1. Chapter #5 Pulse Modulation
King Saud University
College of Applied studies and Community Service
1301CT
By: Nour Alhariqi
Chapter #5 Pulse Modulation
1st semester

2. Outline Sampling Digital communication system Analog pulse modulation
Digital pulse modulation

3. Sampling Process
The sampling process is a basic operation in the digital communication.
In this process, the continuous-time analog signal signal is sampled by measuring its amplitude at a discrete instants.
So, the continuous-time analog signal is converted into a corresponding sequence of samples that are usually spaced uniformly in time.
It is necessary to choose the sampling rate properly, so the sequence of samples uniquely defines the original analog signal.

4. The Sampling Theorem
The sampling theorem shows that a continuous-time signal which is a band-limited to fm Hz can be represented perfectly by a series of samples spaced Ts ( ≤ 1/2 fm) seconds apart.
Ts called sampling period
The band-limited signal is a signal which its Fourier transform is nonzero for  -2π fm < ω < 2π fm.
When m(t) is sampled uniformly at intervals of Ts seconds, the resultant sequence is denoted by m(nTs), for all integer values of n.

5. S(t) is band- limited signalTs
sampling period
S(t) is band- limited signal

6. The Sampling Theorem
Let’s define a sampling rate fs = 1 / Ts which is the number of samples per second.
Thus, the sampling theorem states that a band-limited signal can be recovered completely from a set of samples taken at the rate of fs ( ≥ 2 fm) samples per second.
The preceding sampling theorem is often called the uniform sampling theorem for baseband or low-pass signal.
The minimum sampling rate, 2fm samples per second, called the Nyquist rate; its reciprocal 1/2fm is called Nyquist interval

7. Sampling Process
Let g(t) be a signal whose spectrum is band-limited to fm Hz
Sampling g(t) at a rate of fs Hz (fs samples per second) can be accomplished by multiplying g(t) by an impulse train δTs(t), consisting of unit impulses repeating periodically every Ts seconds, where Ts = 1 / fs

8. Sampling Process
This results sampled signal ğ(t) consists of impulses spaced every Ts seconds.
The nth impulse, located at t=n Ts has a strength g(nTs), the value of g(t) at t = n Ts

9. Sampling Process

10. Sampling Process

11. Sampling Process

12. Sampling Process
2 fm
1/2fm

13. Aliasing
What happens if we sample the signal at a frequency that is lower that the
Nyquist rate? 
If the Nyquist criterion is not satisfied, the adjacent copies of g(t) spectrum will overlap, this phenomenon called aliasing

14. Aliasing With aliasing :
- Some of the frequencies in the original signal will be lost in the reconstructed signal
- unwanted components will be presence in the reconstructed signal.  these components were not present when the original signal was sampled. 
In addition,. 
Aliasing occurs because signal frequencies will overlap if the sampling frequency is too low. 

15. Example
What Nyquist rate is needed for a signal with a bandwidth 10,000Hz ( 1000 to 11,000 Hz)?
The Nyquist rate is equal to twice the highest frequency in the signal
Nyquist rate = 2 * 11,000 = 22,000 samples/sec

16. Analog Pulse Modulation

17. Continuous wave (CW) modulation AM Angle modulation FM PM
Pulse Modulation
Analog Pulse Modulation
PAM
PPM
PDM
Digital Pulse Modulation DM
PCM

18. Introduction

19. Introduction

20. Introduction

21. Pulse Amplitude Modulation (PAM)

22. Pulse Amplitude Modulation (PAM)

23. Pulse Amplitude Modulation (PAM)

24. PDM and PPM

25. Digital Pulse Modulation

26. Digital Pulse Modulation
The digital pulse modulation has two types:
Pulse Code Modulation(PCM)
Delta Modulation(DM)
The process of Sampling which we have already discussed in initial slides is also adopted in digital pulse modulation

27. Pulse Code Modulation(PCM)
PCM is the most basic form of digital pulse modulation.
In PCM, a message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude.
The basic operations performed in the transmitter of a PCM system are sampling, quantizing, and encoding.

28. The basic elements of a PCM system
Before we sample, we have to filter the signal to limit the maximum frequency of the signal as it affects the sampling rate.
Filtering should ensure that we do not distort the signal, i.e. remove high frequency components that affect the signal shape.

29. Sampler
The sampler samples the input continuous-time analog signal at a sampling rate fs (= 1/Ts sec).
There are 3 sampling methods:
Ideal - an impulse at each sampling instant
Natural - a pulse of short width with varying amplitude
Flattop - sample and hold, like natural but with single amplitude value

30. Quantization Process
The analog signal has a continuous range of amplitudes and therefore its samples have a continuous amplitude range.
In the quantization, the signal with continuous amplitude can be approximated by a signal constructed of discrete amplitudes selected on a minimum error basis from an available set.

31. Quantizer
The sampling results is a series of pulses of varying amplitude values ranging between two limits: a min and a max.
The amplitude values are infinite between the two limits.
We need to map the infinite amplitude values onto a finite set of known values.
This is achieved by dividing the distance between min and max into L zones, each of height 
 = (max - min)/L

32. Quantization Levels
The midpoint of each zone is assigned a value from 0 to L-1 (resulting in L values)
Each sample falling in a zone is then approximated to the value of the midpoint.

33. Quantization Zones
Assume we have a voltage signal with amplitutes Vmin=-20V and Vmax=+20V.
We want to use L=8 quantization levels.
Zone width = ( )/8 = 5
The 8 zones are: -20 to -15, -15 to -10, -10 to -5, -5 to 0, 0 to +5, +5 to +10, +10 to +15, +15 to +20
The midpoints are: -17.5, -12.5, -7.5, -2.5, 2.5, 7.5, 12.5, 17.5

34. Quantization Error
When a signal is quantized, we introduce an error - the coded signal is an approximation of the actual amplitude value.
The difference between actual and midpoint value is referred to as the quantization error.
The more zones, the smaller  which results in smaller errors.

35. Encoding
In combining the process of sampling and quantization, the specification of the continuous-time analog signal becomes limited to a discrete set of values.
Representing each of this discrete set of values as a code called encoding process.
Code consists of a number of code elements called symbols.
In binary coding, the symbol take one of two distinct values. in ternary coding the symbol may be one of three distinct values and so on for the other codes.

36. Assigning Codes to Zones
Each zone is assigned a binary code.
The binary code consists of bits.
The number of bits required to encode the zones, or the number of bits per sample, is obtained as follows:
nb = log2 L
Given our example, nb = 3
The 8 zone (or level) codes are therefore: 000, 001, 010, 011, 100, 101, 110, and 111
Assigning codes to zones:
000 will refer to zone -20 to -15
001 to zone -15 to -10, etc.

37. Line Coding
Any of several line codes can be used for the electrical representation of a binary data stream.
Examples of line coding : RZ, NRZ, and Manchester

38. 2 10 t
x(t)
Consider the analog Signal x(t). 2 10 n
X(nTs)
The signal is first sampled Ts

39. 2 4 6 8 n 10
dividing the range into 4 zones n
assign quantized values of 0 to 3 to the midpoint of each zone. 1 2 3

40. n
approximating the value of the sample amplitude to the quantized values. 1 2 3 n
Each zone is assigned a binary code 1 2 3 00 01 10 11

41. n 1 2 3 00 01 10 11
The sequence bits if the samples
Use one of the line code scheme to get the digital signal

42. Delta Modulation

43. Introduction
PCM is a very complex technique. Other techniques have been developed to reduce the complexity of PCM. The simplest is delta modulation.
PCM finds the value of the signal amplitude for each sample; DM finds the change from the previous sample.

44. Delta Modulation
In Delta Modulation, only one bit is transmitted per sample
That bit is a one if the current sample is more positive than the previous sample, and a zero if it is more negative
Since so little information is transmitted, delta modulation requires higher sampling rates than PCM for equal quality of reproduction

45. Delta Modulation
1- A staircase approximation of the message signal is derived
The analog signal is approximated with a series of segments ( staircase approximation signal)
Each segment of the approximated signal is compared to the message signal:
If the approximation fall below the signal at any sampling epoch  the segment is increased by ∆.
If the approximation lies above the signal at any sampling epoch  the segment is diminished by ∆.
So, the time and amplitude axes are quantized.

47. Delta Modulation 2- encoding
This scheme sends only one bit each segment.
if the segment at time tn+1 is higher in amplitude value than the segment at time tn,  then a bit “1” is used to indicate the positive value.
If the segment is lower in value  resulting in a negative value, a “0” is used.

48. This scheme works well for small changes in signal values between samples.
If changes in amplitude are large, this will result in large errors.

49. Merits of Digital Communication Systems

50. Merits of Digital Communication
1- Digital signals are very easy to receive. The receiver has to just detect whether the pulse is low or high ( one or zero).
2- AM & FM signals become corrupted over much short distances as compared to digital signals.
3 - In digital signals, the original signal can be reproduced accurately.

51. Merits of Digital Communication
4- as known, the signals lose power as they travel, which is called attenuation. When AM and FM signals are amplified, the noise also get amplified. But the digital signals can be cleaned up to restore the quality and amplified by the regenerators.
5- The noise may change the shape of the pulses but not the pattern of the pulses.

52. Merits of Digital Communication
6 - AM and FM signals can be received by any one by suitable receiver. But digital signals can be coded so that only the person, who is intended for, can receive them.
7- The digital signals can be stored.