1. Physical Layer
Digital Signals
Lecture 5

2. Two Familiar Signals
A familiar signal in our daily lives is the electrical energy we use at home and at work. The signal we receive from the power company has an amplitude of 2400 V and a frequency of 50 Hz (a simple analog signal). Another signal familiar to us is the power we get from a battery. It is an analog signal with an amplitude of 6 V (or 12 or 24) and a frequency of zero.

3. Digital Signal
A digital signal - a must for computer processing - is described as using binary (0s and 1s), and therefore, cannot take on any fractional values. Digital signals retain a uniform structure, providing a constant and consistent signal.
Because of the inherent reliability of the digital signal, technology using it is rapidly replacing a large percentage of analog applications and devices.

4. Equally, A digital signal uses discrete (discontinuous) values
Equally, A digital signal uses discrete (discontinuous) values. By contrast, non-digital (or analog) systems use a continuous range of values to represent information. Although digital representations are discrete, the information represented can be either discrete, such as numbers or letters, or continuous, such as sounds, images, and other measurements of continuous systems.

5. Example of Digital signal

6. Digital data
Digital Data presented in digital signal

7. Digital signal

8. Two digital signals: one with two signal levels and the other with four signal levels

9. Bit interval (BI) and Bit rate (BR)
Bit interval is the time required to send one single bit
Bit rate is the number of bit interval per second. This means that bit rate is number of bits sent in one second (bps)

10. Relationship Between Bit rate (BR) and Bit Interval (BI)

11. Units of Bit Rate 1 bps 1 kbps = 1000 bps 1 Mbps = 1,000,000 bps
1 Gbps = 1,000,000,000 bps
1 Tbps = 1,000,000,000,000 bps

12. Example 6
A digital signal has a bit rate of 2000 bps. What is the duration of each bit (bit interval)
Solution
The bit interval is the inverse of the bit rate.
Bit interval = 1/ 2000 s = s = x 106 ms = 500 ms

13. Transmission Modes

14. Data Transmission
The transmission of binary data across the link can be accomplished either in parallel mode or serial mode.
Parallel mode multiple bits are sent in each clock pulse
Serial mode one bit is sent with each clock pulse

15. Parallel transmission
In parallel transmission a group of bits are sent at once

16. Serial transmission
In serial mode one bit is sent at a time

17. Parallel and Serial Conversions
Since communication within devices is parallel, conversion devices are required at the interface between the sender and the line (parallel-to-serial) and between the line and the receiver (serial-to-parallel)

18. Serial Transmission
Serial transmission occurs in one of two ways: Asynchronous and synchronous transmission
In asynchronous transmission, we send 1 start bit (0) at the beginning and 1 or more stop bits (1s) at the end of each byte. There may be a gap between each byte.
Asynchronous here means “asynchronous at the byte level,” but the bits are still synchronized; their durations are the same.

19. Asynchronous Transmission

20. In synchronous transmission, we send bits one after another without start/stop bits or gaps. It is the responsibility of the receiver to group the bits.

21. Synchronous transmission

22. Multiplexing

23. What is Multiplexing?
Multiplexing is the set of techniques that allows simultaneous transmission of multiple signals across a single channel or a single link

24. In the above diagram, lines on the left side directs their transmission stream to a multiplexer (MUX), which combine them into a single stream (many to one).
At the receiving end, the stream is fed to the demultiplexer (DEMUX), which separate the stream back into component transmissions (one to many) and direct them to their corresponding lines

25. A multiplexer is a communications device that multiplexes (combines) several signals for transmission over a single medium.
A demultiplexer completes the process by separating multiplexed signals from a transmission line.
Frequently a multiplexer and demultiplexer are combined into a single device capable of processing both outgoing and incoming signals.
A multiplexer is sometimes called a MUX and demultiplexer is called DEMUX

26. Multiplexing versus No Multiplexing
Multiplexing means dividing available bandwidth of a link between several users. Partitioning a link into several channels.
In a each pair has got its own link. If the total BW of each link is not utilized, a portion of that BW is being wasted.

27. Categories of Multiplexing

28. Frequency Division Multiplexing (FDM)
Frequency division multiplexing, a multiplexing technique that uses different frequencies to combine multiple streams of data for transmission over a communications medium.
FDM assigns a discrete carrier frequency to each data stream and then combines many modulated carrier frequencies for transmission.
In FDM, signals to be transmitted must be analog signals. Thus digital signals need to be converted to analog form, if they are to use FDM.
For example, television transmitters use FDM to broadcast several channels at once.  

29. Frequency Division Multiplexing
FDM is being used when the BW of the link is greater than the bandwidths of the signals to be transmitted.
In FDM, signals generated by each sending device modulates different carrier signal.
The modulated signals are then combined into a single composite signal that can be transported by the link

30. FDM Multiplexing Process, Time Domain
In FDM channels must be separated by strips of unused BW or guard bands, to prevent signals from overlapping

31. FDM Demultiplexing example

32. Example 1 of FDM
Assume that a voice channel occupies a bandwidth of 4 kHz. We need to combine three voice channels into a link with a bandwidth of 12 kHz, from 20 to 32 kHz. Show the configuration, using the frequency domain. Assume there are no guard bands.
Solution
We shift (modulate) each of the three voice channels to a different bandwidth, as shown in Figure below. We use the 20- to 24-kHz bandwidth for the first channel, the 24- to 28-kHz bandwidth for the second channel, and the 28- to 32-kHz bandwidth for the third one. Then we combine them as shown in Figure below.

33. Figure Example 1 of FDM

34. Example 2 of FDM
Five channels, each with a 100-kHz bandwidth, are to be multiplexed together. What is the minimum bandwidth of the link if there is a need for a guard band of 10 kHz between the channels to prevent interference?
Solution
For five channels, we need at least four guard bands. This means that the required bandwidth is at least
5 × × 10 = 540 kHz,
as shown in Figure below.

35. Figure for Example 2 of FDM

36. Analog hierarchy

37. Advantages of FDM:
A large number of signals (channels) can be transmitted simultaneously.
FDM does not need synchronization between its transmitter and receiver for proper operation.
Demodulation of FDM is easy.
Disadvantages of FDM:
FDM suffers from the problem of crosstalk.

38. Applications of FDM
FDM is used for FM & AM radio broadcasting. Each AM and FM radio station uses a different carrier frequency. In AM broadcasting, these frequencies use a special band from 530 to 1700 KHz. All these signals/frequencies are multiplexed and are transmitted in air. A receiver receives all these signals but tunes only one which is required. Similarly FM broadcasting uses a bandwidth of 88 to 108 MHz
FDM is used in television broadcasting.
First generation cellular telephone also used FDM.

39. Time Division Multiplexing (TDM)
TDM is a digital multiplexing technique for combining several low-rate channels into one high-rate one.
Time Division Multiplexer 
TDM a type of multiplexing that combines data streams by assigning each stream a different time slot in a set.
TDM repeatedly transmits a fixed sequence of time slots over a single transmission channel.

40. Time Division Multiplexing
TDM allows only one user at a time to transmit, and the sharing of the medium is accomplished by dividing available transmission time among users.
Here, a user uses the entire BW of the channel, but only for a brief moment.

41. Synchronous TDM: Time Slots and Frames
In STDM, the data flow of each input connected is divided into units.
Each input occupies one input time slot.
A unit can be 1 bit, one character, or one block of data
Each input unit becomes one output unit and occupies one output time slot that is if there are n sending devices, there will be n slots in frame i.e. one slot for each device

42. Time Slots and Frames
The input slot is T and the output slot is T/n where n is the number of connections (channels)
Means, a unit in the output connection has shorter duration; it travel faster.
From the diagram above: the data rate of the link is 3 time the data rate of the connection

43. Synchronous TDM: Time Slots and Frames
In TDM, the term synchronous means that the multiplexer allows exactly the same time slots to each device at all times, whether or not a device has something to transmit.
Example: Time slot A is assigned to device A alone and cannot be used by any other device.
Frames: Time slots are grouped into frames. A frame consists of one complete cycle of time slots.

44. Multiplexing Process in STDM
In STDM every device is given the opportunity to transmit a specific amount of data onto the link.
Each device gets its turn in fixed order and for fixed amount of time. This process is known as interleaving.

45. Interleaving

46. Examples of TDM

47. Example 1 on TDM Synchronous time-division multiplexing

48. Example 1 for TDM Synchronous
In Figure above, the data rate for each input connection is 1 kbps. If 1 bit at a time is multiplexed (a unit is 1 bit), what is the duration of (a) each input slot, (b) each output slot, and (c) each frame?
Solution
We can answer the questions as follows:
a. The data rate of each input connection is 1 kbps. This means that the bit duration (Bit Interval -BI) is 1/1000 s or 1 ms. The duration of the input time slot is 1 ms (same as bit duration = BI).

49. Example 1 of TDM Synchronous
b. The duration of each output time slot is one-third of the input time slot. This means that the duration of the output time slot is 1/3 ms.
c. Each frame carries three output time slots. So the duration of a frame is 3 × 1/3 ms, or 1 ms. The duration of a frame is the same as the duration of an input unit.

50. Figure for Example 2 of TDM

51. Example 2 of TDM
Figure above shows synchronous TDM with a data stream for each input and one data stream for the output. The unit of data is 1 bit. Find (a) the input bit duration (BI), (b) the output bit duration, (c) the output bit rate, and (d) the output frame rate.
Solution
We can answer the questions as follows:
a. The input bit duration is the inverse of the bit rate: 1/1 Mbps = 1 μs.
b. The output bit duration is one-fourth of the input bit duration, or ¼ μs.

52. Example 2 of TDM --continue
c. The output bit rate is the inverse of the output bit duration or 1/(4μs) or 4 Mbps. This can also be deduced from the fact that the output rate is 4 times as fast as any input rate; so the output rate = 4 × 1 Mbps = 4 Mbps.
d. The frame rate is always the same as any input rate. So the frame rate is 1,000,000 frames per second. Because we are sending 4 bits in each frame, we can verify the result of the previous question by multiplying the frame rate by the number of bits per frame.

53. Example 3 TDM
Four channels are multiplexed using TDM. If each channel sends 100 bytes/s and we multiplex 1 byte per channel, show the frame traveling on the link, the size of the frame, the duration of a frame, the frame rate, and the bit rate for the link.
Solution
The multiplexer is shown in Figure next slide. Each frame carries 1 byte from each channel; the size of each frame, therefore, is 4 bytes, or 32 bits. Because each channel is sending 100 bytes/s and a frame carries 1 byte from each channel, the frame rate must be 100 frames per second. The bit rate is 100 × 32, or 3200 bps.

54. For Example 3

55. Asynchronous TDM
Asynchronous TDM also known as statistical TDM, transmit data only from active users and does not transmit empty time slots.
To transmit data only from active users only, multiplexor creates a more complex frame that contains data only from those input source that have something to send.
With Asynchronous TDM single data of streams are classified in variable time segments and subsequently transmitted using the asynchronous TDM procedures.

56. Asynchronous TDM
It is also known as statistical time division multiplexing.
Asynchronous TDM is called so because is this type of multiplexing, time slots are not fixed i.e. the slots are flexible.
Here, the total speed of input lines can be greater than the capacity of the path.
In synchronous TDM, if we have n input lines then there are n slots in one frame. But in asynchronous it is not so.
In asynchronous TDM, if we have n input lines then the frame contains not more than m slots, with m less than n (m < n).
In asynchronous TDM, the number of time slots in a frame is based on a statistical analysis of number of input lines.

58. Multiplexing and inverse multiplexing

59. Transmission Impairment
Transmission Media
and
Transmission Impairment