Fundamentals of Communication Theory

1. Fundamentals of Communication Theory Ya Bao Contact message: Room: T700BTelephone: 020 7815 7588Email: baoyb@sbu.ac.uk Assessment: 3-hour written examination – 70%Lab accessed report – 30% (by lab tutor) Website: http://eent3.sbu.ac.uk/staff/baoyb/foct/ Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

2. Introduction of the unit • This unit consists of five topics: • Signals and processes. • Fourier analysis and applications • Random signals and processes • Correlation processes. • Electrical noise Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

3. Chapter One. Signals and processes • Learning outcomes You will be expected to know: • the definitions of deterministic and non-deterministic signals; • mathematical representations of deterministic signals; • the idea of power and energy signal and methods to calculate these parameters; • processes of multiplication, and convolution of time signals. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

4. 1.1 Introduction A Communication System Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

5. 1.2 Sinusoidal expressions • Sinusoidal signal Note: ω=2πf Or, or Where: A is the sinusoid's amplitudeω is the angular velocity of the sinusoid in radian/s, θ is an arbitrary phase in radian. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

6. Time domain graph Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

7. Frequency domain spectra Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

8. 1.3 Classification of signals • Energy signals, Power signals An energy signal is a pulse-like signal that usually exits for only a finite interval of time or has a major portion of its energy concentrated in a finite time interval. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

9. 1.3 Classification of signals (cont1) Anenergy signalis definedto be one fro which the Is finite even when the time interval becomes infinite; i.e., when Average power dissipated by the signal f(t) Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

10. 1.3 Classification of signals (cont2) • Power signal Then the signal f(t) has finite average power and is called a power signal. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

11. 1.3 Classification of signals (cont3) • Periodic, Nonperiodic (aperiodic) A periodic signal is one that repeats itself exactly after a fixed length of time. T – period, it define the duration of one complete cycle of f(t) If energy/cycle is finite then it is power signal. Any signal for which there is no value of period T is said nonperiodic (or aperiodic) signal. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

12. 1.3 Classification of signals (cont4) • Deterministic, non-deterministic (random) Deterministic signal: no uncertainty in its values. • an explicit mathematical expression can be written Random signal: some degree of uncertainty before it actual occurs. (discussed later) • A collection of signals, each of which is different e.g. uncertain starting phase • Future values of the signal may not be predictable. E.g. noise Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

13. 1.4 Multiplication and Convolution • Multiplication in frequency domain is convolution in time domain. • Convolution in frequency domain is multiplication in time domain. • Convolution may be defined Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

14. 1.4 Convolution (con1)-- example • Example: Convolve the two signals g(t) and h(t) in (a) Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

15. 1.4 Convolution (con2)– solution of example • Step 1 Introduce a dummy variable to form g(u) and h(u) F(b) • Step 2 Form g(t-u), F(c). • Step 3 F(d). Place g(t-u) and h(u) on a common set of axes. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

16. 1.4 Convolution (con3)– solution of example • Three distinct regimes: Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

17. 1.4 Convolution (con4)– solution of example • Step 4 Determine the convolution Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

18. 1.4 Convolution (con5)– solution of example Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

19. 1.4 Convolution (con6)– solution of example • The results may be sketched to show pictorially the effect of convolving g(t) and h(t) Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

20. 1.5 Properties of Convolution • Commutative Law Distributive Law Associative Law Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

21. exercise • Find the convolution of the rectangular pulse f1(t) and the triangular pulse f2(t) show in following Fig. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

22. 1.6 Analogue Filters Filter: a circuit that place a a limit upon the range of frequencies it will pass, and rejects any frequencies that fall outside this range. Low pass, high pass, band pass, band stop (notch) Commonly used in communication systems. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/

23. By Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct

24. Bandwidth of a system Bandwidth W -- the interval of positive frequencies over which the magnitude H(w) remains within –3dB. Ya Bao http://eent3.sbu.ac.uk/staff/baoyb/foct/