Post on 03-Feb-2016
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Mr. Thilak de Silva.BSc. Eng., MSc, CEng, FIE(SL), FIET(UK), CITP(UK), MBCS(UK), MIEEE (USA)
M.Sc. in IT - Year 1 Semester II - 2012
Analog and Digital Signals.Periodic and Non-periodic signals.Time domain and Frequency domain
representation.Fourier AnalysisNyquest theorem.
M.Sc. in IT - Year 1 Semester II - 2012
At the end of this session you will have a broad understanding of Analog and Digital signals, Fourier Analysis and Nyquest theorem.
M.Sc. in IT - Year 1 Semester II - 2012
Data is in memory. It is converted in to Signals When
transmitting Need a transmission media to transmit
signals.
Signals can be divided as,▪ Analog Signals, Digital Signals▪ Periodic Signals, Non Periodic Signals
M.Sc. in IT - Year 1 Semester II - 2012
Analog signals are continuous and has infinitely many levels of intensity over a period of time.
Digital signals are discrete and has limited number of levels of intensity over a period of time.
M.Sc. in IT - Year 1 Semester II - 2012
Can be analog or digital.Periodic signals – has a pattern
which repeats over identical periods. (Cycle)
Practically we do not have periodic signals.
Non periodic signals – changes without exhibiting a pattern or cycle that repeats over time.
M.Sc. in IT - Year 1 Semester II - 2012
Periodic analog signal
Non Periodic analog signal
Has 3 parameters, Amplitude Frequency Phase
Time Domain Representation shows changes in signal amplitude with respect to time
Frequency domain representationshow the relationship between amplitude and frequency
M.Sc. in IT - Year 1 Semester II - 2012
A composite signal is made of many sine waves.
Fourier showed that any composite signal is actually a combination of simple sine waves with different frequencies, amplitudes and phases.
These are known as harmonics
M.Sc. in IT - Year 1 Semester II - 2012
A composite periodic Signal
Source - http://train-srv.manipalu.com/wpress/wp-content/uploads/2010/01/clip-image01617.jpg
M.Sc. in IT - Year 1 Semester II - 2012
Use to transform a time domain signal in to frequency components.
Only applicable for periodic signals.According to Fourier analysis any
signal is composed with several frequencies called harmonics.
M.Sc. in IT - Year 1 Semester II - 2012
Fundamental frequency – f(first harmonic)Third harmonic – 3fFifth harmonic – 5f …
Source - http://train-srv.manipalu.com/wpress/wp-content/uploads/2010/01/clip-image01814.jpg M.Sc. in IT - Year 1 Semester II - 2012
Range of frequencies / Difference between the highest and lowest frequencies
Source - http://train-srv.manipalu.com/wpress/wp-content/uploads/2010/01/clip-image02014.jpg M.Sc. in IT - Year 1 Semester II - 2012
When adding two signals the strength of the resulting signal depends on the phase differences, amplitudes, frequencies etc.
Eg:-
In phase (add voltages)
Out phase (deduct voltages)
M.Sc. in IT - Year 1 Semester II - 2012
A digital signal has infinite number of frequency components.
(Bit rate)Speed = 1kb per second
2 ms
F=1/TF=1/2*10F=5ooHzF=0.5Khz
-3
Required Bandwidth (Fundamental frequency) =
½*Bit Rate
T
Bit Pattern = 101010
M.Sc. in IT - Year 1 Semester II - 2012
Bit rate = 1kb per secondBit Pattern = 11001100
F=1/TF=1/4*10F=25oHzF=0.25Khz
-3
Required Bandwidth = 0.25Khz
M.Sc. in IT - Year 1 Semester II - 2012
T
4 ms
At the receiving end the signal is regenerated by looking at the amplitude, IF amplitude is high 1 is generated IF amplitude is low 0 is generated
Therefore we must at least send the fundamental frequency.
That’s why we say that the bandwidth should be at least half of the bit rate.
M.Sc. in IT - Year 1 Semester II - 2012
When frequency getting high the amplitude gets low.
Sending more and more harmonics makes the signal regeneration easy.
But this is expensive due to high bandwidth.
Deciding the number of harmonics we send should be done based on the characteristics of the media.
M.Sc. in IT - Year 1 Semester II - 2012
Periodic Signal Fourier Analysis
Non Periodic Signal Fourier Transform
A Discrete Frequency Spectrum
A Continuous Frequency SpectrumM.Sc. in IT - Year 1 Semester II - 2012
Can have two or more discrete level.
Bit Rate – number of bits sent per second.
Baud rate – signal changing rate per second
Required bandwidth depends on the baud rate.
M.Sc. in IT - Year 1 Semester II - 2012
M.Sc. in IT - Year 1 Semester II - 2012
Source : http://train-srv.manipalu.com/wpress/wp-content/uploads/2010/01/clip-image02214.jpg
We can increase the Bit Rate without increasing the Bandwidth.
But, The error probability is high, Circuit component cost is high, Effect of transmission impairments is
high,
There for we do not use 4 levels practically.
M.Sc. in IT - Year 1 Semester II - 2012
Atténuation DelayNoise Jitter
M.Sc. in IT - Year 1 Semester II - 2012
BitRate = 2 x bandwidth x log2L Assumptions
One signal element carry only one bit No noise, attanuation etc in the
transmission media
If there are noise and attanuation (Shannon Capacity)Capacity = bandwidth x log2(1 +
SNR)M.Sc. in IT - Year 1 Semester II - 2012
If Capacity = 20 Kbp/s &Bit Rate = 3 Kbp/s
Can represent maximum 6 bits per element.
2 = 64 combinations of amplitude or phase differences. (64 QAM)
M.Sc. in IT - Year 1 Semester II - 2012
2 bits per element
6 Kbp/s
3 bits per element
9 Kbp/s
4 bits per element
12 Kbp/s
5 bits per element
15 Kbp/s
6 bits per element
18 Kbp/s
7 bits per element
21 Kbp/s
6
Data Communications and Networking, Forouzan, Chapter 03, 4th Edition
M.Sc. in IT - Year 1 Semester II - 2012
M.Sc. in IT - Year 1 Semester II - 2012