信息科学与电子工程专业英语王朔中

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1、信息科学与电子工程专业英语Technical EnglishFor Information Science and Electronic Engineering信息科学与电子工程专业英语Unit 9Electronics: Digital Signals and Signal Processing信息科学与电子工程专业英语Part IDigital Signal Processing 3New Wordssub-field sub-field 分领域，子领域分领域，子领域分领域，子领域分领域，子领域sonar sonar 声呐声呐声呐声呐sensor array sensor array 传感

2、器阵列传感器阵列传感器阵列传感器阵列biomedical biomedical 生物特征的生物特征的生物特征的生物特征的algorithm algorithm 算法算法算法算法abbreviate abbreviate 缩写，缩略缩写，缩略缩写，缩略缩写，缩略purpose-designed purpose-designed 针对目的设计的针对目的设计的针对目的设计的针对目的设计的application-specific application-specific 面向应用的面向应用的面向应用的面向应用的integrated circuits integrated circuits 集成电路集成

3、电路集成电路集成电路autocorrelation autocorrelation 自相关自相关自相关自相关wavelet wavelet 小波小波小波小波baseband baseband 基带基带基带基带informed informed 有知识的，有见闻的有知识的，有见闻的有知识的，有见闻的有知识的，有见闻的spatial domain spatial domain 空间域空间域空间域空间域cross-correlation cross-correlation 互相关互相关互相关互相关interval interval 间隔间隔间隔间隔discretization discretizat

4、ion 离散化离散化离散化离散化quantization quantization 量化量化量化量化partition partition 分割，分区分割，分区分割，分区分割，分区finite set finite set 有限的集有限的集有限的集有限的集4New Wordstheorem theorem 定理定理定理定理scenarioscenario情节，方案情节，方案情节，方案情节，方案carrier carrier 载波载波载波载波ingredient ingredient 成分，因素成分，因素成分，因素成分，因素demodulation demodulation 解调解调解调解调en

5、hancement enhancement 增强增强增强增强filtering filtering 滤波滤波滤波滤波weighted weighted 加权的加权的加权的加权的characterize characterize 描绘，刻画性质描绘，刻画性质描绘，刻画性质描绘，刻画性质superposition superposition 叠加叠加叠加叠加causal causal 因果关系的因果关系的因果关系的因果关系的converge converge 收敛收敛收敛收敛diverge diverge 发散发散发散发散bounded bounded 有界的有界的有界的有界的transfer f

6、unctions transfer functions 传递函数传递函数传递函数传递函数block diagram block diagram 方框图方框图方框图方框图derive derive 推导推导推导推导magnitude magnitude 大小大小大小大小cepstrum cepstrum 倒谱倒谱倒谱倒谱logarithm logarithm 对数对数对数对数5New WordsFIR (finite impulseresponse filter) FIR (finite impulseresponse filter) 有限冲击响应滤波器有限冲击响应滤波器有限冲击响应滤波器有限冲

7、击响应滤波器IIR (infinite impulse response filter)IIR (infinite impulse response filter)无限冲击响应滤波器无限冲击响应滤波器无限冲击响应滤波器无限冲击响应滤波器field-programmablegate array field-programmablegate array (FPGA) (FPGA) 现场可编程门阵列现场可编程门阵列现场可编程门阵列现场可编程门阵列computer aidedtomography (CAT)computer aidedtomography (CAT)计算机断层扫描计算机断层扫描计算机断

8、层扫描计算机断层扫描seismology seismology 地震学地震学地震学地震学equalization equalization 均衡均衡均衡均衡hifi (high fidelity) hifi (high fidelity) 高保真（音乐）高保真（音乐）高保真（音乐）高保真（音乐）reinforcement reinforcement 加强加强加强加强animation animation 动画动画动画动画loudspeaker loudspeaker 扬声器扬声器扬声器扬声器floating point floating point 浮点浮点浮点浮点arithmetic ari

9、thmetic 算术算术算术算术magnetic resonanceimaging (MRI)magnetic resonanceimaging (MRI)磁共振成像磁共振成像磁共振成像磁共振成像fixed-point arithmeticfixed-point arithmetic定点运算，整数运算定点运算，整数运算定点运算，整数运算定点运算，整数运算61Digital signal processing (DSP) is the study of signals in a Digital signal processing (DSP) is the study of signals in

10、a digital representation and the processing methods of these digital representation and the processing methods of these signals. DSP and analog signal processing are sub-fields of signals. DSP and analog signal processing are sub-fields of signal processing. DSP includes sub-fields like signal proce

11、ssing. DSP includes sub-fields like audio and audio and speech signal processing, sonar and radar signal processing, speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal sensor array processing, spectral estimation, statistical

12、 signal processing, image processing, signal processing for processing, image processing, signal processing for communications, biomedical signal processingcommunications, biomedical signal processing, etc. , etc. 音频及语音信号处理、声纳和雷达信号处理、音频及语音信号处理、声纳和雷达信号处理、音频及语音信号处理、声纳和雷达信号处理、音频及语音信号处理、声纳和雷达信号处理、传感器阵列处

13、理、谱估计、统计信号处理、图传感器阵列处理、谱估计、统计信号处理、图传感器阵列处理、谱估计、统计信号处理、图传感器阵列处理、谱估计、统计信号处理、图像处理、通信信号处理、生物医学信号处理像处理、通信信号处理、生物医学信号处理像处理、通信信号处理、生物医学信号处理像处理、通信信号处理、生物医学信号处理72Since the goal of DSP is usually to measure or filter continuous Since the goal of DSP is usually to measure or filter continuous real-world analog

14、signalsreal-world analog signals, the first step is usually to convert , the first step is usually to convert the signal from an analog to a digital form, by using an analog the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is to

15、digital converter. Often, the required output signal is another analog output signal, which requires a digital to another analog output signal, which requires a digital to analog converter.analog converter.数字信号处理的目标通常是数字信号处理的目标通常是数字信号处理的目标通常是数字信号处理的目标通常是测量连续的真实世界的模拟测量连续的真实世界的模拟测量连续的真实世界的模拟测量连续的真实世界的

16、模拟信号或对其滤波信号或对其滤波信号或对其滤波信号或对其滤波83The algorithms required for DSP are sometimes performed The algorithms required for DSP are sometimes performed using specialized computers, which make use of specialized using specialized computers, which make use of specialized microprocessors called digital signal

17、processors (also microprocessors called digital signal processors (also abbreviated DSP). abbreviated DSP). These process signals in real time, and are These process signals in real time, and are generally purpose-designed application-specific integrated generally purpose-designed application-specif

18、ic integrated circuits (ASICs).circuits (ASICs).1 1 这些（数字信号处理器）实时处理这些（数字信号处理器）实时处理这些（数字信号处理器）实时处理这些（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信号，通常是针对具体目的而设计信号，通常是针对具体目的而设计信号，通常是针对具体目的而设计的专用集成电路（的专用集成电路（的专用集成电路（的专用集成电路（ASICASIC）。）。）。）。93When flexibility and rapid development are more important When flexibility and

19、 rapid development are more important than unit costs at high volume, DSP algorithms may also be than unit costs at high volume, DSP algorithms may also be implemented using field-programmable gate arrays (FPGAs).implemented using field-programmable gate arrays (FPGAs).2 2当灵活性和快速开发比大批量生产的当灵活性和快速开发比大

20、批量生产的当灵活性和快速开发比大批量生产的当灵活性和快速开发比大批量生产的成本更重要时，成本更重要时，成本更重要时，成本更重要时，DSPDSP算法也可以用现场算法也可以用现场算法也可以用现场算法也可以用现场可编程门阵列来实现。可编程门阵列来实现。可编程门阵列来实现。可编程门阵列来实现。104 DSP domainsIn DSP, engineers usually study digital signals in one of the In DSP, engineers usually study digital signals in one of the following domains:

21、 time domain (one-dimensional signals), following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. autocorrelation domain, and wavelet

22、 domains. They choose They choose the domain in which to process a signal by making an the domain in which to process a signal by making an informed guess (or by trying different possibilities) as to which informed guess (or by trying different possibilities) as to which domain best represents the e

23、ssential characteristics of the domain best represents the essential characteristics of the signal.signal.3 3 他们按某些依据来猜测（或试验不同的可能他们按某些依据来猜测（或试验不同的可能他们按某些依据来猜测（或试验不同的可能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）那一个域能够最好地表示信号的本质特性）那一个域能够最好地表示信号的本质特性）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。性来选择在其中进行信号处理的域。性来选择在其

24、中进行信号处理的域。性来选择在其中进行信号处理的域。114A sequence of samples from a measuring device produces a A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete time or spatial domain representation, whereas a discrete Fourier transform produces the frequency

25、domain Fourier transform produces the frequency domain information, that is, the frequency spectrum.information, that is, the frequency spectrum.4 4 Autocorrelation Autocorrelation is defined as the cross-correlation of the signal with itself over is defined as the cross-correlation of the signal wi

26、th itself over varying intervals of time or space.varying intervals of time or space.从测量设备得到的样本序列产生（信号的）从测量设备得到的样本序列产生（信号的）从测量设备得到的样本序列产生（信号的）从测量设备得到的样本序列产生（信号的）时域或空域表示，而离散时域或空域表示，而离散时域或空域表示，而离散时域或空域表示，而离散FourierFourier变换则产变换则产变换则产变换则产生频域表示即频谱。生频域表示即频谱。生频域表示即频谱。生频域表示即频谱。125 Signal samplingWith the i

27、ncreasing use of computers the usage and need of With the increasing use of computers the usage and need of digital signal processing has increased. In order to use an digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog signal o

28、n a computer it must be digitized with an analog to digital converter (ADC). analog to digital converter (ADC). Sampling is usually carried Sampling is usually carried out in two stages, discretization and quantizationout in two stages, discretization and quantization. . 采样通常分两步实现：采样通常分两步实现：采样通常分两步实

29、现：采样通常分两步实现：离散化和量化离散化和量化离散化和量化离散化和量化135In the discretization stage, the space of signals is partitioned In the discretization stage, the space of signals is partitioned into equivalence classes and discretization is carried out by into equivalence classes and discretization is carried out by replaci

30、ng the signal with representative signal of the replacing the signal with representative signal of the corresponding equivalence class.corresponding equivalence class.5 5 In the quantization stageIn the quantization stage the the representative signal values are approximated by values from represent

31、ative signal values are approximated by values from a finite seta finite set. .在离散化阶段，信号空间被分割为在离散化阶段，信号空间被分割为在离散化阶段，信号空间被分割为在离散化阶段，信号空间被分割为相等的区间，用相应区间的代表性相等的区间，用相应区间的代表性相等的区间，用相应区间的代表性相等的区间，用相应区间的代表性信号值代替信号本身。信号值代替信号本身。信号值代替信号本身。信号值代替信号本身。用有限集中的值来近似代表用有限集中的值来近似代表用有限集中的值来近似代表用有限集中的值来近似代表性的信号值性的信号值性的信

32、号值性的信号值146In order for a sampled analog signal to be exactly In order for a sampled analog signal to be exactly reconstructed, the Nyquist-Shannon sampling theorem must reconstructed, the Nyquist-Shannon sampling theorem must be satisfied. be satisfied. This theorem states that the sampling frequenc

33、y This theorem states that the sampling frequency must be greater than twice the bandwidth of the signalmust be greater than twice the bandwidth of the signal. . 定理规定：采样频率必须定理规定：采样频率必须定理规定：采样频率必须定理规定：采样频率必须大于两倍的信号带宽大于两倍的信号带宽大于两倍的信号带宽大于两倍的信号带宽156In practice, In practice, the sampling frequency is oft

34、en significantly more the sampling frequency is often significantly more than twice the required bandwidththan twice the required bandwidth. The most common . The most common bandwidth scenarios are: DCBW (“baseband”); and bandwidth scenarios are: DCBW (“baseband”); and fcfc BW, BW, a frequency band

35、 centered on a carrier frequency (“direct a frequency band centered on a carrier frequency (“direct demodulation”).demodulation”).采样频率通常远大于信号采样频率通常远大于信号采样频率通常远大于信号采样频率通常远大于信号带宽的两倍带宽的两倍带宽的两倍带宽的两倍167A digital to analog converter (DAC) is used to convert the A digital to analog converter (DAC) is used

36、to convert the digital signal back to analog. The use of a digital computer is a digital signal back to analog. The use of a digital computer is a key ingredient into digital control systems.key ingredient into digital control systems.178 Time and space domainsThe most common processing approach in

37、the time or space The most common processing approach in the time or space domain is enhancement of the input signal through a method domain is enhancement of the input signal through a method called filtering. called filtering. Filtering generally consists of some Filtering generally consists of so

38、me transformation of a number of surrounding samples around transformation of a number of surrounding samples around the current sample of the input or output signalthe current sample of the input or output signal. There are . There are various ways to characterize filters; for example: various ways

39、 to characterize filters; for example: 滤波通常由在输入或输出信号当前样本滤波通常由在输入或输出信号当前样本滤波通常由在输入或输出信号当前样本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周围的许多样本的某种变换组成周围的许多样本的某种变换组成周围的许多样本的某种变换组成188- -A “linear” filter is a linear transformation of input A “linear” filter is a linear transformation of input samples; other filters

40、are “non-linear.” samples; other filters are “non-linear.” Linear filters satisfy Linear filters satisfy the superposition condition, i.e., if an input is a weighted the superposition condition, i.e., if an input is a weighted linear combination of different signals, the output is an linear combinat

41、ion of different signals, the output is an equally weighted linear combination of the corresponding equally weighted linear combination of the corresponding output signals.output signals.6 6 线性滤波器满足叠加条件，就是说，如果输入线性滤波器满足叠加条件，就是说，如果输入线性滤波器满足叠加条件，就是说，如果输入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（各信是不同信号的加权线

42、性组合，输出就是（各信是不同信号的加权线性组合，输出就是（各信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。号）相应输出的同样加权线性组合。号）相应输出的同样加权线性组合。号）相应输出的同样加权线性组合。198- -A “causal” filter uses only previous samples of the input or A “causal” filter uses only previous samples of the input or output signals; while a “non-causal” filter uses future i

43、nput output signals; while a “non-causal” filter uses future input samples. A non-causal filter can usually be changed into a samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it. causal filter by adding a delay to it. - -A “time-invariant” filter has cons

44、tant properties over time; A “time-invariant” filter has constant properties over time; other filters such as adaptive filters change in timeother filters such as adaptive filters change in time. . “ “时不变时不变时不变时不变” ”滤波器对时间具有不变的性质，滤波器对时间具有不变的性质，滤波器对时间具有不变的性质，滤波器对时间具有不变的性质，诸如自适应滤波器等其它滤波器随时间而诸如自适应滤波器等其

45、它滤波器随时间而诸如自适应滤波器等其它滤波器随时间而诸如自适应滤波器等其它滤波器随时间而改变改变改变改变208- -Some filters are “stable”, others are “unstable”. Some filters are “stable”, others are “unstable”. A stable A stable filter produces an output that converges to a constant value filter produces an output that converges to a constant value wi

46、th time, or remains bounded within a finite intervalwith time, or remains bounded within a finite interval. An . An unstable filter produces output which diverges. unstable filter produces output which diverges. 稳定的滤波器产生的输出随时间收敛于一个稳定的滤波器产生的输出随时间收敛于一个稳定的滤波器产生的输出随时间收敛于一个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

47、间隔内保持有界不变的值，或在有限的时间间隔内保持有界不变的值，或在有限的时间间隔内保持有界不变的值，或在有限的时间间隔内保持有界218- -A “finite impulse response” (FIR) filter uses only the input A “finite impulse response” (FIR) filter uses only the input signal, signal, while an “infinite impulse response” filter (IIR) uses while an “infinite impulse response”

48、filter (IIR) uses both the input signal and previous samples of the output both the input signal and previous samples of the output signalsignal. FIR filters are always stable, while IIR filters may . FIR filters are always stable, while IIR filters may be unstable. be unstable. 而无限脉冲响应（而无限脉冲响应（而无限脉

49、冲响应（而无限脉冲响应（IIRIIR）滤波器）滤波器）滤波器）滤波器同时使用输入信号和以前的输出同时使用输入信号和以前的输出同时使用输入信号和以前的输出同时使用输入信号和以前的输出信号样本信号样本信号样本信号样本229Most filters can be described in Z-domain (a superset of the Most filters can be described in Z-domain (a superset of the frequency domain) by their transfer functions. frequency domain) by t

50、heir transfer functions. A filter may A filter may also be described as a difference equation, a collection of also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or zeroes and poles or, if it is an FIR filter, an impulse respo

51、nse or step response.step response.7 7 滤波器也可以用差分方程或一组零极点滤波器也可以用差分方程或一组零极点滤波器也可以用差分方程或一组零极点滤波器也可以用差分方程或一组零极点表示，对于表示，对于表示，对于表示，对于FIRFIR滤波器还可以用冲击响应滤波器还可以用冲击响应滤波器还可以用冲击响应滤波器还可以用冲击响应或阶跃响应表示。或阶跃响应表示。或阶跃响应表示。或阶跃响应表示。239The output of an FIR filter to any given input may be The output of an FIR filter to any

52、 given input may be calculated by convolving the input signal with the impulse calculated by convolving the input signal with the impulse response. response. Filters can also be represented by block diagrams Filters can also be represented by block diagrams which can then be used to derive a sample

53、processing which can then be used to derive a sample processing algorithm to implement the filter using hardware instructionsalgorithm to implement the filter using hardware instructions. .滤波器还可以用结构图来表示，它能滤波器还可以用结构图来表示，它能滤波器还可以用结构图来表示，它能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，以便使用硬用来推导样本处理算法，以便使用硬用来推导样本处理算法，以便使用

54、硬用来推导样本处理算法，以便使用硬件指令实现滤波器件指令实现滤波器件指令实现滤波器件指令实现滤波器2410 Frequency domainSignals are converted from time or space domain to the Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. frequency domain usually through the Fourier transform. The The

55、Fourier transform converts the signal information to a Fourier transform converts the signal information to a magnitude and phase component of each frequencymagnitude and phase component of each frequency. Often the . Often the Fourier transform is converted to the power spectrum, which Fourier tran

56、sform is converted to the power spectrum, which is the magnitude of each frequency component squared.is the magnitude of each frequency component squared.FourierFourier变换将信号信息变换成每个变换将信号信息变换成每个变换将信号信息变换成每个变换将信号信息变换成每个频率的幅度和相位成分频率的幅度和相位成分频率的幅度和相位成分频率的幅度和相位成分2511The most common purpose for analysis of

57、signals in the The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The frequency domain is analysis of signal properties. The engineer can study the spectrum to get information of which engineer can study the spectrum to get information of which

58、frequencies are present in the input signal and which are frequencies are present in the input signal and which are missing.missing.2612There are some commonly used frequency domain There are some commonly used frequency domain transformations. transformations. For example, the cepstrum converts a s

59、ignal For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the to the frequency domain through Fourier transform, takes the logarithm, and then applies another Fourier transform. This logarithm, and then applies another Fourier transform. This emphasiz

60、es the frequency components with smaller magnitude emphasizes the frequency components with smaller magnitude while retaining the order of magnitudes of frequency while retaining the order of magnitudes of frequency ponents.8 8例如倒谱用例如倒谱用例如倒谱用例如倒谱用FourierFourier变换将信号转换到频域，取对数，变换将信号转换到频域，取对数，变换将信号转换到频

61、域，取对数，变换将信号转换到频域，取对数，然后再作第二次然后再作第二次然后再作第二次然后再作第二次FourierFourier变换。这就强调了幅度较小变换。这就强调了幅度较小变换。这就强调了幅度较小变换。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。的频率成分同时保持了频率分量的数量级。的频率成分同时保持了频率分量的数量级。的频率成分同时保持了频率分量的数量级。2713 ApplicationsThe main applications of DSP are audio signal processing, The main applications of DSP are audio

62、 signal processing, audio compression, digital image processing, video audio compression, digital image processing, video compression, speech processing, speech recognition, digital compression, speech processing, speech recognition, digital communications, radar, sonar, seismology, and biomedicine.

63、 communications, radar, sonar, seismology, and biomedicine. 2813Specific examples are speech compression and transmission in Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in digital mobile phones, room matching equalization of

64、 sound in HiFi and sound reinforcement applications, weather HiFi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-analysis and

65、control of industrial processes, computer-generated animations in movies, medical imaging such as CAT generated animations in movies, medical imaging such as CAT scans and MRI, image manipulation, high fidelity loudspeaker scans and MRI, image manipulation, high fidelity loudspeaker crossovers and e

66、qualization, and audio effects for use with crossovers and equalization, and audio effects for use with electric guitar amplifiers.electric guitar amplifiers.2914 ImplementationDigital signal processing is often implemented using Digital signal processing is often implemented using specialized micro

67、processors such as the MC56000 and the specialized microprocessors such as the MC56000 and the TMS320. TMS320. These often process data using fixed-point These often process data using fixed-point arithmetic, although some versions are available which use arithmetic, although some versions are avail

68、able which use floating point arithmetic and are more powerfulfloating point arithmetic and are more powerful. . 它们通常使用定点算法处理数据，它们通常使用定点算法处理数据，它们通常使用定点算法处理数据，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，运算尽管也有一些使用浮点算法，运算尽管也有一些使用浮点算法，运算尽管也有一些使用浮点算法，运算能力更强大能力更强大能力更强大能力更强大3014For faster applications FPGAs might be used

69、. Beginning in For faster applications FPGAs might be used. Beginning in 2007, multicore implementations of DSPs have started to 2007, multicore implementations of DSPs have started to emerge. For faster applications with vast usage, ASICs might emerge. For faster applications with vast usage, ASICs

70、 might be designed specifically. For slow applications, a traditional be designed specifically. For slow applications, a traditional slower processor such as a microcontroller can cope.slower processor such as a microcontroller can cope.信息科学与电子工程专业英语Part IIGeneral Concepts of Digital Signal Processi

71、ng 32New Wordsspecial-purposespecial-purpose专用专用专用专用terminology terminology 术语术语术语术语sinusoidal sinusoidal 正弦的正弦的正弦的正弦的contextcontext上下文，背景上下文，背景上下文，背景上下文，背景casually casually 随便地随便地随便地随便地rigid rigid 坚硬的，刚性的坚硬的，刚性的坚硬的，刚性的坚硬的，刚性的pursuepursue追求，从事追求，从事追求，从事追求，从事excitationexcitation激励激励激励激励differential e

72、quation differential equation 微分方程微分方程微分方程微分方程difference equationdifference equation差分方程差分方程差分方程差分方程time-invarianttime-invariant时不变的时不变的时不变的时不变的lumped systemlumped system集总系统集总系统集总系统集总系统incrementincrement增量增量增量增量presampling presampling 预采样预采样预采样预采样waveformwaveform波形波形波形波形strategystrategy策略策略策略策略mult

73、iplexmultiplex复用复用复用复用dynamic rangedynamic range动态范围动态范围动态范围动态范围compatible compatible 兼容兼容兼容兼容subtractionsubtraction减法减法减法减法33New Wordsmultiplication multiplication 乘法乘法乘法乘法reconstruction reconstruction 重建重建重建重建holding circuit holding circuit 保持电路保持电路保持电路保持电路extrapolate extrapolate 外推外推外推外推interpola

74、te interpolate 内插内插内插内插curve-fitting curve-fitting 曲线拟合曲线拟合曲线拟合曲线拟合prescribed prescribed 预定的预定的预定的预定的intervene intervene 插入，干预插入，干预插入，干预插入，干预intervening intervening 期间的期间的期间的期间的bandlimited bandlimited 限带的限带的限带的限带的aliasing aliasing 混叠混叠混叠混叠erroneous erroneous 错误的错误的错误的错误的wagon wagon 四轮马车四轮马车四轮马车四轮马车s

75、poke spoke 轮辐轮辐轮辐轮辐spurious spurious 假的，伪造的假的，伪造的假的，伪造的假的，伪造的arbitrarily arbitrarily 任意地任意地任意地任意地uncertainty uncertainty 不确定性不确定性不确定性不确定性quantum quantum 量子，量化量子，量化量子，量化量子，量化demltiplexer demltiplexer 解复用器解复用器解复用器解复用器telemetry telemetry 遥测遥测遥测遥测341There have been tremendous demands in the use of digit

76、al There have been tremendous demands in the use of digital computers and special-purpose digital circuitry for computers and special-purpose digital circuitry for performing varied signal processing functions that were performing varied signal processing functions that were originally achieved with

77、 analog equipment. The continued originally achieved with analog equipment. The continued evolution of inexpensive integrated circuits has led to a variety evolution of inexpensive integrated circuits has led to a variety of microcomputers and minicomputers that can be used for of microcomputers and

78、 minicomputers that can be used for various signal processing functions. various signal processing functions. 351It is now possible to build special-purpose digital processors It is now possible to build special-purpose digital processors within much smaller size and lower cost constraints of system

79、s within much smaller size and lower cost constraints of systems previously all analog in nature.previously all analog in nature.1 1现在有可能在比以往全模拟系统现在有可能在比以往全模拟系统现在有可能在比以往全模拟系统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小得多，而且成本也低得多的限小得多，而且成本也低得多的限小得多，而且成本也低得多的限制下构成专用数字处理器。制下构成专用数字处理器。制下构成专用数字处理器。制下构成专用数字处理器。362We wi

80、ll provide a general discussion of the basic concepts We will provide a general discussion of the basic concepts associated with digital signal processing. To do so, it is associated with digital signal processing. To do so, it is appropriate to discuss some common terms and assumptions. appropriate

81、 to discuss some common terms and assumptions. Wherever possible, the definitions and terminology will be Wherever possible, the definitions and terminology will be established in accordance with the recommendations of the established in accordance with the recommendations of the IEEE Group on Audio

82、 and ElectroacousticsIEEE Group on Audio and Electroacoustics. .可能之处，定义和术语将依照可能之处，定义和术语将依照可能之处，定义和术语将依照可能之处，定义和术语将依照IEEEIEEE音频和电声小组的推荐音频和电声小组的推荐音频和电声小组的推荐音频和电声小组的推荐373An analog signal is a function that is defined over a continuous An analog signal is a function that is defined over a continuous ran

83、ge of time and in which the amplitude may assume a range of time and in which the amplitude may assume a continuous range of valuescontinuous range of values. Common examples are the . Common examples are the sinusoidal function, the step function, the output of a sinusoidal function, the step funct

84、ion, the output of a microphone, etc. The term microphone, etc. The term analoganalog apparently originated from apparently originated from the field of analog computation, in which voltages and the field of analog computation, in which voltages and currents are used to represent physical variables,

85、 but it has currents are used to represent physical variables, but it has been extended in usage.been extended in usage.模拟信号是定义在连续时间上的模拟信号是定义在连续时间上的模拟信号是定义在连续时间上的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函数，其幅度取值是连续的函数，其幅度取值是连续的函数，其幅度取值是连续的384Continuous-time signal is a function that is defined over a Continuous-ti

86、me signal is a function that is defined over a continuous range of time, but in which the amplitude may continuous range of time, but in which the amplitude may either have a continuous range of values or a finite number of either have a continuous range of values or a finite number of possible valu

87、espossible values. In this context, an analog signal could be . In this context, an analog signal could be considered as a special case of a continuous-time signal. In considered as a special case of a continuous-time signal. In practice, however, the terms practice, however, the terms analoganalog

88、and and continuous-timecontinuous-time are are interchanged casually in usage and are often used to mean the interchanged casually in usage and are often used to mean the same thing. same thing. 连续时间信号是定义在连续时间上连续时间信号是定义在连续时间上连续时间信号是定义在连续时间上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的函数，但是它的幅度可能是连续的函数，但是它的幅度可能是连续

89、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值也可以是有限的可能值值也可以是有限的可能值值也可以是有限的可能值394Because of the association of the term Because of the association of the term analoganalog with physical with physical analogies, preference has been established for the term analogies, preference has been established for the term continu

90、ous-timecontinuous-time. Nevertheless, there will be cases in which the . Nevertheless, there will be cases in which the term term analoganalog will be used for clarity, particularly where it will be used for clarity, particularly where it relates to the term relates to the term digitaldigital. .2 2

91、由于由于由于由于“ “模拟模拟模拟模拟” ”一词与物理类比的关联，已经一词与物理类比的关联，已经一词与物理类比的关联，已经一词与物理类比的关联，已经确立了优先使用确立了优先使用确立了优先使用确立了优先使用“ “连续时间连续时间连续时间连续时间” ”这一术语。不这一术语。不这一术语。不这一术语。不过有时为了清楚起见也用过有时为了清楚起见也用过有时为了清楚起见也用过有时为了清楚起见也用“ “模拟模拟模拟模拟” ”一词，特一词，特一词，特一词，特别是与别是与别是与别是与“ “数字数字数字数字” ”相联系时。相联系时。相联系时。相联系时。405The term quantization describ

92、es the process of representing a The term quantization describes the process of representing a variable by a set of distinct valuesvariable by a set of distinct values. A quantized variable is one . A quantized variable is one that may assume only distinct valuesthat may assume only distinct values.

93、 .经量化的变量只能经量化的变量只能经量化的变量只能经量化的变量只能取离散值取离散值取离散值取离散值416A discrete-time signal is a function that is defined only at a A discrete-time signal is a function that is defined only at a particular set of values of timeparticular set of values of time. This means that the . This means that the independent v

94、ariable, time, is quantized. If the amplitude of a independent variable, time, is quantized. If the amplitude of a discrete-time signal is permitted to assume a continuous range discrete-time signal is permitted to assume a continuous range of values, the function is said to be a sampled-data signal

95、. A of values, the function is said to be a sampled-data signal. A sampled-data signal could arise from sampling an analog sampled-data signal could arise from sampling an analog signal at discrete values of time.signal at discrete values of time.离散时间信号是定义在某些离散时间信号是定义在某些离散时间信号是定义在某些离散时间信号是定义在某些特定时间值

96、上的函数特定时间值上的函数特定时间值上的函数特定时间值上的函数427A digital signal is a function in which both time and amplitude A digital signal is a function in which both time and amplitude are quantized. A digital signal may always be represented by a are quantized. A digital signal may always be represented by a sequence of

97、numbers in which each number has a finite sequence of numbers in which each number has a finite number of digits.number of digits.438The terms The terms discrete-timediscrete-time and and digitaldigital are often interchanged in are often interchanged in practice and are often used to mean the same

98、thing. practice and are often used to mean the same thing. A great A great deal of the theory underlying discrete-time signals is deal of the theory underlying discrete-time signals is applicable to purely digital signals, so it is not always applicable to purely digital signals, so it is not always

99、 necessary to make rigid distinctionsnecessary to make rigid distinctions. The term . The term discrete-timediscrete-time will more often be used in pursuing theoretical developments, will more often be used in pursuing theoretical developments, and the term and the term digitaldigital will more oft

100、en be used in describing will more often be used in describing hardware or software realizations.hardware or software realizations.许多基于离散时间信号的定理适用于许多基于离散时间信号的定理适用于许多基于离散时间信号的定理适用于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纯数字信号，因此没有必要总是对两纯数字信号，因此没有必要总是对两纯数字信号，因此没有必要总是对两者作严格的区分者作严格的区分者作严格的区分者作严格的区分449A system c

101、an be described by any of the preceding terms A system can be described by any of the preceding terms according to the type of hardware or software employed and according to the type of hardware or software employed and the type of signals presentthe type of signals present. Thus, reference can be m

102、ade to . Thus, reference can be made to analog systemsanalog systems, , continuous-time systemscontinuous-time systems, , discrete-time systemsdiscrete-time systems, , digital systemsdigital systems, etc., etc.根据使用的硬件或软件的类型和当前根据使用的硬件或软件的类型和当前根据使用的硬件或软件的类型和当前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信号的类型，一个系统

103、可以用任意的信号的类型，一个系统可以用任意的信号的类型，一个系统可以用任意的前述术语来描述前述术语来描述前述术语来描述前述术语来描述4510A linear system is one in which the principle of superposition A linear system is one in which the principle of superposition applies. applies. A linear system can be described by linear differential A linear system can be describ

104、ed by linear differential or difference equationsor difference equations. A time-invariant linear system is one . A time-invariant linear system is one in which the parameters are fixed and do not vary with time.in which the parameters are fixed and do not vary with time.线性系统可以用线性的微分线性系统可以用线性的微分线性系统

105、可以用线性的微分线性系统可以用线性的微分或差分方程来描述或差分方程来描述或差分方程来描述或差分方程来描述4611A lumped system is one that is composed of finite nonzero A lumped system is one that is composed of finite nonzero elements satisfying ordinary differential or difference equation elements satisfying ordinary differential or difference equatio

106、n relationships, as opposed to a distributed system, satisfying relationships, as opposed to a distributed system, satisfying partial differential equation relationships.partial differential equation relationships.3 3 集总系统是由有限非零元素构成，满足集总系统是由有限非零元素构成，满足集总系统是由有限非零元素构成，满足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，

107、与满足常微分（或差分）方程的系统，与满足常微分（或差分）方程的系统，与满足常微分（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。偏微分方程的分布式系统相对应。偏微分方程的分布式系统相对应。偏微分方程的分布式系统相对应。4712The standard form for numerical processing of a digital signal The standard form for numerical processing of a digital signal is the binary number system. The binary number system is

108、 the binary number system. The binary number system makes use only of the values 0 and 1 to represent all possible makes use only of the values 0 and 1 to represent all possible numbers. numbers. 4812The number of levels The number of levels mm that can be represented by a number that can be represe

109、nted by a number having having n n binary digits (bits) is given by binary digits (bits) is given byConversely, if Conversely, if mm is the number of possible levels required, the is the number of possible levels required, the number of bits required is the smallest integer greater than or number of

110、 bits required is the smallest integer greater than or equal to log2 equal to log2 mm. .4 4可用可用可用可用n n位二进制（位二进制（位二进制（位二进制（n n比特）表示的等级数比特）表示的等级数比特）表示的等级数比特）表示的等级数mm由由由由mm= 2= 2n n给出。反过来，如果给出。反过来，如果给出。反过来，如果给出。反过来，如果mm是要求的等是要求的等是要求的等是要求的等级数，所需的比特数是大于等于级数，所需的比特数是大于等于级数，所需的比特数是大于等于级数，所需的比特数是大于等于log2 log

111、2 mm的的的的最小整数。最小整数。最小整数。最小整数。m = 2n4913The process by which digital signal processing is achieved will The process by which digital signal processing is achieved will be illustrated by a simplified system in which the signal is be illustrated by a simplified system in which the signal is assumed to v

112、ary from 0 to 7 volts and in which 8 possible assumed to vary from 0 to 7 volts and in which 8 possible levels (at 1 V increments) are used for the binary numbers.levels (at 1 V increments) are used for the binary numbers.5 5实现数字处理的过程将用一个简化系统实现数字处理的过程将用一个简化系统实现数字处理的过程将用一个简化系统实现数字处理的过程将用一个简化系统来说明，假定信

113、号在来说明，假定信号在来说明，假定信号在来说明，假定信号在0V0V到到到到7V7V之间变化，之间变化，之间变化，之间变化，以以以以1V1V为增量，用为增量，用为增量，用为增量，用8 8种可能的值表示成二种可能的值表示成二种可能的值表示成二种可能的值表示成二进制数。进制数。进制数。进制数。5013A block diagram is shown in Figure 9.1, and some waveforms A block diagram is shown in Figure 9.1, and some waveforms of interest are shown in Figure 9.

114、2. The signal is first passed of interest are shown in Figure 9.2. The signal is first passed through a continuous-time presampling filter whose function through a continuous-time presampling filter whose function will be discussed later. will be discussed later. Pre-sampling filterSampler and A/D c

115、onverterDigital signal processorD/A converter and filtersAnalog signal inAnalog signal out0000100111111111101000110018T0T2T3T4T5T6T7Tt8T0T2T3T4T5T6T7Ttx(t) and quantized samples5113The signal is then read at intervals of The signal is then read at intervals of T T seconds by a sampler. seconds by a

116、sampler. These samples must then be quantized to one of the standard These samples must then be quantized to one of the standard levels. Although there are different strategies employed in the levels. Although there are different strategies employed in the quantization process, one common approach,

117、which will be quantization process, one common approach, which will be assumed here, is that a sample is assigned to the nearest level. 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 Thus, a sample of value 4.2 V would

118、be quantized to 4 V, and a sample of value 4.6 V would be quantized to 5 V.sample of value 4.6 V would be quantized to 5 V.5214This process for the signal given is illustrated in Figure 9.2. This process for the signal given is illustrated in Figure 9.2. The pulses representing the signal have been

119、made very The pulses representing the signal have been made very narrow to illustrate the fact that other signals may be inserted, narrow to illustrate the fact that other signals may be inserted, or multiplexed, in the empty space. These pulses may then be or multiplexed, in the empty space. These

120、pulses may then be represented as binary numbers. represented as binary numbers. In order that these numbers In order that these numbers could be seen on the figure, each has been shown over much of could be seen on the figure, each has been shown over much of the space in a given interval.the space

121、 in a given interval. 为了使这些数字可以从图中看到，每组为了使这些数字可以从图中看到，每组为了使这些数字可以从图中看到，每组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都显示在给定间隔的空档处都显示在给定间隔的空档处都显示在给定间隔的空档处5314In practice, if other signals are to be inserted, the pulses In practice, if other signals are to be inserted, the pulses representing the bits of the binary

122、numbers could be made representing the bits of the binary numbers could be made very short. very short. A given binary number could then be read in a A given binary number could then be read in a very short interval at the beginning of a sampling period, thus very short interval at the beginning of

123、a sampling period, thus leaving most of the time available for other signalsleaving most of the time available for other signals. .一个给定的二进制数就可以在采样周期一个给定的二进制数就可以在采样周期一个给定的二进制数就可以在采样周期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，这样就给其它开始的很短间隔内读到，这样就给其它开始的很短间隔内读到，这样就给其它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信号留出了大部分的可用时间信号留出了大部

124、分的可用时间信号留出了大部分的可用时间5415The process by which an analog sample is quantized and The process by which an analog sample is quantized and converted to a binary number is called analog-to-digital (A/D) converted to a binary number is called analog-to-digital (A/D) conversion. In general,conversion. In gen

125、eral, the dynamic range of the signal must the dynamic range of the signal must be compatible with that of the A/D converter employed, and be compatible with that of the A/D converter employed, and the number of bits employed must be sufficient for the the number of bits employed must be sufficient

126、for the required accuracy.required accuracy.信号的动态范围要和所用的信号的动态范围要和所用的信号的动态范围要和所用的信号的动态范围要和所用的A/DA/D转换器转换器转换器转换器相一致，为了达到所要求的精确度，要相一致，为了达到所要求的精确度，要相一致，为了达到所要求的精确度，要相一致，为了达到所要求的精确度，要使用足够的比特数使用足够的比特数使用足够的比特数使用足够的比特数5516The signal can now be processed by the type of unit The signal can now be processed by

127、 the type of unit appropriate for the application intended. This unit may be a appropriate for the application intended. This unit may be a general-purpose computer or minicomputer, or it may be a general-purpose computer or minicomputer, or it may be a special unit designed specifically for this pu

128、rpose. At any rate, special unit designed specifically for this purpose. At any rate, it is composed of some combination of standard digital circuits it is composed of some combination of standard digital circuits capable of performing the various arithmetic functions of capable of performing the va

129、rious arithmetic functions of addition, subtraction, multiplication, etc. In addition, it has addition, subtraction, multiplication, etc. In addition, it has logic and storage capability.logic and storage capability.5617At the output of the processor, the digital signal can be At the output of the p

130、rocessor, the digital signal can be converted to analog form again. This is achieved by the converted to analog form again. This is achieved by the process of digital-to-analog (D/A) conversion. In this step, the process of digital-to-analog (D/A) conversion. In this step, the binary numbers are fir

131、st successively converted back to binary numbers are first successively converted back to continuous-time pulses. The continuous-time pulses. The gapsgaps between the pulses are then between the pulses are then filled in by a reconstruction filter. filled in by a reconstruction filter. 5717This filt

132、er may consist of a holding circuit, which is a special This filter may consist of a holding circuit, which is a special circuit designed to hold the value of a pulse between successive circuit designed to hold the value of a pulse between successive sample values. sample values. In some cases, the

133、holding circuit may be In some cases, the holding circuit may be designed to interpolate the output signal between successive designed to interpolate the output signal between successive points according to some prescribed curve-fitting strategy.points according to some prescribed curve-fitting stra

134、tegy.6 6 In In addition to a holding circuit, a basic continuous-time filter addition to a holding circuit, a basic continuous-time filter may be employed to provide additional smoothing between may be employed to provide additional smoothing between points.points.在某些情况下，可设计保持电路，将在某些情况下，可设计保持电路，将在某些

135、情况下，可设计保持电路，将在某些情况下，可设计保持电路，将输出信号在连续样点之间按照设定的输出信号在连续样点之间按照设定的输出信号在连续样点之间按照设定的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。曲线拟合方法进行内插。曲线拟合方法进行内插。曲线拟合方法进行内插。5818A fundamental question that may arise is whether or not some A fundamental question that may arise is whether or not some information has been lost in the proc

136、ess. After all, information has been lost in the process. After all, the signal the signal has been sampled only at discrete intervals of time; is there has been sampled only at discrete intervals of time; is there something that might be missed in the intervening time something that might be missed

137、 in the intervening time intervalsintervals? Furthermore, in the process of quantization, the ? Furthermore, in the process of quantization, the actual amplitude is replaced by the nearest standard level, actual amplitude is replaced by the nearest standard level, which means that there is a possibl

138、e error in amplitude.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；在介于信号仅仅在离散的时间间隔处被采样；在介于信号仅仅在离散的时间间隔处被采样；在介于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时间间隔内是否有一些信息丢失了呢时间间隔内是否有一些信息丢失了呢时间间隔内是否有一些信息丢失了呢5919In regard to the sampling question, it will be shown that, if the In regard

139、 to the sampling question, it will be shown that, if the signal is bandlimited, and if the sampling rate is greater than signal is bandlimited, and if the sampling rate is greater than or equal to twice the highest frequency, the signal can or equal to twice the highest frequency, the signal can the

140、oretically be recovered from its discrete samples.theoretically be recovered from its discrete samples.7 7 关于采样的问题，我们将表明，如果信号带宽关于采样的问题，我们将表明，如果信号带宽关于采样的问题，我们将表明，如果信号带宽关于采样的问题，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，有限，并且采样率大于等于最高频率的两倍，有限，并且采样率大于等于最高频率的两倍，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。理论上信号就能从离散的样本恢复。理

141、论上信号就能从离散的样本恢复。理论上信号就能从离散的样本恢复。6019This corresponds to a minimum of two samples per cycle at This corresponds to a minimum of two samples per cycle at the highest frequency. In practice, this sampling rate is usually the highest frequency. In practice, this sampling rate is usually chosen to be some

142、what higher than the minimum rate (say, chosen to be somewhat higher than the minimum rate (say, three or four times the highest frequency) in order to ensure three or four times the highest frequency) in order to ensure practical implementation. For example, if the highest practical implementation.

143、 For example, if the highest frequency of the analog signal is 5 kHz, the theoretical frequency of the analog signal is 5 kHz, the theoretical minimum sampling rate is 10,000 samples per second, and a minimum sampling rate is 10,000 samples per second, and a practical system would employ a rate some

144、what higher. practical system would employ a rate somewhat higher. 6119The input continuous-time signal is often passed through a The input continuous-time signal is often passed through a low-pass analog presampling filter to ensure that the highest low-pass analog presampling filter to ensure that

145、 the highest frequency is within the bounds for which the signal can be frequency is within the bounds for which the signal can be recovered.recovered.8 8常将输入的连续时间信号通过一个低通模常将输入的连续时间信号通过一个低通模常将输入的连续时间信号通过一个低通模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拟预采样滤波器，以确保最高频率落在信拟预采样滤波器，以确保最高频率落在信拟预采样滤波器，以确保最高频率落在信号能

146、够完全恢复的界限之内。号能够完全恢复的界限之内。号能够完全恢复的界限之内。号能够完全恢复的界限之内。6220If a signal is not sampled at a sufficiently high rate, a If a signal is not sampled at a sufficiently high rate, a phenomenon known as aliasing results. phenomenon known as aliasing results. This concept results in This concept results in a freq

147、uency being mistaken for an entirely different frequency a frequency being mistaken for an entirely different frequency upon recoveryupon recovery. For example, suppose a signal with frequencies . For example, suppose a signal with frequencies ranging from dc to 5 kHz is sampled at a rate of 6 kHz,

148、which ranging from dc to 5 kHz is sampled at a rate of 6 kHz, which is clearly too low to ensure recovery. If recovery is attempted, is clearly too low to ensure recovery. If recovery is attempted, a component of the original signal at 5 kHz now appears to be a component of the original signal at 5

149、kHz now appears to be at 1 kHz, resulting in an erroneous signal. at 1 kHz, resulting in an erroneous signal. 混叠会导致在恢复时一个频率混叠会导致在恢复时一个频率混叠会导致在恢复时一个频率混叠会导致在恢复时一个频率被误作为完全不同的频率被误作为完全不同的频率被误作为完全不同的频率被误作为完全不同的频率6320A common example of this phenomenon is one we will call the A common example of this pheno

150、menon is one we will call the wagon wheel effectwagon wheel effect, probably noticed by the reader in western , probably noticed by the reader in western movies as the phenomenon in which the wheels appear to be movies as the phenomenon in which the wheels appear to be rotating backwards.rotating ba

151、ckwards.9 9 一个普通例子就是我们称之为一个普通例子就是我们称之为一个普通例子就是我们称之为一个普通例子就是我们称之为“ “车轮车轮车轮车轮效应效应效应效应” ”的现象，就是读者在西部电影的现象，就是读者在西部电影的现象，就是读者在西部电影的现象，就是读者在西部电影中也许注意到的车轮看起来向后转动中也许注意到的车轮看起来向后转动中也许注意到的车轮看起来向后转动中也许注意到的车轮看起来向后转动的情况。的情况。的情况。的情况。6420Since each individual frame of a film is equivalent to a discrete Since each i

152、ndividual frame of a film is equivalent to a discrete sampling operation, if the rate of spokes passing a given angle sampling operation, if the rate of spokes passing a given angle is too large for a given movie frame rate, the wheels appear to is too large for a given movie frame rate, the wheels

153、appear to be turning either backwards or at a very slow speed.be turning either backwards or at a very slow speed.1010 因为影片的每一帧相当于一次离散的采样，因为影片的每一帧相当于一次离散的采样，因为影片的每一帧相当于一次离散的采样，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如果相对于电影帧频而言轮辐越过的给定角如果相对于电影帧频而言轮辐越过的给定角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度过大，轮子看起来就

154、会向后转动或以很慢度过大，轮子看起来就会向后转动或以很慢度过大，轮子看起来就会向后转动或以很慢的速度转动。的速度转动。的速度转动。的速度转动。6520The effect of a presampling filter removes the possibility that a The effect of a presampling filter removes the possibility that a spurious signal whose frequency is too high for the system will spurious signal whose frequen

155、cy is too high for the system will be mistaken for one in the proper frequency range.be mistaken for one in the proper frequency range.1111采样前预滤波消除了这种对系统而言采样前预滤波消除了这种对系统而言采样前预滤波消除了这种对系统而言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过高的伪信号被错误地当作适当频率过高的伪信号被错误地当作适当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。频率范围内的另一信号的可能性。频率范

156、围内的另一信号的可能性。频率范围内的另一信号的可能性。6621With respect to the quantization error, it can be seen that With respect to the quantization error, it can be seen that the the error can be made as small as one chooses if the number of error can be made as small as one chooses if the number of bits can be made arbitr

157、arily largebits can be made arbitrarily large. Of course, there is a . Of course, there is a practical maximum limit, so it is necessary to tolerate some practical maximum limit, so it is necessary to tolerate some error from this phenomenon. Even in continuous-time error from this phenomenon. Even

158、in continuous-time systems, there may be noise present which would introduce systems, there may be noise present which would introduce uncertainty in the actual magnitude. In fact, the uncertainty uncertainty in the actual magnitude. In fact, the uncertainty present in the digital sampling process i

159、s called quantization present in the digital sampling process is called quantization noise.noise.如果使用任意多的比特数，如果使用任意多的比特数，如果使用任意多的比特数，如果使用任意多的比特数，可使误差任意小可使误差任意小可使误差任意小可使误差任意小6722Let Let E Emaxmax and and E Eminmin represent the maximum and minimum represent the maximum and minimum values of the signa

160、l, and let values of the signal, and let q q represent the vertical distance represent the vertical distance between successive quantum levels. Using between successive quantum levels. Using n n and and mm as as previously defined, we havepreviously defined, we have(9-2)6822Assuming that a sample be

161、tween two successive quantum Assuming that a sample between two successive quantum levels is assigned to the nearest quantum level, the peak levels is assigned to the nearest quantum level, the peak quantization noise and peak percentage quantization noise quantization noise and peak percentage quan

162、tization noise values arevalues are6923In many cases, the In many cases, the variancevariance of the quantization noise is more of the quantization noise is more important than the maximum value. The variance important than the maximum value. The variance is directly is directly proportional topropo

163、rtional to the the average poweraverage power associated with the noise. If associated with the noise. If the signal is assumed to be uniformly distributed between the signal is assumed to be uniformly distributed between quantum levels, it can be shown by statistical analysis that the quantum level

164、s, it can be shown by statistical analysis that the noise variance noise variance s s s s2 2 is is与与与与.成正比成正比成正比成正比7023The root-mean-square (EMS) (or standard deviation) value of The root-mean-square (EMS) (or standard deviation) value of this noise component isthis noise component isComparing (9-6)

165、 with (9-3), it is seen that the RMS noise Comparing (9-6) with (9-3), it is seen that the RMS noise component is times the peak noise component. component is times the peak noise component. 7124In view of the preceding discussion, it appears that In view of the preceding discussion, it appears that

166、 no no information is lost in the sampling operation provided that the information is lost in the sampling operation provided that the sampling rate is high enoughsampling rate is high enough, and the quantization error can , and the quantization error can be reduced to an insignificantly small leve

167、l by choosing a be reduced to an insignificantly small level by choosing a sufficient number of bits to represent each binary number. sufficient number of bits to represent each binary number. These concepts then permit us to represent a continuous-time These concepts then permit us to represent a c

168、ontinuous-time signal in terms of a series of discrete binary numbers, which signal in terms of a series of discrete binary numbers, which may be processed directly with digital circuits.may be processed directly with digital circuits.如果采样速率足够高的话，采样如果采样速率足够高的话，采样如果采样速率足够高的话，采样如果采样速率足够高的话，采样操作就不会造成信息

169、丢失操作就不会造成信息丢失操作就不会造成信息丢失操作就不会造成信息丢失7225The rather involved procedure of A/D conversion, processing, The rather involved procedure of A/D conversion, processing, and final D/A conversion may seem like a lot of effort in order and final D/A conversion may seem like a lot of effort in order to handle o

170、ne signal channel. Indeed, in many cases such a to handle one signal channel. Indeed, in many cases such a complex process may not be economically feasible for a single complex process may not be economically feasible for a single signalsignal. One of the great advantages of the digital concept is t

171、he . One of the great advantages of the digital concept is the possibility of processing a number of channels with the same possibility of processing a number of channels with the same arithmetic unitarithmetic unit. . 数字概念的一个很大优势就是可以用数字概念的一个很大优势就是可以用数字概念的一个很大优势就是可以用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同一个算

172、术单元处理许多信道同一个算术单元处理许多信道同一个算术单元处理许多信道7325This process can be achieved by a process called This process can be achieved by a process called time-division time-division multiplexingmultiplexing (TDM). It was observed in the sampled signal (TDM). It was observed in the sampled signal shown in Figure 9.2

173、that there was a relatively long period shown in Figure 9.2 that there was a relatively long period between successive samples of the signal. During this period, between successive samples of the signal. During this period, samples of additional signals are fed into the processor.samples of addition

174、al signals are fed into the processor.7426This concept is illustrated in Figure 9.3. Each channel is read This concept is illustrated in Figure 9.3. Each channel is read in a sequential order, and the corresponding values are in a sequential order, and the corresponding values are converted into bin

175、ary numbers in the same sequence. These converted into binary numbers in the same sequence. These numbers enter into the processing unit and, after suitable numbers enter into the processing unit and, after suitable processing, appear at the output in the appropriate order. processing, appear at the

176、 output in the appropriate order. 7526This composite digital signal must first be separated into the This composite digital signal must first be separated into the original different channels by means of a demultiplexer, which original different channels by means of a demultiplexer, which is synchro

177、nized with the input sampling signal. The channels is synchronized with the input sampling signal. The channels then undergo the D/A conversion required for output.then undergo the D/A conversion required for output.Digital signal processorDemultiplexerMultiplexerSyncSignalsSignals Figure 9.3 Multip

178、lexed digital processing system7627In the preceding discussions, we have assumed that both the In the preceding discussions, we have assumed that both the starting and final signals in the system are in continuous-time starting and final signals in the system are in continuous-time form. Actually, t

179、here are many systems in which one or both form. Actually, there are many systems in which one or both are already digital in form. In such cases the A/D conversion are already digital in form. In such cases the A/D conversion and/or the D/A conversion may not be required, thus and/or the D/A conver

180、sion may not be required, thus simplifying the system. simplifying the system. 7727For example, assume that a number of continuous-time For example, assume that a number of continuous-time telemetry signals are to be processed by a digital unit, but the telemetry signals are to be processed by a dig

181、ital unit, but the output data is to be kept in digital form for scientific data output data is to be kept in digital form for scientific data reduction and computation. In this case, the A/D unit at the reduction and computation. In this case, the A/D unit at the input is required, but no conversion is needed at the output.input is required, but no conversion is needed at the output.