAM is a combination of ASK and PSK
Two different signals sent simultaneously on the same carrier frequency
A popular analog signaling technique used in some wireless standards. By using two copies of the same carrier frequency, one is shifted 90 degree with respect to the other.

31. Quadrature Amplitude Modulation

32. 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

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

34. Amplitude Modulation Amplitude Modulation
cos2fct = carrier
x(t) = input signal
na = modulation index
Ratio of amplitude of input signal to carrier
a.k.a double sideband transmitted carrier (DSBTC)
Normalized to unity amplitude
Amplitude modulation (AM) is a form of modulation in which the amplitude of a carrier wave is varied in direct proportion to that of a modulating signal.
Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency ωc, taking its phase to be a reference phase of zero, is
c(t) = Csin(ωct).
The equation for the simple sine wave of frequency ωm (the signal we wish to broadcast) is
m(t) = Msin(ωmt + φ),
with φ its phase offset relative to c(t).
Amplitude modulation is performed simply by adding m(t) to C. The amplitude-modulated signal is then
y(t) = (C + Msin(ωmt + φ))sin(ωct)
The formula for y(t) above may be written
The broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from ωc, known as sidebands. For the sinusoidal signals used here, these are at ωc + ωm and ωc − ωm. As long as the broadcast (carrier wave) frequencies are sufficiently spaced out so that these side bands do not overlap, stations will not interfere with one another.
As with other modulation indices, in AM, this quantity indicates by how much the modulated variable varies around its 'original' level. For AM, it relates to the variations in the carrier amplitude and is defined as: .
So if h = 0.5, the carrier amplitude varies by 50% above and below its unmodulated level, and for h = 1.0 it varies by 100%.

35. Amplitude modulation

36. Spectrum of AM signal
Look at the spectrum of the AM signal. The spectrum of AM signal consists of the original carrier plus the spectrum of the input signal translated to Fc. The portion of the spectrum for the upper sideband, lower sideband. Duplicated, mirror of modulating signal.
A voice signal with a bandwidth that extends from 300 to 3000 hz being modulated on a 60-khz carrier. The resulting signal contains an upper bandside of 60.3 to 63khz, a lower sideband khz.
S(t) contains unnecessary componets, because each of the sidebands contains the complete spectrum of m(t).

37. 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.

38. 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
A popular variant of AM, known as single sideband, takes advantage of the fact by sending.
No power is used to transmit the carrier or the other sideband.
Another variant is double sideband suppressed carrier (DSBSC), which filters out the carrier frequency and sends both sidebands.
Vestigial sideband (VSB), uses one sideband and reduced-power carrier.
A constant carrier provides a clocking method by which to time the arrivals of bits.

39. Other variants
Double sideband suppressed carrier (DSBSC): filters out the carrier frequency and sends both sidebands.
Vestigial sideband (VSB), uses one sideband and reduced-power carrier.

40. Angle Modulation Angle modulation Phase modulation
Phase is proportional to modulating signal
np = phase modulation index
Frequency modulation and phase modulation are special cases of angle modulation.

41. Angle Modulation Frequency modulation
Derivative of the phase is proportional to modulating signal
nf = frequency modulation index
Frequency can be defined as the rate of change of phase of a signal.

42. 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
Amplitude modulation is a linear process and produces frequencies that are sum and difference of the carrier signal and the components of the modulating signal. Angle modulation includes a term of the form cos( (t)) , which is nonlinear and will produce a wide range of frequencies. In most cases, infinite bandwidth is required to transmit FM and PM signals.

43. Angle Modulation Carson’s rule The formula for FM becomes where
Am is the maximum value of m(t). F is the peak derivation
F=1/2PI nfAm Hz.
An increase in the magnitude of m(t) will increase F , which should increase the transmitted bandwidth Bt.

44. Basic Encoding Techniques
Analog data to digital signal
Pulse code modulation (PCM)
Delta modulation (DM)
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. The device used for converting analog data into digital form for transmission and recovering the original analog data from the digit, is called as a codec

45. 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
NRZ-L is short for nonreturn to zero. Is the most common way to transmit digital signals. It uses two different voltage levels to represent two binary digits. Negative 1, positive 0

46. 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
Conservative procedure for intelligibility.
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 contains all the information of the original signal. The function f(t) may be reconstructed from these samples.
If voice data are limited to frequencies below 4000Hz, 8000 samples per second would be sufficient to characterize the voice signal completely.

47. Pulse Code Modulation
Approximated quantized

48. 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

49. 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

50. Delta Modulation

51. 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

52. 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