Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion o Digital transmission through baseband channels Signal space representation o Optimal receivers Digital modulation techniques o Channel coding Synchronization o Information theory Communications Engineering
Communications Engineering 1 Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion Digital transmission through baseband channels Signal space representation Optimal receivers Digital modulation techniques Channel coding Synchronization Information theory
gnal, random variable, random process and spectra Information Output Source Transmitter Channel Receiver Signal uncertain Noise 1州M Communications Engineering
Communications Engineering 2 Signal, random variable, random process and spectra
gnal, random variable, random process and spectra Ignals o Review of probability and random variables o Random processes: basic concepts o Gaussian and white processes Selected from Chapter 2.1-2.6, 5.1-5.3 Communications Engineering
Communications Engineering 3 Signal, random variable, random process and spectra Signals Review of probability and random variables Random processes: basic concepts Gaussian and White processes Selected from Chapter 2.1-2.6, 5.1-5.3
象)Sgnl In communication systems. a signal is any function that carries information. Also called information bearing signal Communications Engineering
Communications Engineering 4 Signal In communication systems, a signal is any function that carries information. Also called information bearing signal
象)Si gna o Continuous-time signal vS. discrete-time signal Continuous-valued signal VS. discrete-valued signal Continuous-time continuous-valued: analog signal Discrete-time and discrete-valued digital signal Discrete-time and continuous-valued: sampled signal Continuous-time and discrete-valued: quantized signal Communications Engineering
Communications Engineering 5 Signal Continuous-time signal vs. discrete-time signal Continuous-valued signal vs. discrete-valued signal Continuous-time continuous-valued: analog signal Discrete-time and discrete-valued: digital signal Discrete-time and continuous-valued : sampled signal Continuous-time and discrete-valued: quantized signal
象)Si gna Timet Timet Analog Digital Time. t Time t Sampled Quantized Communications Engineering
Communications Engineering 6 Signal
象)Sgnl Energy vs. power signal 7/2 Energy Er E=x(odt=lim x(dt T T/2 > Power P=lim「x()at T→∞ A signal is an energy signal iff energy is limited A signal is a power signal iff power is limited Communications Engineering
Communications Engineering 7 Signal Energy vs. power signal ➢ Energy ➢ Power ➢ A signal is an energy signal iff energy is limited ➢ A signal is a power signal iff power is limited
象)Sgnl Fourier transform +∞ X( 2Tft X()em !df Sinc 0) n(↑ 5V1V53 6(0)+ Communications Engineering
Communications Engineering 8 Signal Fourier Transform
MaN)Random variable Review of probability and random variables Two events a and B Conditional probability P(aB) Joint probability P(AB=P(AP(BA=P(BP(AB) A and b are independent iff P(AB=P(APB) >Let A,j=1, 2, n be mutually exclusive events with A∩4=②v≠,U4=92. Then for any event B, we have P(B)=∑P(B∩A) ∑P(BlA)P(A) Communications Engineering
Communications Engineering 9 Random variable Review of probability and random variables ➢ Two events A and B ➢ Conditional probability P(A|B) ➢ Joint probability P(AB)=P(A)P(B|A)=P(B)P(A|B) ➢ A and B are independent iff P(AB)=P(A)P(B) ➢ Let be mutually exclusive events with . Then for any event , we have Aj , j =1,2, ,n = i = i Aj Ai , i j, A B
MaN)Random variable Review of probability and random variables Bayes' Rule: Let A,j=1, 2, . n be mutually exclusive such that UA; =Q2. For any nonzero probability event B we have p(4B)=2(42 P(B P(BLAP(Ai) ∑=1P(B|A)P(A Communications Engineering
Communications Engineering 10 Random variable Review of probability and random variables ➢ Bayes’ Rule: Let be mutually exclusive such that . For any nonzero probability event B, we have Aj , j =1,2, ,n j = j A