象)Si gna Timet Timet Analog Digital Time. t Time t Sampled Quantized Communications Engineering
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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