1. Physical Layer: Data and Signals
: Data Communication and Computer Networks
Asst. Prof. Chaiporn Jaikaeo, Ph.D.
Computer Engineering Department
Kasetsart University, Bangkok, Thailand

2. Outline Analog and digital data/signals
Time and frequency domain views of signals
Bandwidth and bit rate
Transmitting digital signals as analog
Theoretical data rate
Signal impairment

3. Analog vs. Digital Data Analog data Digital data
Data take on continuous values
E.g., human voice, temperature reading
Digital data
Data take on discrete values
E.g., text, integers

4. Analog vs. Digital Signals
To be transmitted, data must be transformed to electromagnetic signals
Analog signals
have an infinite number of values in a range
Digital signals
Have a limited number of values
value
time
value
time

5. Data and Signals Analog Data Analog Signal Digital Data Analog Signal
Telephone
Analog Data
Analog Signal
Modem
Digital Data
Analog Signal
Codec
Analog Data
Digital Signal
Digital transmitter
Digital Data
Digital Signal

6. x(t) = x(t+T) - < t < 
Periodic Signals
A periodic signal completes a pattern within a timeframe, called a period
A signal x(t) is periodic if and only if
x(t) = x(t+T) - < t < 
value
time
period

7. Sine Waves Simplest form of periodic signal
General form: x(t) = A×sin(2ft + )
period T = 1/f
peak amplitude
time
signal strength
phase / phase shift

8. Varying Sine Waves A = 1, f = 1,  = 0 A = 2, f = 1,  = 0

9. Time vs. Frequency Domains
Consider the signal + =
Demo: sine.py

10. Time vs. Frequency Domains1 -1 2 4
time
signal strength 1 -1 2 4
signal strength
frequency
Time Domain Representation
 plots amplitude as a function of time
Frequency Domain Representation
 plots each sine wave’s peak amplitude against its frequency
Demo: Equalizer

11. Fourier Analysis
Joseph Fourier ( )
Any periodic signal can be represented as a sum of sinusoids
known as a Fourier Series
E.g., a square wave: = +
+ …

12. Fourier Analysis Every periodic signal consists of DC component
AC components
Fundamental frequency (f0)
Harmonics (multiples of f0)
fundamental frequency
3rd harmonic
5th harmonic …
DC component
AC components

13. Fourier Series: Representations
Amplitude-phase form
Sine-cosine form
Complex exponential form (Euler formula)
Note:
cn are complex
j = -1
ejx = cos x + j sin x
Demo: Falstad

14. Fourier Series: Representation
Sine-cosine representation

15. Fourier Series: Representation
Amplitude-phase representation

16. Fourier Series: Representation
Euler formula representation
Note the Euler's Formula:
eix = cos x + i sin x

17. Aperiodic Signals
Consider a pulse train of period T, and the width of each pulse is  t
x(t) T
/2
-/2

18. Aperiodic Signals t x(t) T f X(f) f0 t x(t) T f X(f) f0 t x(t) T =  f

19. The time and frequency domains of a nonperiodic signal

20. Frequency Spectrum
Frequency domain representation shows the frequency spectrum of a signal
E.g., square wave f0
3f0
5f0
7f0
9f0
11f0
...

21. Bandwidth A property of a medium Also a property of a single spectrum
Indicates the difference between the highest and the lowest frequencies allowed to pass
<highest freq allowed> – <lowest freq allowed>
Also a property of a single spectrum
Cutoff frequency
(half of power is lost)

22. Bandwidth of a Medium f f Transmission medium t t 1 (low-pass channel)
gain
freq f0
3f0
5f0
7f0
...
9f0 f f0
3f0
5f0 f
Transmission medium t t

23. Example What is the bandwidth of this signal?
A medium can pass frequencies from 4000 to 7000 Hz. Can the above signal pass through?

24. Digital Signals Properties: Bit rate – number of bits per second
Bit interval – duration of 1 bit 1
...
time
amplitude
bit interval

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

26. The time and frequency domains of periodic and nonperiodic digital signals

27. Baseband transmission
 Sending a digital signal over a channel without changing it to an analog signal
Baseband transmission requires a low-pass channel

28. Note
A digital signal is a composite analog signal with an infinite bandwidth.

29. Baseband transmission using a dedicated medium

30. Digital vs. Analog Using one harmonic Bit rate = 6 Digital f = 01
1 sec
Bit rate = 6
Digital 1
f = 0
Analog 1
Bit rate = 6
Digital 1
f = 3
Analog

31. Digital vs. Analog Using more harmonics
Adding 3rd harmonic to improve quality 1
Bit rate = 6
Digital 1
f0 = 3, fmax = 9
Analog

32. Table 3.2 Bandwidth requirements

33. Digital vs. Analog Bandwidth
Digital bandwidth
Expressed in bits per second (bps)
Analog bandwidth
Expressed in Hertz (Hz)
Bit rate and bandwidth are proportional to each other

34. Low-Pass and Band-Pass Channels
Low-pass channel
Band-pass channel
frequency f1
gain
frequency f1 f2
gain

35. Modulation of a digital signal for transmission on a bandpass channel

36. Transmission Impairment
Attenuation
Distortion
Noise

37. Signal Attenuation Attenuation  Loss of energy
Signal strength falls off with distance
Attenuation depends on medium
Attenuation is an increasing function of frequency
Transmission medium

38. Relative Signal Strength
Measured in Decibel (dB)
P1 and P2 are signal powers at points 1 and 2, respectively
Positive dB  signal is amplified (gains strength)
Negative dB  signal is attenuated (loses strength)
dB = 10 log10 (P2/P1)
Point 1
Point 2

39. Example
Sometimes the decibel is used to measure signal power in milliwatts. In this case, it is referred to as dBm and is calculated as dBm = 10 log10 Pm , where Pm is the power in milliwatts. Calculate the power of a signal with dBm = −30.
Solution
We can calculate the power in the signal as

40. Example
The loss in a cable is usually defined in decibels per kilometer (dB/km). If the signal at the beginning of a cable with −0.3 dB/km has a power of 2 mW, what is the power of the signal at 5 km?
Solution
The loss in the cable in decibels is 5 × (−0.3) = −1.5 dB. We can calculate the power as

41. Signal Distortion Distortion  Change in signal shape
Only happens in guided media
Propagation velocity varies with frequency

42. Noise
Noise  Undesirable signals added between the transmitter and the receiver
Types of noise
Thermal
Due to random motion of electrons in a wire

43. Noise Types of noise (cont’d) Crosstalk Impulse
Signal from one line picked up by another
Impulse
Irregular pulses or spikes
E.g., lightning
Short duration
High amplitude
Wire 1
Wire 2

44. Signal-to-Noise Ratio
Signal-to-Noise Ratio (SNR)

45. Example
The power of a signal is 10 mW and the power of the noise is 1 μW; what are the values of SNR and SNRdB ?
Solution
The values of SNR and SNRdB can be calculated as follows:

46. Data Rate: Noiseless Channels
Nyquist Theorem
Bit rate in bps
Bandwidth in Hz
L – number of signal levels
Bit Rate = 2 × Bandwidth × log2L
Harry Nyquist ( )

47. Example
We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz. How many signal levels do we need?
Solution
We can use the Nyquist formula as shown:
Since this result is not a power of 2, we need to either increase the number of levels or reduce the bit rate. If we have 128 levels, the bit rate is 280 kbps. If we have 64 levels, the bit rate is 240 kbps.

48. Data Rate: Noisy Channels
Shannon Capacity
Capacity (maximum bit rate) in bps
Bandwidth in Hz
SNR – Signal-to-Noise Ratio
Capacity = Bandwidth × log2(1+SNR)
Claude Elwood Shannon ( )

49. Example
A telephone line normally has a bandwidth of The signal-to-noise ratio is usually Calculate the theoretical highest bit rate of a regular telephone line.
This means that the highest bit rate for a telephone line is kbps. If we want to send data faster than this, we can either increase the bandwidth of the line or improve the signal-to-noise ratio.

50. Example
We have a channel with a 1-MHz bandwidth. The SNR for this channel is 63. What are the appropriate bit rate and signal level?
Solution
First, use the Shannon capacity
followed by the Nyquist formula 6 8

51. Note
The Shannon capacity gives us the upper limit; the Nyquist formula tells us how many signal levels we need.

52. Network Performance Bandwidth Throughput Latency (delay) Hertz
Bits per second (bps)
Throughput
Actual data rate
Latency (delay)
Time it takes for an entire message to completely arrive at the destination

53. Latency Composed of Propagation time Transmission time Queuing time
Processing time
Entire
message
propagation
time
transmission
time

54. Latency Sender Receiver First bit leaves Data bits Propagation time
First bit arrives
Transmission time
Last bit leaves
Last bit arrives
Time
Time

55. Bandwidth-Delay Product
The link is seen as a pipe
Cross section = bandwidth
Length = delay
Bandwidth-delay product defines the number of bits that can fill the link

56. Figure Filling the link with bits for case 1

57. Summary Data need to take form of signal to be transmitted
Frequency domain representation of signal allows easier analysis
Fourier analysis
Medium's bandwidth limits certain frequencies to pass
Bit rate is proportional to bandwidth
Signals get impaired by attenuation, distortion, and noise