1. Signal Encoding Techniques
Lecture 18

2. 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

3. Where We Stand @ Present
Antenna and Propagation
Data Link: Flow and Error control
Data Link
Improved utilization: Multiplexing
Physical Layer
Data Communication: Synchronization, Error detection and correction
Transmission Media
Transmission Medium
Encoding: From data to signals
Signals and their transmission over media, Impairments

4. Data Signal Combination

5. Data, Signaling and its Treatment

6. What's Going Up… Digital Data Digital Signal Analog Signal Analog Data
Less complex, less expensive
than digital-analog modulation equipment
Use of modern digital transmission
And switching equipment
Some transmission media will only
propagate analog signals
Efficient use of transmission
channel : FDM

7. 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

8. Encoding Techniques Analog data as analog signal
Digital data as digital signal
Digital data as analog signal: Converter (Modem)
Analog data as digital signal: Converter (Codec)
Analog data as analog signal
In 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. Basic Encoding Techniques

16. 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)

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. Multiple Frequency-Shift Keying (MFSK)

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

25. 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

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

27. 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

28. 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

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

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

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)

35. Spectrum of AM signal

36. Amplitude Modulation Transmitted power
Pt = total transmitted power in s(t)
Pc = transmitted power in carrier

37. 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

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

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

40. 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

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

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

43. 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

44. 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

45. Pulse Code Modulation

46. 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

48. PCM
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.

49. PCM 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.

50. Sampling Rate
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

51. PCM (Example)
Example
A complex low-pass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal?
Solution
The 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.

52. PCM (Example)
Example
A complex bandpass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal?
Solution
We 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.

53. PCM Quantization
Quantization and encoding of a sampled signal

54. Original Signal Recovery
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.

55. 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 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.

56. PCM
A total of 28 quantization levels are possible, so the normalized step size is 2–8 =
The actual step size, in volts, is: x 10V = V
The maximum normalized quantized voltage is = Thus the actual maximum quantized voltage is: x 10V = 9.961V
The normalized step size is The maximum error that can occur is one-half the step size. Therefore, the normalized resolution is:
The actual resolution is
The percentage resolution is

58. 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

59. Delta Modulation

60. 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

61. 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

62. 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)