Communication Systems Engineering Episode 3 Part 3 doc

... F[(t)] = ∫ −∞ δ (t)e − jft dt = e 0 = 1 δ () t δ () ⇔ 1 0 Eytan Modiano Slide 4 1 Lecture 3: The Sampling Theorem Eytan Modiano AA Dept. Eytan Modiano Slide 1 The Fourier Transform ... f )e jft df • Notation: X(f) = F[x(t)] X(t) = F-1 [X(f)] x(t) � X(f) Eytan Modiano Slide 3 Notes about Sampling Theorem • When sampling at rate 2W the reconstruction filter must be a ....

Ngày tải lên: 07/08/2014, 12:21

... group transmits (1,2 ,3, 4) (1,2 ,3) 4 success collision (2 ,3) collision idle collision (2 ,3) success success Notice that after the idle slot, collision between (2 ,3) was sure to happen ... first success is 2, so the expected number of slots to transmit 2 packets is 3 slots Throughput over the 3 slots = 2 /3 – In practice above algorithm cannot really work Cannot as...

Ngày tải lên: 07/08/2014, 12:21

... – Soon we will learn that you only need H(Q) bits ∆ − ∆ R 1 R 2 R 3 R 4 q 1 = -3 /2 q 4 = 3 /2 q 2 =∆/2 q 3 =∆/2 Eytan Modiano Slide 8 Sampling • Sampling provides a discrete-time ... / 2 x 2 f (x)dx = ∆ ∫ −∆ / 2 x 2 dx = 12 1 A 2 A 2 [] = 2 A ∫ − A xdx = 3 A 2 / 3 A 2 / 3 SQNR = ∆ 2 / 12 = ( 2 AN) 2 / 12 = N 2 ,(∆ = 2 A / N) / Eytan Mo...

Ngày tải lên: 07/08/2014, 12:21

Ngày tải lên: 07/08/2014, 12:21

Ngày tải lên: 07/08/2014, 12:21

... 1-May L22 6-May L 23 8-May L24 13- May L25 15-May L26 5/19 - 5/ 23 Topic Reading Packet communications, DLC, error checking using CRC Tanenbaum 3 ARQ techniques Tanenbaum 3. 4, 3 Multiple access: ... times: Tuesdays and Thursdays • Text: Communications Systems Engineering, Proakis and Salehi • Grading – 10% weekly Homework Assignments – 30 % each of 3 exams – Fin...

Ngày tải lên: 07/08/2014, 12:21

... ∑ P i Log ( ) ≤ ∑ P i Log(M) = Log(M) i=1 P i i=1 Eytan Modiano Slide 6 1 16 .36 : Communication Systems Engineering Lecture 2: Entropy Eytan Modiano Eytan Modiano Slide 1 HX px HX ... rule: H(X 1 , , X n ) = H(X 1 ) + H(X 2 |X 1 ) + H(X 3 |X 2 ,X 1 ) + …+ H(X n |X n-1 …X 1 ) 2. H(X,Y) = H(X) + H(Y|X) = H(Y) + H(X|Y) 3. If X 1 , , X n are independent then: H(X...

Ngày tải lên: 07/08/2014, 12:21

... {2,2,2 ,3, 3}, (verify that Kraft inequality holds!) n 1 n 2 n 3 n 4 n 5 Eytan Modiano Slide 11 Huffman code example A = {a 1 ,a 2 ,a 3 , a 4 , a 5 } and p = {0 .3, 0.25,0.25, 0.1, 0.1} a 1 0 .3 a 2 ... 0.1} a 1 0 .3 a 2 0.25 a 3 0.25 a 4 0.1 a 5 0.1 0 .3 0.25 0.25 0.2 0 .3 0.25 0.45 + + + 0.55 0.45 + 1.0 1 0 0 1 0 1 0 1 Letter Codeword a 1 11 a 2 10 a 3 01 a 4 001...

Ngày tải lên: 07/08/2014, 12:21

... M − 1 , K = [( [( y 3 3 M E = 2 ( M − 1 ) E s 3 g Transmitted energy = E s = ( M − 1 ) E g 2 3 E b ( QAM ) = Energy / bit = ( M − 1 ) E g 3Log 2 () M • Compare to ... , A m ∈ { + / − 1 } x y 16 − QAM ⇒ A m , A m ∈ { + / − 1, + / − 3 } Eytan Modiano Slide 16 -3 -1 1 3 -3 -1 1 3 Bandpass signals • To transmit a baseband signal S(t) throu...

Ngày tải lên: 07/08/2014, 12:21

...    Probability of error for M-PAM M 2 − 1 M 2 − 1 E av = 3 E g => E bav = 3Log 2 () E g M E = 3Log 2 () E bav M g M 2 − 1  Log M M E bav − 2 2 0 6 1 () ... = 2 Q  sin( π / M), P eb = es    Log 2 ()M Eytan Modiano Slide 29 Noise in communication systems S(t) Channel r(t) = S(t) + n(t) r(t) n(t) • Noise is additional “unwanted” ......

Ngày tải lên: 07/08/2014, 12:21