27 The effect of amplitude modulation is to lift the baseband frequency to the carrier frequency level, a much higher one. Once the frequency becomes higher, its corresponding wavelength becomes smaller. An antenna is now possible.
28 After we receive, how can we take out of it? Answer: Multiply by.
35 This inner product property gives us the fundamental mechanism of detecting 1 or 0. Let the sent signal be denoted as. We perform two inner products: and Decision rule: If, say that 1 is sent. If, say that 0 is sent.
36 Suppose that we have two bits to send. Can we bundle them together and send the bundled result at the same time? Answer: Of course, we can.
37 Let the two bits be demoted as and. or 0. Let if Let if
38 The sent signal is Our job is to determine the values of and.
40 Can we bundle 256 bits together and send them at the same time? Answer: Yes, as along as the signals are orthogonal to one another. This is the basic principle of ADSL: OFDM (Orthogonal Frequency Division Method).
41 Can we extend the above idea to two users case? Answer: We can.
42 Let User 1 use to represent 1 and to represent 0. Let User 2 use to represent 1 and to represent 0. if i=j and if i j. and are orthogonal.
43 The sent signal is denoted as where and. To determine, we perform inner products:
44 Fig. 11 Signature Signals Generated from Hadamand matrix H 8. All of the signals are orthogonal to each other.
45 We can also view the problem as a vector analysis problem. Assume that User 6 sends 1 and User 8 sends 0.
46 V6=(1,-1,1,-1,-1,,1,-1,1) V8=(1,1,-1,-1,-1,-1,1,1) The inner product of v6 and v8 is 1-1-1+1+1-1-1+1=0
48 This is the principle of CDMA (code division multiple access). It can be extended to more than two users. It was used by the military as an encryption method before.
49 Suppose we send a signal entirely in digital form, can we say that this signal is an analog signal? Yes, we can because according to Fourier series analysis, a pulse also contains a set of cosine functions.
52 Obviously, the smaller the pulse-width is, the more frequency components it contains. One may even say that the smaller the pulse-width is, the more information it may contain. Note that if a pulse has a small pulse-width, it means that within a second, a large number of pulses can be sent. This corresponds to high bit rate. Now, we know why a wire which has a high bit rate may be called broadband.
53 It is important to observe the following: Bits are represented by analog signals. There are no digital signals in the world.
54 It iIt i Maxwell s Equations Equations Concerning with Electromagnetic Waves
55 Electric Field Induced by Charges Fig. 12 Coulomb s Law.
56 Magnetic Field Induced by a Current Segment Fig. 13 Magnetic Flux Density Induced by a Current.
57 Do the electric field and magnetic field affect each other? No, not in the static field. Yes, if the fields are time-varying.
77 In ancient times, human beings built spectacular buildings. But, modern communications systems were possible only recently. Why? Answer: Modern communication systems can not exist without sophisticated mathematics.