Technical English
For Information and Communication Engineering
Unit 4
Digital Signals and Signal Processing
Part I
Digital Signal Processing
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sub-field 分领域，子领域 subsensor array 传感器阵列 algorithm 算法 purpose-designed 针对目的设计的 purposeintegrated circuits 集成电路 wavelet 小波 informed 有知识的，有见闻的 cross-correlation 互相关 crossdiscretization 离散化 partition 分割，分区 sonar 声呐 biomedical 生物特征的 abbreviate 缩写，缩略 application-specific 面向应用的 applicationautocorrelation 自相关 baseband 基带 spatial domain 空间域 interval 间隔 quantization 量化 finite set 有限的集
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theorem 定理 carrier 载波 demodulation 解调 filtering 滤波 characterize 描绘，刻画性质 causal 因果关系的 diverge 发散 transfer functions 传递函数 derive 推导 cepstrum 倒谱 scenario情节，方案 scenario情节，方案 ingredient 成分，因素 enhancement 增强 weighted 加权的 superposition 叠加 converge 收敛 bounded 有界的 block diagram 方框图 magnitude 大小 logarithm 对数
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FIR (finite impulse response filter) 有限冲击响应滤波器 field-programmable gate array field(FPGA) 现场可编程门阵列 seismology 地震学 hifi (high fidelity) 高保真（音乐） animation 动画 floating point 浮点 magnetic resonance imaging (MRI) 磁共振成像 IIR (infinite impulse response filter) 无限冲击响应滤波器 computer aided tomography (CAT) 计算机断层扫描 equalization 均衡 reinforcement 加强 loudspeaker 扬声器 arithmetic 算术 fixed-point arithmetic fixed定点运算，整数运算
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Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are sub-fields of subsignal processing. DSP includes sub-fields like audio and subspeech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, image processing, signal processing for communications, biomedical signal processing, etc. processing, 音频及语音信号处理、声纳和雷达信号处理、 传感器阵列处理、谱估计、统计信号处理、图 像处理、通信信号处理、生物医学信号处理
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Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert realsignals, the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is another analog output signal, which requires a digital to analog converter. 数字信号处理的目标通常是 测量连续的真实世界的模拟 信号或对其滤波
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The algorithms required for DSP are sometimes performed using specialized computers, which make use of specialized microprocessors called digital signal processors (also abbreviated DSP). These process signals in real time, and are generally purpose-designed application-specific integrated purposeapplicationcircuits (ASICs).1 这些（数字信号处理器）实时处理 信号，通常是针对具体目的而设计 的专用集成电路（ASIC）。 的专用集成电路（ASIC）。
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When flexibility and rapid development are more important than unit costs at high volume, DSP algorithms may also be implemented using field-programmable gate arrays (FPGAs).2 field-
4 DSP domains
In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), (onespatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an 当灵活性和快速开发比大批量生产的 成本更重要时，DSP算法也可以用现 成本更重要时，DSP算法也可以用现 场可编程门阵列来实现。 informed guess (or by trying different possibilities) as to which which domain best represents the essential characteristics of the signal.3 他们按某些依据来猜测（或试验不同的可能 性）那一个域能够最好地表示信号的本质特 性来选择在其中进行信号处理的域。
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A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is, the frequency spectrum.4 Autocorrelation is defined as the cross-correlation of the signal with itself over crossvarying intervals of time or space. 从测量设备得到的样本序列产生（信号的） 时域或空域表示，而离散Fourier变换则产 时域或空域表示，而离散Fourier变换则产 生频域表示即频谱。
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5 Signal sampling
With the increasing use of computers the usage and need of digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). Sampling is usually carried out in two stages, discretization and quantization. quantization.
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In the discretization stage, the space of signals is partitioned into equivalence classes and discretization is carried out by replacing the signal with representative signal of the corresponding equivalence class.5 In the quantization stage the representative signal values are approximated by values from a finite set. set. 在离散化阶段，信号空间被分割为 相等的区间，用相应区间的代表性 信号值代替信号本身。
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In order for a sampled analog signal to be exactly reconstructed, the Nyquist-Shannon sampling theorem must Nyquistbe satisfied. This theorem states that the sampling frequency must be greater than twice the bandwidth of the signal. signal.
采样通常分两步实现： 离散化和量化
定理规定：采样频率必须 大于两倍的信号带宽
用有限集中的值来近似代表 性的信号值
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In practice, the sampling frequency is often significantly more than twice the required bandwidth. The most common bandwidth. bandwidth scenarios are: DC~BW (“baseband”); and fc±BW, (“ baseband” fc± BW, a frequency band centered on a carrier frequency (“direct (“ demodulation”). demodulation” 采样频率通常远大于信号 带宽的两倍
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A digital to analog converter (DAC) is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient into digital control systems.
8 Time and space domains
The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Filtering generally consists of some transformation of a number of surrounding samples around the current sample of the input or output signal. There are signal. various ways to characterize filters; for example:
滤波通常由在输入或输出信号当前样本 周围的许多样本的某种变换组成
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A “linear” filter is a linear transformation of input samples; linear” other filters are “non-linear.” Linear filters satisfy the non- linear.” superposition condition, i.e., if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.6 线性滤波器满足叠加条件，就是说，如果输入 是不同信号的加权线性组合，输出就是（各信 号）相应输出的同样加权线性组合。
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A “causal” filter uses only previous samples of the input or causal” output signals; while a “non-causal” filter uses future input non- causal” samples. A non-causal filter can usually be changed into a noncausal filter by adding a delay to it.
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Some filters are “stable”, others are “unstable”. A stable stable” unstable” filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An interval. unstable filter produces output which diverges.
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A “time-invariant” filter has constant properties over time; time- invariant” other filters such as adaptive filters change in time. time. “时不变”滤波器对时间具有不变的性质， 时不变” 诸如自适应滤波器等其它滤波器随时间而 改变
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稳定的滤波器产生的输出随时间收敛于一个 不变的值，或在有限的时间间隔内保持有界
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A “finite impulse response” (FIR) filter uses only the input response” signal, while an “infinite impulse response” filter (IIR) uses response” both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may signal. be unstable. Most filters can be described in Z-domain (a superset of the Zfrequency domain) by their transfer functions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response.7
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The output of an FIR filter to any given input may be calculated by convolving the input signal with the impulse response. Filters can also be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. instructions.
而无限脉冲响应（IIR）滤波器 而无限脉冲响应（IIR）滤波器 同时使用输入信号和以前的输出 信号样本
滤波器也可以用差分方程或一组零极点 表示，对于FIR滤波器还可以用冲击响应 表示，对于FIR滤波器还可以用冲击响应 或阶跃响应表示。
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滤波器还可以用结构图来表示，它能 用来推导样本处理算法，以便使用硬 件指令实现滤波器
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10 Frequency domain
Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the frequency. Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.
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The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to get information of which frequencies are present in the input signal and which are missing.
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There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, and then applies another Fourier transform. This emphasizes the frequency components with smaller magnitude while retaining the order of magnitudes of frequency components.8
Fourier变换将信号信息变换成每个 Fourier变换将信号信息变换成每个 频率的幅度和相位成分
例如倒谱用Fourier变换将信号转换到频域，取对 例如倒谱用Fourier变换将信号转换到频域，取对 数，然后再作第二次Fourier变换。这就强调了幅度 数，然后再作第二次Fourier变换。这就强调了幅度 较小的频率成分同时保持了频率分量的数量级。
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13 Applications
The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, radar, sonar, seismology, and biomedicine.
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Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in HiFi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computercomputergenerated animations in movies, medical imaging such as CAT scans and MRI, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers.
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14 Implementation
Digital signal processing is often implemented using specialized microprocessors such as the MC56000 and the TMS320. These often process data using fixed-point fixedarithmetic, although some versions are available which use floating point arithmetic and are more powerful. powerful.
它们通常使用定点算法处理数据， 尽管也有一些使用浮点算法，运算 能力更强大
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For faster applications FPGAs might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller can cope.
New Words
special-purpose专用 special- purpose专用 sinusoidal 正弦的 terminology 术语 context上下文，背景 context上下文，背景 rigid 坚硬的，刚性的 excitation激励 excitation激励 difference equation差分方程 equation差分方程 lumped system集总系统 system集总系统 presampling 预采样 strategy策略 strategy策略 dynamic range动态范围 range动态范围 subtraction减法 subtraction减法
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Part II
General Concepts of Digital Signal Processing
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casually 随便地 pursue追求，从事 pursue追求，从事 differential equation 微分方程 time-invariant时不变的 time- invariant时不变的 increment增量 increment增量 waveform波形 waveform波形 multiplex复用 multiplex复用 compatible 兼容
New Words
multiplication 乘法 holding circuit 保持电路 interpolate 内插 prescribed 预定的 intervening 期间的 aliasing 混叠 wagon 四轮马车 spurious 假的，伪造的 uncertainty 不确定性 demultiplexer 解复用器 reconstruction 重建 extrapolate 外推 curve-fitting 曲线拟合 curveintervene 插入，干预 bandlimited 限带的 erroneous 错误的 spoke 轮辐 arbitrarily 任意地 quantum 量子，量化 telemetry 遥测
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There have been tremendous demands in the use of digital computers and special-purpose digital circuitry for specialperforming varied signal processing functions that were originally achieved with analog equipment. The continued evolution of inexpensive integrated circuits has led to a variety variety of microcomputers and minicomputers that can be used for various signal processing functions.
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It is now possible to build special-purpose digital processors specialwithin much smaller size and lower cost constraints of systems previously all analog in nature.1
现在有可能在比以往全模拟系统 小得多，而且成本也低得多的限 制下构成专用数字处理器。
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We will provide a general discussion of the basic concepts associated with digital signal processing. To do so, it is appropriate to discuss some common terms and assumptions. Wherever possible, the definitions and terminology will be established in accordance with the recommendations of the IEEE Group on Audio and Electroacoustics. Electroacoustics.
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An analog signal is a function that is defined over a continuous range of time and in which the amplitude may assume a continuous range of values. Common examples are the values. sinusoidal function, the step function, the output of a microphone, etc. The term analog apparently originated from the field of analog computation, in which voltages and currents are used to represent physical variables, but it has 可能之处，定义和术语将依照 IEEE音频和电声小组的推荐 IEEE音频和电声小组的推荐
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Continuous-time signal is a function that is defined over a Continuouscontinuous range of time, but in which the amplitude may either have a continuous range of values or a finite number of possible values. In this context, an analog signal could be values. considered as a special case of a continuous-time signal. In continuouspractice, however, the terms analog and continuous-time are continuousinterchanged casually in usage and are often used to mean the same thing. 模拟信号是定义在连续时间上的 函数，其幅度取值是连续的
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been extended in usage.
连续时间信号是定义在连续时间上 的函数，但是它的幅度可能是连续 值也可以是有限的可能值
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Because of the association of the term analog with physical analogies, preference has been established for the term continuous-time. Nevertheless, there will be cases in which the continuous- time. term analog will be used for clarity, particularly where it relates to the term digital.2 digital.
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The term quantization describes the process of representing a variable by a set of distinct values. A quantized variable is one values. that may assume only distinct values. values.
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A discrete-time signal is a function that is defined only at a discreteparticular set of values of time. This means that the time. independent variable, time, is quantized. If the amplitude of a discrete-time signal is permitted to assume a continuous range discrete经量化的变量只能 取离散值 of values, the function is said to be a sampled-data signal. A sampledsampled-data signal could arise from sampling an analog sampledsignal at discrete values of time. 离散时间信号是定义在某些 特定时间值上的函数
由于“模拟”一词与物理类比的关联，已经确 由于“模拟” 立了优先使用“连续时间”这一术语。不过有 立了优先使用“连续时间” 时为了清楚起见也用“模拟”一词，特别是与 时为了清楚起见也用“ 模拟” “数字”相联系时。 数字”
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A digital signal is a function in which both time and amplitude are quantized. A digital signal may always be represented by a sequence of numbers in which each number has a finite number of digits.
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The terms discrete-time and digital are often interchanged in discretepractice and are often used to mean the same thing. A great deal of the theory underlying discrete-time signals is discreteapplicable to purely digital signals, so it is not always necessary to make rigid distinctions. The term discrete-time distinctions. discretewill more often be used in pursuing theoretical developments, and the term digital will more often be used in describing hardware or software realizations. 许多基于离散时间信号的定理适用于 纯数字信号，因此没有必要总是对两 者作严格的区分
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A system can be described by any of the preceding terms according to the type of hardware or software employed and the type of signals present. Thus, reference can be made to present. analog systems, continuous-time systems, discrete-time systems, systems, continuoussystems, discretesystems, digital systems, etc. systems, 根据使用的硬件或软件的类型和当前 信号的类型，一个系统可以用任意的 前述术语来描述
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A linear system is one in which the principle of superposition applies. A linear system can be described by linear differential or difference equations. A time-invariant linear system is one equations. timein which the parameters are fixed and do not vary with time.
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A lumped system is one that is composed of finite nonzero elements satisfying ordinary differential or difference equation relationships, as opposed to a distributed system, satisfying partial differential equation relationships.3
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The standard form for numerical processing of a digital signal is the binary number system. The binary number system makes use only of the values 0 and 1 to represent all possible numbers.
线性系统可以用线性的微分 或差分方程来描述
集总系统是由有限非零元素构成，满足 常微分（或差分）方程的系统，与满足 偏微分方程的分布式系统相对应。
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The number of levels m that can be represented by a number having n binary digits (bits) is given by
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The process by which digital signal processing is achieved will be illustrated by a simplified system in which the signal is assumed to vary from 0 to 7 volts and in which 8 possible levels (at 1 V increments) are used for the binary numbers.5
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A block diagram is shown in Figure 9.1, and some waveforms of interest are shown in Figure 9.2. The signal is first passed through a continuous-time presampling filter whose function continuouswill be discussed later.
Analog signal in Presampling filter Sampler and A/D converter Digital signal processor D/A converter and filters Analog signal out
m=
2n
Conversely, if m is the number of possible levels required, the number of bits required is the smallest integer greater than or equal to log2 m .4 可用n位二进制（n比特）表示的等级数m 可用n 位二进制（n 比特）表示的等级数m 由m= 2n给出。反过来，如果m是要求的等 给出。反过来，如果m 级数，所需的比特数是大于等于log2 m的 级数，所需的比特数是大于等于log2 最小整数。
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实现数字处理的过程将用一个简化系统 来说明，假定信号在0V到7V之间变化， 来说明，假定信号在0V到7V之间变化， 以1V为增量，用8种可能的值表示成二 1V为增量，用8 进制数。
x(t) and quantized samples
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T
2T
3T
4T
5T
6T
7T
8T
t
000
010
T 2T
011
3T
111
4T
111
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5T
100
6T 7T
011
8T
001
t
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The signal is then read at intervals of T seconds by a sampler. These samples must then be quantized to one of the standard levels. Although there are different strategies employed in the quantization process, one common approach, which will be assumed here, is that a sample is assigned to the nearest level. Thus, a sample of value 4.2 V would be quantized to 4 V, and a sample of value 4.6 V would be quantized to 5 V.
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This process for the signal given is illustrated in Figure 9.2. The pulses representing the signal have been made very narrow to illustrate the fact that other signals may be inserted, inserted, or multiplexed, in the empty space. These pulses may then be represented as binary numbers. In order that these numbers could be seen on the figure, each has been shown over much of the space in a given interval. 为了使这些数字可以从图中看到，每组 都显示在给定间隔的空档处
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In practice, if other signals are to be inserted, the pulses representing the bits of the binary numbers could be made very short. A given binary number could then be read in a very short interval at the beginning of a sampling period, thus leaving most of the time available for other signals. signals. 一个给定的二进制数就可以在采样周期 开始的很短间隔内读到，这样就给其它 信号留出了大部分的可用时间
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The process by which an analog sample is quantized and converted to a binary number is called analog-to-digital (A/D) analog- toconversion. In general, the dynamic range of the signal must be compatible with that of the A/D converter employed, and the number of bits employed must be sufficient for the required accuracy.
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The signal can now be processed by the type of unit appropriate for the application intended. This unit may be a general-purpose computer or minicomputer, or it may be a generalspecial unit designed specifically for this purpose. At any rate, rate, it is composed of some combination of standard digital circuits capable of performing the various arithmetic functions of addition, subtraction, multiplication, etc. In addition, it has 信号的动态范围要和所用的A/D转换器 信号的动态范围要和所用的A/D转换器 相一致，为了达到所要求的精确度，要 使用足够的比特数
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At the output of the processor, the digital signal can be converted to analog form again. This is achieved by the process of digital-to-analog (D/A) conversion. In this step, the digital- tobinary numbers are first successively converted back to continuous-time pulses. The gaps between the pulses are then continuousfilled in by a reconstruction filter.
logic and storage capability.
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This filter may consist of a holding circuit, which is a special circuit designed to hold the value of a pulse between successive sample values. In some cases, the holding circuit may be designed to interpolate the output signal between successive points according to some prescribed curve-fitting curvestrategy.6 In
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A fundamental question that may arise is whether or not some information has been lost in the process. After all, the signal has been sampled only at discrete intervals of time; is there something that might be missed in the intervening time intervals? Furthermore, in the process of quantization, the intervals? actual amplitude is replaced by the nearest standard level, which means that there is a possible error in amplitude. 信号仅仅在离散的时间间隔处被采样；在介于 时间间隔内是否有一些信息丢失了呢
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In regard to the sampling question, it will be shown that, if the the signal is bandlimited, and if the sampling rate is greater than bandlimited, or equal to twice the highest frequency, the signal can theoretically be recovered from its discrete samples.7
addition to a holding circuit, a basic continuous-time filter continuousmay be employed to provide additional smoothing between points. 在某些情况下，可设计保持电路，将 输出信号在连续样点之间按照设定的 曲线拟合方法进行内插。
关于采样的问题，我们将表明，如果信号带宽 有限，并且采样率大于等于最高频率的两倍， 理论上信号就能从离散的样本恢复。
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This corresponds to a minimum of two samples per cycle at the highest frequency. In practice, this sampling rate is usually usually chosen to be somewhat higher than the minimum rate (say, three or four times the highest frequency) in order to ensure practical implementation. For example, if the highest frequency of the analog signal is 5 kHz, the theoretical minimum sampling rate is 10,000 samples per second, and a practical system would employ a rate somewhat higher.
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The input continuous-time signal is often passed through a continuouslow-pass analog presampling filter to ensure that the highest lowfrequency is within the bounds for which the signal can be recovered.8
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If a signal is not sampled at a sufficiently high rate, a phenomenon known as aliasing results. This concept results in a frequency being mistaken for an entirely different frequency upon recovery. For example, suppose a signal with frequencies recovery. ranging from dc to 5 kHz is sampled at a rate of 6 kHz, which 常将输入的连续时间信号通过一个低通 模拟预采样滤波器，以确保最高频率落 在信号能够完全恢复的界限之内。 is clearly too low to ensure recovery. If recovery is attempted, a component of the original signal at 5 kHz now appears to be at 1 kHz, resulting in an erroneous signal. 混叠会导致在恢复时一个频率 被误作为完全不同的频率
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A common example of this phenomenon is one we will call the wagon wheel effect, probably noticed by the reader in western effect, movies as the phenomenon in which the wheels appear to be rotating backwards.9
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Since each individual frame of a film is equivalent to a discrete discrete sampling operation, if the rate of spokes passing a given angle is too large for a given movie frame rate, the wheels appear to be turning either backwards or at a very slow speed.10
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The effect of a presampling filter removes the possibility that a spurious signal whose frequency is too high for the system will be mistaken for one in the proper frequency range.11
一个普通例子就是我们称之为“车轮 一个普通例子就是我们称之为“ 效应”的现象，就是读者在西部电影 效应” 中也许注意到的车轮看起来向后转动 的情况。
因为影片的每一帧相当于一次离散的采样， 如果相对于电影帧频而言轮辐越过的给定角 度过大，轮子看起来就会向后转动或以很慢 的速度转动。
采样前预滤波消除了这种对系统而言 频率过高的伪信号被错误地当作适当 频率范围内的另一信号的可能性。
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With respect to the quantization error, it can be seen that the error can be made as small as one chooses if the number of bits can be made arbitrarily large. Of course, there is a large. practical maximum limit, so it is necessary to tolerate some error from this phenomenon. Even in continuous-time systems, continuousthere may be noise present which would introduce uncertainty in the actual magnitude. In fact, the uncertainty present in the digital sampling process is called quantization noise. 如果使用任意多的比特数， 可使误差任意小
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Let Emax and Emin represent the maximum and minimum values of the signal, and let q represent the vertical distance between successive quantum levels. Using n and m as previously defined, we have
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Assuming that a sample between two successive quantum levels is assigned to the nearest quantum level, the peak quantization noise and peak percentage quantization noise values are
q=
Emax ? Emin Emax ? Emin = m 2n
(9-2)
Peak Quantization Noise =
q 2
(9-3)
Peak Percentage Quantization Noise =
100% 2m
(9-4)
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In many cases, the variance of the quantization noise is more important than the maximum value. The variance is directly proportional to the average power associated with the noise. If the signal is assumed to be uniformly distributed between quantum levels, it can be shown by statistical analysis that the noise variance σ2 is
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The root-mean-square (RMS) (or standard deviation) value of root- meanthis noise component is
24
In view of the preceding discussion, it appears that no information is lost in the sampling operation provided that the (9-6) sampling rate is high enough, and the quantization error can enough, be reduced to an insignificantly small level by choosing a sufficient number of bits to represent each binary number. These concepts then permit us to represent a continuous-time continuoussignal in terms of a series of discrete binary numbers, which may be processed directly with digital circuits. 如果采样速率足够高的话，采样 操作就不会造成信息丢失
σ=
q 2 3
Comparing (9-6) with (9-3), it is seen that the RMS noise (9(9component is 1 / 3 times the peak noise component.
σ2 =
q 12
2
(9-5)
与......成正比 ......成正比
69 70
71
25
The rather involved procedure of A/D conversion, processing, and final D/A conversion may seem like a lot of effort in order to handle one signal channel. Indeed, in many cases such a complex process may not be economically feasible for a single signal. One of the great advantages of the digital concept is the signal. possibility of processing a number of channels with the same arithmetic unit. unit. 数字概念的一个很大优势就是可以用 同一个算术单元处理许多信道
72
25
This process can be achieved by a process called time-division timemultiplexing (TDM). It was observed in the sampled signal shown in Figure 9.2 that there was a relatively long period between successive samples of the signal. During this period, samples of additional signals are fed into the processor.
26
This concept is illustrated in Figure 9.3. Each channel is read in a sequential order, and the corresponding values are converted into binary numbers in the same sequence. These numbers enter into the processing unit and, after suitable processing, appear at the output in the appropriate order.
73
74
26
This composite digital signal must first be separated into the original different channels by means of a demultiplexer, which demultiplexer, is synchronized with the input sampling signal. The channels then undergo the D/A conversion required for output.
Sync Signals Multiplexer
???
27
In the preceding discussions, we have assumed that both the starting and final signals in the system are in continuous-time continuousform. Actually, there are many systems in which one or both are already digital in form. In such cases the A/D conversion and/or the D/A conversion may not be required, thus
Signals Digital signal processor Demultiplexer
???
27
For example, assume that a number of continuous-time continuoustelemetry signals are to be processed by a digital unit, but the output data is to be kept in digital form for scientific data reduction and computation. In this case, the A/D unit at the input is required, but no conversion is needed at the output.
simplifying the system.
Figure 9.3 Multiplexed digital processing system
75 76 77
读书破万卷下笔如有神 第五章习题答案 5.1 1.大小形状方向位置 2.符合最小条件 3.大于 4.垂直度平面度 5.零件长度L 6. 5 9 7.跳动公差跳动公差是关联实际要素绕基准轴回转一周或几周时所允许的最大跳动量，是以特定的测量方法定义的公差项目，用以综合限制被测要素的形状和位置误差。 8.模拟拟合 9.单一包容原则要求是尺寸公差与形位公差相互有关的一种相关要求.它只适用于单一尺寸要素(圆柱面,两反向的平行平面)的尺寸公差与形位公差之间的关系。采用包容要求的尺寸要素,其实际轮廓应遵守最大实体边界,即其体外作用尺寸不超出其最大实体尺寸,且局部实际尺寸不超出其最小实体尺寸. 10.空间直线 5.2 1-5：×√√××6-8：××√ 5.3 1-5：C D B C C 6-8：B A D 5.4 1、径向跳动测量和轴向跳动测量分别可以测量哪些几何误差？ 答：径向跳动可以测量圆度误差、同心度误差、圆柱度误差及同轴度误差。 轴向跳动可以测量平面度误差和垂直度误差。 2、最大实体状态和最大实体实效状态的区别是什么？ 答：最大实体状态是指实际要素在给定长度内，处处位于极限尺寸之间并且实体最大时的状态。最大实体实效状态则是指实际要素首先要保证处于最大实体状态，同时还要满足其中心要素的形状或位置误差等于给出的公差值，只有满足这两个条件才算是处于最大实体实效状态。 3、当被测要素遵守包容要求时，其实际尺寸和体外作用尺寸的合格条件如何？答：符合包容要求的被测实际要素的合格条件为： DM = DminDa≤DL = Dmax Dfe≥
dL = dmin ≤dfe dM = dmax≥da 读书破万卷下笔如有神 4、基准形式有哪几种？何为三基面体系？ 答：基准有三种：单一基准、公共基准和三基面体系。 面是确定和测量零件上各要素几何关系的起点。 5.5将下列技术要求正确标注在零件图中： （1）φd3的圆度公差为0.002mm，轴肩A的平面度公差为0.015mm； （2）φd2的外圆尺寸要求为φ110h6，φd3的尺寸为φ45k6； （3）轴肩B对轴肩A的平行度公差为0.01mm； （4）φd3轴线对轴肩A的垂直度公差为0.02mm； （5）2×φd1的轴线对其公共轴线的同轴度要求为0.01mm； （6）φd3表面粗糙度Ra的允许值为1.6μm, 两个φd1表面粗糙度Ra的最大值为0.8μm，其余各加工面的表面粗糙度Ra的允许值为6.3μm。； 5.6
第六章键和花键的互换性及其检测 一．判断题（正确的打√，错误的打×） 1．平键联接中，键宽与轴槽宽的配合采用基轴制。（√） 2．矩形花键的定心尺寸应按较高精度等级制造，非定心尺寸则可按粗糙精度级制造。（√） 3．矩形花键定心方式，按国家标准只规定大径定心一种方式。（×） 二．选择题（将下列题目中所有正确的论述选择出来） 1．花键的分度误差，一般用（ B ）公差来控制。 A．平行度；B．位置度；C．对称度；D．同轴度。 2.对键槽应提出 C 形位公差要求 A.平面度； B.位置度； C.对称度； D.平行度 三．填空题 1．单键分为平键半圆键楔键三种，其中以平键应用最广。 2．花键按键廓形状的不同可分为矩形花键渐开线花键三角形花键。其中应用最广的是矩形花键。 3．花键联结与单键联结相比，其主要优点是定心精度高，导向性好，承载能力强四、问答题 1平键连接为什么只对键（键槽）宽规定较严的公差？ 答：特点：依靠键的侧面与键槽的侧面的接触传递运动与动力。主要几何参数：键宽、键长、键高，槽宽、深、长。 因平键连接是通过键的侧面分别与轴槽和轮毂槽的侧面互相连接来传递运动和扭矩的，因此，键宽和键槽宽b是决定配合性质的主要互换性参数，是配合尺寸，应规定较严格的公差。 2平键连接的配合采用何种基准制？花键连接采用何种基准制？ 答:平键是标准件，平键连接的配合采用基轴制配合，花键连接采用基孔制。 3矩形花键的主要参数有哪些？定心方式有哪几种？哪种方式是常用的？为什么？ 答：矩形花键的主要参数有：大径D 小径d 键宽和键槽宽B 定心：确定配合轴线。 定心方式有三种：按大径D定心、按小径d定心、按键宽B定心 小径d定心最常见，由于花键结合面的硬度要求较高，需淬火处理，为了保证定心表面的尺寸精度和形状精度，淬火后需进行磨削加工。从加工工艺性看，小径便于用磨削方法进行精加工，因此，国标规定采用小径d定心，对定心小径d采用较小的公差等级。 (2)装配图上的标记： 6×26×H6/g6×30×H10/a11×6×H7/f7
第五章习题答案 5.1 1.大小形状方向位置 2.符合最小条件 3.大于 4.垂直度平面度 5.零件长度L 6. 5 9 7.跳动公差跳动公差是关联实际要素绕基准轴回转一周或几周时所允许的最大跳动量，是以特定的测量方法定义的公差项目，用以综合限制被测要素的形状和位置误差。 8.模拟拟合 9.单一包容原则要求是尺寸公差与形位公差相互有关的一种相关要求.它只适用于单一尺寸要素(圆柱面,两反向的平行平面)的尺寸公差与形位公差之间的关系。采用包容要求的尺寸要素,其实际轮廓应遵守最大实体边界,即其体外作用尺寸不超出其最大实体尺寸,且局部实际尺寸不超出其最小实体尺寸. 10.空间直线 5.2 1-5：×√√××6-8：××√ 5.3 1-5：C D B C C 6-8：B A D 5.4 1、径向跳动测量和轴向跳动测量分别可以测量哪些几何误差？ 答：径向跳动可以测量圆度误差、同心度误差、圆柱度误差及同轴度误差。 轴向跳动可以测量平面度误差和垂直度误差。 2、最大实体状态和最大实体实效状态的区别是什么？ 答：最大实体状态是指实际要素在给定长度内，处处位于极限尺寸之间并且实体最大时的状态。最大实体实效状态则是指实际要素首先要保证处于最大实体状态，同时还要满足其中心要素的形状或位置误差等于给出的公差值，只有满足这两个条件才算是处于最大实体实效状态。 3、当被测要素遵守包容要求时，其实际尺寸和体外作用尺寸的合格条件如何？答：符合包容要求的被测实际要素的合格条件为： Dfe≥DM = Dmin Da≤DL = Dmax dfe≤dM = dmax da≥dL = dmin
4、基准形式有哪几种？何为三基面体系？ 答：基准有三种：单一基准、公共基准和三基面体系。 面是确定和测量零件上各要素几何关系的起点。 5.5将下列技术要求正确标注在零件图中： （1）φd3的圆度公差为0.002mm，轴肩A的平面度公差为0.015mm； （2）φd2的外圆尺寸要求为φ110h6，φd3的尺寸为φ45k6； （3）轴肩B对轴肩A的平行度公差为0.01mm； （4）φd3轴线对轴肩A的垂直度公差为0.02mm； （5）2×φd1的轴线对其公共轴线的同轴度要求为0.01mm； （6）φd3表面粗糙度Ra的允许值为1.6μm, 两个φd1表面粗糙度Ra的最大值为0.8μm，其余各加工面的表面粗糙度Ra的允许值为6.3μm。； 试分析零件图中几何公差标注的含义，按要求填空。