📚 Analogue and Digital Signals | 模拟信号与数字信号
In modern physics and communication technology, signals are used to carry information from one place to another. Signals can be classified into two main types: analogue and digital. Understanding their differences, advantages, and limitations is essential for topics such as data transmission, telecommunications, and digital electronics in A-Level Physics.
在现代物理和通信技术中，信号被用来将信息从一个地方传送到另一个地方。信号主要分为两种类型：模拟信号和数字信号。理解它们之间的区别、优点和局限性，对于A-Level物理中的数据传输、电信和数字电子学等主题至关重要。
1. Introduction: What is a Signal? | 引言：什么是信号？
A signal is any physical quantity that varies with time, space, or other variables and carries information. In communication systems, signals can be electrical voltages, electromagnetic waves, or light pulses. The fundamental purpose of a signal is to represent data, such as sound, images, or sensor readings, in a form that can be transmitted over a distance.
信号是随着时间、空间或其他变量变化并携带信息的物理量。在通信系统中，信号可以是电压、电磁波或光脉冲。信号的基本目的是以能够远距离传输的形式来表示数据，例如声音、图像或传感器读数。
A signal is often described mathematically as a function of time, for example V(t) for a voltage signal. The shape of this function determines the type of signal – whether it is analogue or digital.
信号通常用时间函数来数学描述，例如电压信号 V(t)。这个函数的形状决定了信号的类型——是模拟信号还是数字信号。
2. Analogue Signals: Continuous Variation | 模拟信号：连续变化
An analogue signal is continuous in both time and amplitude. It can take any value within a given range. For example, the voltage output from a microphone varies smoothly and continuously to mirror the sound pressure of a voice or music. The wave shape is a direct analogue of the original physical quantity.
模拟信号在时间和幅值上都是连续的，它可以取给定范围内的任何值。例如，麦克风输出的电压平滑连续地变化，以反映人声或音乐的声压。波形是原始物理量的直接模拟。
Common examples of analogue signals include audio signals from a vinyl record player, the varying voltage from a thermocouple measuring temperature, and the amplitude-modulated radio waves used in traditional AM broadcasting.
模拟信号的常见例子包括黑胶唱机输出的音频信号、测量温度的热电偶产生的变化电压，以及传统调幅广播中使用的调幅无线电波。
Because the information is encoded directly in the instantaneous amplitude of the signal, any change in amplitude – whether intended or unintended – alters the information.
由于信息直接编码在信号的瞬时幅值中，幅值的任何变化——无论是有意还是无意——都会改变信息。
3. Digital Signals: Discrete Levels | 数字信号：离散电平
A digital signal consists of a sequence of discrete values. In most digital systems, only two states are used: a high level (often representing binary digit 1) and a low level (binary 0). These states are typically represented by voltage levels, such as +5 V for 1 and 0 V for 0, giving a square-wave-like appearance over time.
数字信号由一系列离散值组成。在大多数数字系统中，只使用两种状态：高电平（通常表示二进制数字1）和低电平（二进制0）。这些状态通常由电压电平表示，例如用 +5 V 代表 1，0 V 代表 0，从而在时间上呈现方波形状。
Unlike an analogue signal, the exact amplitude of a digital signal does not carry the information; it is the timing and sequence of the state changes that convey data. A small voltage fluctuation around the ideal high level does not change the binary value as long as the receiver can still distinguish between high and low.
与模拟信号不同，数字信号的确切幅度并不携带信息；而是状态变化的时间和顺序来传递数据。只要接收器仍能区分高电平和低电平，理想高电平附近的小电压波动并不会改变二进制值。
Digital signals can encode text, numbers, sound, and images by using groups of bits. For instance, in PCM (Pulse Code Modulation), an audio sample is represented by a 16-bit binary number.
数字信号通过使用比特组来编码文本、数字、声音和图像。例如，在脉冲编码调制（PCM）中，一个音频样本由一个16位的二进制数表示。
4. Noise and Its Effect on Signals | 噪声及其对信号的影响
Noise is any unwanted random electrical or electromagnetic disturbance that superimposes on a signal. Sources of noise include thermal agitation of electrons in a conductor, interference from nearby equipment, and cosmic background radiation. Noise is unavoidable in any communication channel.
噪声是任何叠加在信号上的不需要的随机电或电磁干扰。噪声的来源包括导体中电子的热运动、附近设备的干扰以及宇宙背景辐射。在任何通信信道中，噪声都是不可避免的。
In an analogue signal, noise directly degrades the quality of the information because the signal's instantaneous amplitude carries the data. Once noise is added, it is extremely difficult to remove without also distorting the original signal. This leads to a reduction in the signal-to-noise ratio (SNR) and can make quiet passages in music sound hissy or cause 'snow' on analogue television.
在模拟信号中，噪声会直接降低信息质量，因为信号的瞬时幅度携带数据。一旦加入了噪声，要将其去除而不使原始信号失真是非常困难的。这会导致信噪比（SNR）下降，可能使音乐中安静的部分出现嘶嘶声，或在模拟电视上产生“雪花”。
In contrast, a digital signal can tolerate a significant amount of noise. As long as the noise does not push the signal level across the decision threshold that separates a 0 from a 1, the receiver can still correctly identify the intended bit. This gives digital systems a much higher immunity to noise.
相比之下，数字信号可以容忍相当多的噪声。只要噪声没有将信号电平推过区分 0 和 1 的判定阈值，接收器仍能正确识别预期的比特。这使得数字系统具有更高的抗噪声能力。
5. The Need for Digital Communication | 数字通信的必要性
Because analogue signals suffer irreversible degradation from noise over long distances and through multiple amplifiers, modern communication systems have shifted to digital transmission. Digital signals can be regenerated, stored, and processed by computers and microprocessors, offering flexibility that analogue systems cannot match.
由于模拟信号在长距离和经过多级放大器时，会因噪声而发生不可逆的劣化，现代通信系统已转向数字传输。数字信号可以被再生、存储，并由计算机和微处理器处理，提供了模拟系统无法比拟的灵活性。
Additionally, many sources of information today – such as internet data, digital cameras, and computer files – are inherently digital. Even when the original source is analogue (e.g., human voice), converting it to digital at an early stage allows the use of efficient digital signal processing (DSP) and error correction techniques.
此外，当今许多信息源（如互联网数据、数码相机和计算机文件）本质上就是数字的。即使原始信息是模拟的（例如人类语音），在早期阶段将其转换为数字信号，就可以使用高效的数字信号处理（DSP）和纠错技术。
6. Sampling an Analogue Signal | 模拟信号的采样
To convert an analogue signal into a digital one, the first step is sampling. Sampling means measuring the instantaneous amplitude of the analogue waveform at regular time intervals. The sampling rate (or sampling frequency) is the number of samples taken per second, measured in hertz (Hz).
要将模拟信号转换为数字信号，第一步是采样。采样是指以固定的时间间隔测量模拟波形的瞬时幅度。采样速率（或采样频率）是每秒采集的样本数，单位为赫兹（Hz）。
The Nyquist–Shannon sampling theorem is a fundamental principle: to be able to perfectly reconstruct the original analogue signal from its samples, the sampling frequency fₛ must be at least twice the highest frequency fₘ present in the signal. This minimum rate is called the Nyquist rate.
奈奎斯特-香农采样定理是一个基本原理：为了能够从样本中完美重建原始模拟信号，采样频率 fₛ 必须至少是信号中最高频率 fₘ 的两倍。这个最低速率称为奈奎斯特速率。
fₛ ≥ 2fₘ
If the sampling rate is too low, an effect called aliasing occurs, where high-frequency components appear as lower, incorrect frequencies in the reconstructed signal. To prevent aliasing, an anti-aliasing low-pass filter is used before sampling to remove frequencies above half the sampling frequency.
如果采样速率太低，就会发生混叠，高频分量在重建的信号中表现为错误的低频分量。为了防止混叠，在采样之前使用抗混叠低通滤波器来去除高于采样频率一半的频率。
7. Quantization and Digital Encoding | 量化和数字编码
After sampling, the continuous amplitude of each sample must be converted into a discrete digital value. This process is called quantization. The total amplitude range is divided into a finite number of equally spaced levels. The actual sample amplitude is then rounded to the nearest quantization level.
采样之后，每个样本的连续幅度必须转换为离散的数字值。这个过程称为量化。总的幅度范围被划分为有限个等间距的电平。实际的样本幅度然后被四舍五入到最接近的量化电平。
er of levels is 2ⁿ. For example, an 8-bit quantizer provides 2⁸ = 256 levels. Each quantized level is then assigned a unique binary code.
可用的量化电平数量由每个样本使用的比特数决定。如果每个样本使用 n 比特，电平数量为 2ⁿ。例如，8 位量化器提供 2⁸ = 256 个电平。然后为每个量化电平分配一个唯一的二进制代码。
Number of levels = 2ⁿ
Encoding is the final step where the sequence of quantized levels is turned into a stream of binary digits. This bit stream is the digital signal that will be transmitted or stored.
编码是最后一步，量化电平序列被转换为二进制数字流。这个比特流就是要传输或存储的数字信号。
Quantization necessarily introduces a small error because the original amplitude is rarely an exact match to a quantization level. This quantization error (or quantization noise) can be made acceptably small by using a higher bit depth, which increases the number of levels and makes the digital representation more accurate.
量化必然会引入一个小误差，因为原始幅度很少与量化电平完全匹配。通过使用更高的比特深度，增加电平数量，可以使这种量化误差（或量化噪声）变得可以接受，从而使数字表示更加精确。
8. Analogue-to-Digital Conversion (ADC) | 模拟到数字转换
Analogue-to-Digital Conversion (ADC) is the complete process that combines sampling, quantization, and encoding. An ADC circuit takes an analogue input voltage and produces a corresponding binary output number at a rate determined by a clock signal. ADCs are found in devices such as digital audio interfaces, sensor data loggers, and digital oscilloscopes.
模拟到数字转换（ADC）是结合了采样、量化和编码的完整过程。ADC电路接收模拟输入电压，并以时钟信号决定的速率产生相应的二进制输出数字。ADC广泛应用于数字音频接口、传感器数据记录仪和数字示波器等设备中。
Key performance parameters of an ADC include its sampling rate and resolution (the number of bits). For example, a 16-bit ADC can distinguish 65 536 (2¹⁶) different voltage levels, allowing very fine amplitude detail to be captured.
ADC的关键性能参数包括其采样速率和分辨率（比特数）。例如，一个16位的ADC可以区分 65 536（2¹⁶）个不同的电压电平，从而捕获非常精细的幅度细节。
The reverse process, Digital-to-Analogue Conversion (DAC), is used to reconstruct an analogue signal from digital data, for instance when playing a digital music file through a speaker.
相反的过程，即数字到模拟转换（DAC），用于从数字数据重建模拟信号，例如通过扬声器播放数字音乐文件时。
9. Advantages and Disadvantages of Digital Systems | 数字系统的优缺点
Digital communication and storage systems offer several major advantages over analogue systems. The most important is noise immunity: digital signals can be stripped of noise during regeneration, allowing error-free transmission over long distances. Digital data can also be compressed, encrypted, and easily processed by computers. Furthermore, error detection and correction codes can identify and fix bit errors.
数字通信和存储系统与模拟系统相比有几个主要优点。最重要的是抗噪声能力：数字信号在再生过程中可以去除噪声，从而实现长距离的无错误传输。数字数据也可以被压缩、加密，并轻松由计算机处理。此外，错误检测和纠正码可以识别并修复比特错误。
However, digital systems also have limitations. Converting an analogue signal to digital requires an ADC and, if the signal is to be heard or viewed, a DAC, which adds complexity. Digitizing a signal often requires a higher bandwidth than the original analogue signal, especially when using high sampling rates and bit depths. Quantization error and aliasing must be carefully managed.
然而，数字系统也有局限性。将模拟信号转换为数字信号需要ADC，如果要收听或观看信号，还需要DAC，这增加了复杂性。数字化一个信号通常需要比原始模拟信号更高的带宽，尤其是在使用高采样速率和比特深度时。量化误差和混叠必须小心处理。
Despite these trade-offs, the benefits of digital technology – reliability, versatility, and compatibility with computing systems – have driven its widespread adoption in telephony, broadcasting, and data storage.
尽管存在这些权衡，数字技术的好处——可靠性、多功能性和与计算系统的兼容性——已经推动了它在电话、广播和数据存储领域的广泛应用。
10. Regeneration and Error Detection | 再生与错误检测
One of the most powerful features of digital transmission is the ability to regenerate the signal. When a digital pulse travels along a cable or fibre, it gradually weakens and accumulates noise. A regenerator (or repeater) detects the incoming pulses, determines whether each is a 0 or a 1, and then transmits a new, clean pulse with the correct timing. This process completely removes any accumulated noise.
数字传输最强大的特点之一是能够再生信号。当数字脉冲沿着电缆或光纤传播时，它会逐渐减弱并累积噪声。再生器（或中继器）检测到来的脉冲，判断每个脉冲是 0 还是 1，然后以正确的时序发送一个干净的新脉冲。这个过程完全去除了所有累积的噪声。
Because regeneration recreates the signal rather than just amplifying it, there is no build-up of noise over many stages. This contrasts sharply with analogue amplifiers, which always amplify the noise along with the signal.
由于再生是重新创建信号而不只是放大信号，因此不会在许多级联中积累噪声。这与模拟放大器形成鲜明对比，模拟放大器总是将噪声与信号一起放大。
To further protect data, digital systems often incorporate error detection methods. A simple example is the use of a parity bit: an extra bit is added to a group of data bits so that the total number of 1s is always even (even parity) or odd (odd parity). The receiver can then detect if a single-bit error has occurred. More sophisticated techniques like cyclic redundancy checks (CRCs) can detect and sometimes correct multiple errors.
为了进一步保护数据，数字系统通常包含错误检测方法。一个简单的例子是使用奇偶校验位：在数据比特组中添加一个额外的比特，使得 1 的总数为偶数（偶校验）或奇数（奇校验）。这样接收器就可以检测出是否发生了单比特错误。更复杂的技术，如循环冗余校验（CRC），可以检测到多个错误，有时还能纠正错误。
Published by TutorHao | Physics Revision Series | aleveler.com
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