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# Lecture 1 introduction and signals analysis

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### Lecture 1 introduction and signals analysis

1. 1. Introduction to Communication System and Signal Analysis Dr. Khawaja Bilal Mahmood Course: Communication Systems (EL-322)
2. 2. Communication System A Communication system in the most simplest form can be defined as any system which can help with the transmission of useful information from one point to another.
3. 3. Components of Communication System Information Source Transmitter Channel Information User Receiver Typical Block Diagram of a Communication System
4. 4. Telecommunication Telegraph Fixed line telephone Cable Wired networks Internet Fiber communications Communication bus inside computers to communicate between CPU and memory
5. 5. Wireless Communications Satellite TV (Pictures transmission) Cordless phone Cellular phone Wireless LAN, WiFi and Wireless MAN, WiMAX Bluetooth Ultra Wide Band Wireless Laser Microwave GPS Ad hoc/Sensor Networks
6. 6. Analog or Digital Common Misunderstanding: Any transmitted signals are (ANALOG. NO DIGITAL SIGNAL CAN BE TRANSMITTED) The channel we transmit information through is not digital in nature It looks at the signal as voltage waveform as a function of time. Analog Message: continuous in amplitude and over time AM, FM for voice sound Traditional TV for analog video First generation cellular phone (analog mode) Record player Digital message: 0 or 1, or discrete value VCD, DVD 2G/3G cellular phone Data on your disk
7. 7. Power, Distortion, Noise
8. 8. Transmitter Characteristics A carrier signal is required to carry information which can then be transmitted over the channel. Typically, a carrier signal would be a pure sine wave a high frequency signal. This process is called Modulation Could modify the Amplitude of the carrier to get AM Also FM or PM can be achieved by modifying the frequency and Phase of the carrier signal The mathematical expression for the carrier signal will be given on the next slide as
9. 9. Transmitter Characteristics Change parameters of a carrier vam ( t ) = Ac cos ( 2π f c t + θ c ) Information signal: Ac(t) fc(t) θ(t) Analog Digital Ac(t) fc(t) θ(t) : amplitude modulation : frequency modulation : phase modulation Ac(t) and θ(t) ⇒ QAM (Digital) AM FM PM ASK FSK PSK
10. 10. Communication Channel Physical medium Free space Cables Optical fibres Easier to work with Relatively cleaner Less prone to undesired effects as we face in free space Pair of copper wires / coaxial cables offer larger bandwidths A communication channel block also models Channel Attenuation Noise Distortion
11. 11. Noise in Communication Channel Channel is the main source of noise in communication systems Transmitter or Receiver may also induce noise in the system Noise in Communication Systems There are mainly 2-types of noise sources Internal noise source ( are mainly internal to the communication system) External noise source External Noise Sources Natural Man-made
12. 12. Noise in Communication Channel Lightening Discharges Biggest natural source which causes large amounts of EM-radiation It’s a very large magnitude waveform / impulse or A narrow burst of large energy. Very important because they have the potential to interfere over a large frequency range. Since actually it’s a pulse of finite duration The spectrum of a pulse of finite duration is defined by Sinc function If the lightening discharge is of ‘Ƭ’ seconds, the spectrum can be given by This is always b/w +1 to -1 Sinc (f Ƭ) = Sin π f Ƭ πfƬ
13. 13. Noise in Communication Channel Since this is the function of frequency, we will have α 1 / f Also sometimes called atmospheric noise This noise have spectrum which decays with frequency Also this noise affect more at lower frequency bands then at higher frequency bands In time domain This noise is characterised by large amplitude narrow pulses Also called Impulsive noise AM Broadcast Radio (550KHz to 1.6MHz) more affected by this noise FM Broadcast Radio (>50MHz) Not much affected by this noise
14. 14. Noise in Communication Channel Man-made Noise Sources High voltage power-line discharges Electrical motor noise generated by armature and switching taking place in the motor Ignition noise in automobiles and aircraft At Telephone exchanges where switching (electrical) takes place is a source of Impulsive Noise. Radio Frequency Interference (RFI) Many users communicate at the same time High density transmission environment particularly in the context of mobile communication A lot of wireless systems are working in parallel Interference RADAR communication taking place Satellite communications / Wireless and mobile communication etc
15. 15. Noise in Communication Channel Radio Frequency Interference (RFI) Natural Source Due to extra-terrestrial sources Sun and stars are the sources of this noise Internal Noise Sources Fading effects due to multi-paths propagation b/w transmitter and receiver. Constructive or Destructive Thermal Noise Occurs due to interference occurs at the receiver random motion of free electrons in a conductor or a semi-conductor. Tx Rx Even when the voltage is not applied the electrons stays in random motion. Thermal noise is present in almost all electrical component like diodes, resistors, transistors etc. Multi-path Fading effect
16. 16. Noise in Communication Channel Since there are thousands of these components used overall effect of the thermal noise is quite significant. the Shot Noise Random arrival of charged carriers in semiconductor devices i.e. transistor / diodes All active devices have charged carriers The move between junction (PN junctions) This random motion generates Shot Noise Collectively Thermal and Shot Noise can significantly degrade the performance of a communication system
17. 17. Signal Analysis Signal analysis is very important in communication theory and system and circuit design. In order to predict and understand electronic system and circuit behavior, we use the results of mathematical analysis. The most common representation of signals and waveforms is in the time domain. However, most signal analysis techniques work only in the frequency domain.
18. 18. Time & Frequency Domains… In a digital communications link design, a good grounding is needed in the relationship between the shape of a digital waveform in the time domain and its corresponding spectral content in the frequency domain. Time domain signal as a function of time. Analog signal signal’s amplitude varies continuously over time, i.e. no discontinuities. Digital signal data represented by sequence of 0’s and 1’s (e.g., square wave).
19. 19. Time / Frequency Domains The performance of a digital communications link is constrained by two primary factors: Channel Bandwidth how much of the frequency spectrum do we give each user? System Noise both thermal (kTB) and man made! Both of these effects are more evident in frequency domain
20. 20. Time / Frequency Domains A grasp of the frequency content of various types of time domain data signals is key to understand the interaction between: System data / Symbol rate Modulation type Pulse shape and Channel bandwidth It is difficult to extract the above information from the time domain waveform but frequency domain waveform gives all this information.
21. 21. Time domain – Sine Wave zero crossing amplitude (volts) period t time (seconds) frequency = 1/t if t = 1 ms, f= 1 kHz
22. 22. Frequency Domain Signal consists of components of different frequencies. Spectrum of signal: Range of frequencies a signal contains. Absolute bandwidth: Width of signal’s spectrum or spectrum occupied by the signal Bandwidth also refers to the information transmission capability
23. 23. Frequency Domain – Sine Wave amplitude (volts) 1 kHz frequency (hertz)
24. 24. Frequency Domains The frequency domain is simply another way of representing a signal. For example, consider a simple sinusoid
25. 25. Frequency Domain The time - amplitude axes on which the sinusoid is shown define the time plane. If an extra axis is added to represent frequency, then the sinusoid would be
26. 26. Frequency Domain Analysis The frequency - amplitude axes define the frequency plane in a manner similar to the way the time plane is defined by the time - amplitude axes. The frequency plane is orthogonal to the time plane, and intersects with it on a line which is the amplitude axis. The actual sinusoid can be considered to be as existing some distance along the frequency axis away from the time plane. This distance along the frequency axis is the frequency of the sinusoid, equal to the inverse of the period of the sinusoid.
27. 27. Frequency Analysis • Fast & efficient insight on signal’s building blocks. • Simplifies original problem – • Powerful & complementary to time domain analysis techniques. • Several transforms in DSPing: Fourier, Laplace, z, etc. • Based primarily on Fourier series & Transform analysis time, t General Transform as problemproblem-solving tool frequency, f F S(f) = F[s(t)] s(t) synthesis s(t), S(f) : Transform Pair
28. 28. Time Domain Representation Can Only Seldom Reveal Small Signal Impairments
29. 29. Frequency Domain Representation of the Same Signal Reveals More!
30. 30. Spectrum Examples Time Domain Frequency Domain
31. 31. The Phasor: Definition The Phasor is a complex number that carries the amplitude and phase angle information of a sinusoidal function. Euler’s identity 1 jθ e + e − jθ 2 1 jθ sin θ = − j e − e − jθ 2 e jθ = cosθ + j sin θ e ± jθ = cosθ ± j sin θ cos θ = ℜ{e jθ } jθ sin θ = ℑ{e } cosθ = [ ] [ Real e − jθ = cosθ − j sin θ Imaginary v = Vm cos( t +φ) = Vmℜ{e ω ] j (ωt +φ ) jωt jφ } = Vmℜ{e e }
32. 32. The Phasor v = ℜ{Vm e jφ e jωt } Complex number that carries the amplitude and phase angle of the given sinusoidal function. Phasor Transform V = Vm e jφ = Ρ{Vm cos(ωt + φ )} (polar form) Phasor transform of Vmcos(ωt+φ) ω φ The Phasor transform transfers the sinusoidal function from the time domain to the complex-number domain (the frequency domain), since the response depends on ω. V = Vm cos φ + jVm sin φ (rectangular form)
33. 33. Complex Exponential
34. 34. Phasor Signals and Spectra (cont.) A sinusoid is usually represented by a complex exponential or Phasor form Euler’s Theorem: e ± j θ = c o s θ ± j s i n θ Theorem: −1 and θ is an arbitrary angle where j θ = ω0t + φ , then any sinusoid can be written Let as the real part of a complex exponential: exponential: e j (ω0t +φ )  A cos(ω0t + φ ) = A Re    Ae jφ e jω0t  = Re  
35. 35. Phasor Signals and Spectra (cont.) The diagram shows a Phasor representation of a signal because the term inside the brackets may be viewed as a rotating vector in a complex plane whose axes are the real and imaginary parts. The phasor has length A, rotate countercounter-clockwise at a rate f0 revolution per second, and at time t = 0 makes an angle φ with respect to the positive real axis. The three parameters that completely specifies a phasor: phasor: 1) Amplitude; Amplitude; 2) Phase angle; and angle; 3) Rotational frequency Phasor representation
36. 36. Phasor Signals and Spectra (cont) To describe the same phasor in the frequency domain, the domain, corresponding amplitude and phase must be associated with the particular frequency, f0, giving us the LINE SPECTRA. SPECTRA. (Line spectra have great conceptual value when extended to more complicated signals) Amplitude Spectrum Phase Spectrum
37. 37. Line Spectra
38. 38. Basic Identities
39. 39. Fourier Series and Fourier Transform Fourier series representation for periodic signals Fourier transform for general periodic and nonnon-periodic signals
40. 40. Fourier Series and Fourier Transform Defined for periodic signals. Periodic signals repeats themselves over time and given by property x (t+To) = x(t) for all values of T0
41. 41. Reading Assignment Go through Time and frequency domain concepts Fourier Transforms and FFTs in your own time. Check Bruce Carlson or Haykin’s books for further reading