Two theorems Nyquist theorem Nyquist proved that for an ideal channel with a bandwidth of W hertz, the maximum symbol (signal) rate is 2W baud. This limitation is due to the presence of intersymbol interference. If the transmitted signal contains M status values ​​(the number of states of the signal is M), then the maximum data transmission rate (channel capacity) that the W hertz channel can carry is: C = 2 & TImes; W & TImes; log 2M (bps) for The fixed channel bandwidth can increase the data transmission rate by increasing the number of different signal units. However, this increases the burden on the receiving end because, each time the receiving end receives a symbol, it no longer distinguishes only one of the two possible signal values, but must distinguish one of the M possible signals. The noise on the transmission medium will limit the actual value of M. The existing transmission channels mainly include analog channels and digital channels. The analog channels are generally only used to transmit analog signals, while the digital channels are generally only used to transmit digital signals. Sometimes, if necessary, it may be necessary to transmit analog signals by digital channels or digital signals by analog channels. In this case, we need to convert the transmitted data to the type of data that the channel can transmit, that is, analog signals and numbers. Signal conversion, which is the main content of coding and modulation. Of course, the problem of how analog data and digital data are transmitted through the channel is also an important part of coding and modulation. In the following, we introduce the modulation and coding of data from analog signals using analog channels, analog signals using digital channels, digital signals using analog channels, and digital signals using digital channels. Four aspects (2) Manchester coding: 0 and 1 are represented by changes in voltage, and hopping occurs in the middle of each symbol. High to low transitions represent 0, and low to high transitions represent 1 (note: some tutorials have opposite descriptions of this section and are correct). A jump occurs in the middle of each symbol, and the receiver can extract this change as a synchronization signal. This type of encoding is also known as the Self-Synchronizing Code. The disadvantage is that double the transmission bandwidth is required (ie the signal rate is twice the data rate). Energy Saving Sewing Machine Motor Energy Saving Sewing Machine Motor,Single Sewing Machine Motor,Industrial Servo Motor,Single Phase Motor LISHUI SHUANGZHENG MOTOR CO.,LTD. , https://www.szservomotor.com
Shannon's theorem Nyquist considers the ideal channel without noise, and Nyquist's theorem states that when all other conditions are the same, the channel bandwidth is doubled and the data transmission rate is doubled. But for noisy channels, the situation will quickly deteriorate. Let us now consider the relationship between data transmission rate, noise and bit error rate. The presence of noise can destroy one or more bits of data. If the data transmission rate is increased, the time taken per bit will be shorter, and therefore the noise will affect more bits, and the bit error rate will be larger. For the transmission of digital data over noisy channels, the signal-to-noise ratio is very important because it sets a reachable data transmission rate upper limit for noisy channels, ie for channels with a bandwidth of W hertz and a signal-to-noise ratio of S/N. The maximum data transmission rate (channel capacity) is: C = W × log 2 (1 + S / N) (bps) Shannon's theorem gives the error-free data transmission rate. Shannon also proved that, assuming that the actual data transmission rate of the channel is lower than the error-free data transmission rate, it is theoretically possible to use an appropriate signal coding to achieve a error-free data transmission rate. Unfortunately, Shannon did not give a way to find this code. It is undeniable that Shannon's theorem does provide a standard for measuring the performance of actual communication systems.
Coding and Modulation Due to the limitations of the transmission medium and its format, the signals of both communicating parties cannot be directly transmitted, and must be processed in a certain way so that it can be adapted to the characteristics of the transmission medium before being transmitted to the destination without error. Modulation refers to the use of analog signals to carry digital or analog data; and coding refers to the use of digital signals to carry digital or analog data. 
1. Analog signals are transmitted using analog channels: Sometimes analog data can be transmitted directly on the analog channel, but this is not commonly used in network data transmission. People still modulate the analog data and then transmit it over the analog channel. The purpose of modulation is to modulate the analog signal onto a high frequency carrier signal for long distance transmission. At present, the existing modulation methods mainly include Amplitude Modulation (AM), Frequency Modulation (FM), and Phase Modulation (PM).
2. The analog signal is transmitted using the digital channel: the analog signal is transmitted on the digital channel. First, the analog signal is converted into a digital signal. The process of the conversion is a digital process, and the digitization process mainly includes two steps of adopting and quantifying. Common methods for encoding analog signals into digital channel transmission are: Pulse Amplitude Modulation (PAM), Pulse Code Modulation (PCM), Differential Pulse Code Modulation (DPCM), and Increment. Pulse Modulation (DM).
3. Digital signal transmission using analog channel: The process of transmitting a digital signal using an analog channel is a modulation process, which is a process of changing the characteristics of an analog signal by digital data represented by a digital signal (binary 0 or 1), that is, binary The process of modulating data onto an analog signal. A sine wave can be defined by three characteristics: amplitude, frequency and phase. When we change any of these features, there is another form of wave. If the original wave is used to represent binary 1, then the deformation of the wave can represent binary 0; vice versa. Any of the three characteristics of the wave can be changed in this way, so that we have at least three mechanisms for modulating digital data into analog signals: Amplitude-Shift Keying (ASK), frequency shifting Frequency-Shift Keying (FSK) and Phase-Shift Keying (PSK). In addition, there is a mechanism that combines amplitude and phase changes called Quadrature Amplitude Modulation (QAM). Among them, quadrature amplitude modulation is the most efficient, and it is also the technology often used in all modems.
4. Digital signals are transmitted using digital channels: if the digital signals are transmitted on a digital channel, the digital signals need to be encoded first. For example, this is generally the case when data is transferred from a computer to a printer. In this manner, the digital signal must first be encoded, i.e., the binary 0 and 1 digital signals produced by the computer are converted into a series of voltage pulses that can be transmitted over the conductor. Encoding the source can reduce the data rate and improve the information efficiency. Encoding the channel can improve the anti-interference ability of the system.
At present, common data coding methods mainly include non-return to zero code, Manchester coding and differential Manchester coding.
(1) Non-return to zero code: The binary digits 0 and 1 are respectively represented by two levels, commonly used -5V for 1, and +5V for 0. The disadvantage is that there is a DC component, the transformer cannot be used in transmission; there is no self-synchronization mechanism, and external synchronization must be used for transmission.
(3) Differential Manchester coding: hopping still occurs in the middle of each symbol, with or without hopping at the beginning of the symbol to indicate 0 and 1. There are jumps that represent 0 and no jumps that represent 1 (note: some tutorials have opposite descriptions about this part and are correct).