高频电子技术

2.1.3 The Maximum Data Rate of a Channel
As early as 1924, an AT&T(美国电话电报公司 ) engineer, Henry Nyquist, realized that even a perfect channel has a finite transmission capacity. He derived an equation expressing the maximum data rate for a finite bandwidth noiseless channel. In 1948, Claude Shannon carried Nyquist’s work further and extended it to the case of a channel subject to random (that is, thermodynamic(热力学的)) noise. Nyquist proved that if an arbitrary signal(随机信号) has been run through a low-pass filter of bandwidth H, the filtered signal can be completely reconstructed by making only 2H(exact) sample per second.
Chapter 2
The Physical Layer
The hybrid reference model to be used in this book. The physical layer defines the mechanical(机械), electrical(电 气), and timing interfaces(定时接口) to the network. Contents of the chapter: 1. theoretical analysis of data transmission. 2. three kinds of transmission media: guided (copper wire and fiber optics), wireless (terrestrial radio), and satellite. 3. three examples of communication systems.
2.2 Guided Transmission Data
The purpose of the physical layer is to transport a raw bit stream(原始比特流 from one machine to another. 原始比特流) 原始比特流 Various physical media(物理介质) can be used for the actual transmission. Each one has its own niche(合适的位置) in terms of bandwidth, delay, cost, and ease of installation and maintenance.
2.2.1 Magnetic Media (磁性媒体)
One of the most common ways to transport data from one computer to another is to write them onto magnetic tape or removable media (可移动存储媒体 (e.g., recordable DVDs), 可移动存储媒体) 可移动存储媒体 physically transport the tape or disks to the destination machine, and read them back again.
So the function is:
gb (t ) = u (t − 1) − u (t − 3) + u (t − 6) − u (t − 7)
2.1.2 Bandwidth-Limited Signals
So the Fourier analysis of this signal yields（产生） the coefficients（系数 ）: 1 an = [cos(πn / 4) − cos(3πn / 4) + cos(6πn / 4 ) − cos(7πn / 4)] πn 1 bn = [sin (3πn / 4) − sin (πn / 4) + sin (7πn / 4) − sin (6πn / 4)] πn c = 3/ 4
T
2 c= T
∫
0
g (t )dt
2.1.2 Bandwidth-Limited Signals
An example: the transmission of the ASCII character ‘b’ encoded in an 8-bit byte. The bit pattern that is to be transmitted is 01100010. the figure below shows the voltage output by the transmitting computer.
2.1.3 The Maximum Data Rate of a Channel
If the signal consists of V discrete levelLeabharlann Baidu, Nyquist’s theorem states: max imum data rate = 2 H log 2 V bits / sec For example, a noiseless 3-KHz channel cannot transmit binary (two-level) signal at a rate exceeding 6000bps. So far we have considered only noiseless channels. If random noise is present, the situation deteriorates(恶化) rapidly. And there is always random noise present due to the motion of the molecules in the system. The amount of thermal noise present is measured by the ratio of the signal power to the noise power, called the signal-to-noise ratio. If we denote(以…为符号) the signal power by S and the noise power by N, the signal-to-noise ratio is S/N. Usually, the ratio itself is not quoted(引用); instead, the quantity 10log10S/N is given. These units are called decibels (dB).
2.1.3 The Maximum Data Rate of a Channel
Shannon’s major result is that the maximum data rate of a noisy channel whose bandwidth is H Hz, and whose signal-to-noise ratio is S/N, is given by
2.1 The Theoretical Basis for Data Communication
Information can be transmitted on wires by varying(改变) some physical property such as voltage(电压) or current(电流). f(t)----a single-valued function(单值函数) to representing the value of voltage or current. So we can model the behavior of the signal(对信号的状态建 模) and analyze it mathematically(数学分析).
1 g (t ) = c + 2
∑ a sin(2πnft ) + b cos(2πnft ) (2-1)
n n n =1
∞
Fourier series
1 f = , is the fundamental frequency (基频，基波). T
an and bn are the sine and cosine amplitudes(幅度) of the nth harmonics (谐波). c is a constant.
T
∫
0
0, for k ≠ n sin( 2πkft ) sin( 2πnft )dt = T / 2, for k = n
Only one term of the summation survives: an, The bn summation vanished completely. In the same way, we can derive bn.
T
an =
2 T
∫
0
T
g (t ) sin( 2πnft )dt
bn =
2 T
∫
0
g (t ) cos(2πnft )dt
2.1.1 Fourier Analysis
By just integrating both sides of the equation as it stands, we can find c.
2.1.1 Fourier Analysis
A data signal that has a finite duration can be handled by just imagining that it repeats the entire pattern over and over forever (i.e, the interval from T to 2T is the same as from 0 to T, etc.). The an amplitudes can be computed for any given g(t) by multiplying both sides of Eq.(equation，公式)(2-1) by sin(2Πkft) and then integrating from 0 to T. Since
max imum number of
bits / sec = H log 2 (1 + S / N )
For example, a channel of 3000-Hz bandwidth with a signal to thermal noise ratio of 30 dB can never transmit much more than 30,000bps. Shannon’s result was derived from information-theory arguments and applies to any channel subject to thermal noise.
2.1.1 Fourier Analysis
In the early 19th century, the French mathematician Jean-Baptiste Fourier proved that any reasonably behaved periodic function(周期信 号), g(t) with period T can be constructed as the sum of a (possibly infinite) number of sines and cosines: