Digital Signal Processing(1 Introduction)-讲义

About The Course

Digital Signal Processing SCUT Lecture 1 IntroductionIntroduction on DSP& A/D D/A Conversion

Bibliography

Textbook: A.V. Oppenheim, R.W. Schafer, J.R. Buck, Discrete-time Signal Processing, Second Edition. Prentice Hall, 1999. Tsinghua University Press, 2004. References: S. K.Mitra, Digital Signal Processing: A Computer-based Approach, Second Edition. Mcgraw-hill, 2001. Tsinghua University Press, 2004. 程佩青编,《数字信号处理教程》(第二版),清华大学出版社, 2000

SCUT

SCUT

Digital Signal Processing, 2014, Y.Zeng

Yan Zeng South China University of Technology 2014

SCUT第1页

Digital Signal Processing, 2014, Y.Zeng

第2页

About The Course Instructor: Yan Zeng,– Phone: 8711 4480 (H), 189 2512 0953– Office: Building#18 (412)– E-Mail: yzeng@, zengyan.gz@– E-Mail for submitting reports: scutoptics@ Grading Policy–Exercises and Reports: 20%–Final exam: 80% Exercises and Reports: There are proper exercises, homeworks or reports every week, which must be delivered on every Wednesday.Digital Signal Processing, 2014, Y.Zeng第3页

About The Course

SCUT

眼界决定境界，视野决定胸怀，行动决定命运！ 广泛阅读，善于思考，勤于实践！仰望星空，脚踏实地！

SCUT

I will give you many careful and trenchant discussion on DSP theories, methods and a wild view to modern science and technoloty. Wish you have a great journey in the course!

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第4页

Chapter 1 Introduction Background Aim& Motivation What is DSP Characteristics of DSP Basic Framework Main Application and Some Examples Sampling and Quantization( A/D D/A Conversion)

1.1 Background

SCUT

建安24年(公元219年)腊月，曹操与华佗。25年正月，操卒于头风之病。

SCUT

1821年1月，折磨拿破仑一辈子的头痛更加剧烈了，5月，一代枭雄陨落。他的病症和死亡原因，给人类留下了一个千古之谜。

1888年圣诞节前夕，剧烈的头疼折磨着文森特·梵高，这位饱受磨难的艺术天才、印象画派大师突然割掉了自己的耳朵。 19个月后，他举枪自杀。 Before 1900, you were more likely to look to religion than to science for an explanation of how the world worked. But now we search solutions in science and technology.

SCUTDigital Signal Processing, 2014, Y.Zeng第5页

SCUT

Digital Signal Processing, 2014, Y.Zeng

第6页

1.1 BackgroundHuman has been making a very great progress in science and technology, which changed the world forever, and improved our life forever.Please gave us some examples of modern science an technologies.Avigation

1.1 Background-Maths and Physics

SCUT

How did they happen?

How did we get these great achievements and how will we improve them?

SCUT

Mathematics Physics Chemistry ...... Basics o

f modern science and technology: Laws of Nature, Philosophy of Nature

SpaceflightMedicine&Healthy

Computer& Internet

Communication Sensors, Sensors, Autocontrol& Robotization

Mass Production

SCUT

nuclear energy

Precision-machine第7页

SCUTDigital Signal Processing, 2014, Y.Zeng第8页

Digital Signal Processing, 2014, Y.Zeng

1.1 Background-Maths and Physics Modern Science: Mathematics, Physics, and Chemistry, etc.

1.1 Background-Maths and Physics Modern Science: Mathematics, Physics, and Chemistry, etc.

SCUT......

SCUT

Johannes Kepler Galileo Galilei 1571–1630 1564–1642 Isaac Newton 1643–1727 Carl Friedrich Gauss 1777–1855

James Watt 1736-1819

Michael Faraday 1791– 1867

James Clerk Maxwell 1831–1879 W. T.1st Baron Kelvin 1824– 1907

SCUT

From exploring nature phenomenon to searching the laws of nature, philosophy of natureDigital Signal Processing, 2014, Y.Zeng第9页

They brought us the 1st. and 2nd. industrial revolution, and released people from heavy physical labor and enlarged man's power.

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 10页

1.1 Background-Maths and Physics Modern Science: Mathematics, Physics, and Chemistry, etc.

1.1 Background-Maths and Phisics Some great heads told us the laws of nature.

SCUT

SCUT

Robert Boyle 1627– 1691

Antoine Lavoisier 1743–1794

Dmitri Mendeleev Maria Sklodowska-Curie 1834– 1907 1867—1934

Like the Great Geographical Discoveries, sciensts made a great discoveries of matters, and let us deepen the understanding of the world around us.

SCUT

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 11页

The Fifth Solvay International Conference on Electrons and Photons-1927 Digital Signal Processing, 2014, Y.Zeng

第 12页

1.1 Background-Three Theories Imformatics:信息科学Tree Gorgeous Theories,which created in 40s~ 60s in 20th century, provided the foundations of modern electronic-information science and technology.

1.1 Background-Three Theories Imformatics:信息科学Informatics is the science of information, the practice of information processing, and the engineering of information systems. Informatics studies the structure, algorithms, behavior, and interactions of natural and artificial systems that store, process, access, and communicate information. In addition, it studies human-computer interaction and how an interface can be built to maximize user-efficiency. It also develops its own conceptual and theoretical foundations and utilizes foundations developed in other fields. Since the advent of computers, individuals and organizations increasingly process information digitally. This has led to the study of informatics that has computational, biological, cognitive and social aspects, including study of the social impact of information technologies. -https:///wiki/Informatics_(academic_field) It started a glorious times of our own, which is called information times. It m

ade and is making a great revolution of our life.

SCUT

SCUT

Information Theory (信息论) C.E. Shannon

System Theory (系统论) Cybernetics (控制论) L.V. Bertalanffy N.Wiener Rapid advances in IC design and manufacture are producing ever more powerful DSP devices at decreasing cost.

SCUT

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 13页

Digital Signal Processing, 2014, Y.Zeng

第 14页

1.1 Background-Three Theories Outline of DSP technology development

1.1 Background-Three Theories Outline of DSP technology development 随着大规模集成电路技术的发展，1982年世界上诞生了首枚DSP芯片。这种DSP器件采用微米工艺NMOS技术制作，虽功耗和尺寸稍大，但运算速度却比MPU快了几十倍，尤其在语音合成和编码解码器中得到了广泛应用。DSP芯片的问世是个里程碑，它标志着DSP应用系统由大型系统向小型化迈进了一大步。 至80年代中期，随着CMOS技术的进步与发展，第二代基于CMOS工艺的DSP芯片应运而生，其存储容量和运算速度都得到成倍提高，成为语音处理、图像硬件处理技术的基础。 80年代后期，第三代DSP芯片问世，运算速度进一步提高，其应用于范围逐步扩大到通信、计算机领域。 90年代DSP发展最快，相继出现了第四代和第五代DSP器件。现在的DSP属于第五代产品，它与第四代相比，系统集成度更高，将DSP芯核及外围元件综合集成在单一芯片上。这种集成度极高的DSP芯片不仅在通信、计算机领域大显身手，而且逐渐渗透到人们日常消费领域。 经过30多年的发展，DSP产品的应用已扩大到人们的学习、工作和生活的各个方面，并逐渐成为电子产品更新换代的决定因素。目前，对DSP爆炸性需求的时代已经来临，前景十分可观。

SCUT

SCUT

在DSP出现之前数字信号处理只能依靠MPU(微处理器)来完成。但MPU较低的处理速度无法满足高速实时的要求。因此，直到70年代，有人才提出了 DSP的理论和算法基础。那时的DSP仅仅停留在教科书上，即便是研制出来的 DSP系统也是由分立元件组成的，其应用领域仅局限于军事、航空航天部门。

SCUTDigital Signal Processing, 2014, Y.Zeng第 15页

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 16页

1.1 Background DSP Achievements Military – Secure communication– Radar processing– Sonar processing– Missile guidance Telecommunications – Data communication– Echo cancellation– Spread spectrum– Adaptive equalization– ADPCM transcoders Biomedical& Instrumentation/Control– Patient monitoring– CT Scanners– ECG(心电图) analysis– EEG(脑电图) brain mappers– X-ray storage/enhancement– Frequency analysis Digital Signal Processing, 2014, Y.Zeng Internet& wirelesss commun

ication– Signal compression and coding– Modem– Noise reduction– Data encrypting Speech/audio– Speech recognition/synthesis– Text to speech– Digital audio– Equalization(均衡化) Image/video Processing– Pattern recognition– Robotic vision (computer vision)– Image enhancement– Facsimile– Satellite weather map– Computer Animation

1.1 Background

SCUT

通信(Communication):整个通信领域几乎没有不受数字信号处理技术影响的地方。 (占60%) DSP主要应用于现代通信产品中。如：蜂窝电话(Cellularphone)、ADSL调制解调器、线缆调制解调器(Cable modem)、蓝牙技术(blue-tooth)产品，数字电话应答机(digital telephone answering device)、全球定位系统(global positioning system, GPS ),卫星电话(satellite phone)、电话会议(conference speaker phone)、电视电话会议编译码器(video conferencing code )、IP电话(voice over IP)、IP传真(fax over IP)、智能天线(smart antenna)、PCS用户端(subscriber set)等。工业(Industry):现代工业从信号采集、信号分析、控制信号产生等大量采用DSP技术。仪器仪表：频谱分析、函数发生、数据采集、地震预测、设备可靠性分析等。自动控制：控制、深空作业、自动驾驶、机器人控制、磁盘控制等。图像/图形：二维和三维图形处理、图像压缩与传输、图像识别、动画、机器视觉、多媒体、电子地图、视频分析等。军事(Military):保密通信、雷达处理、声呐处理、导航、全球定位、跳频电台、搜索和反搜索等。医疗：CT、心电图、超声设备、诊断仪器、病人监护、助听等。家用电器：数字音响、数字电视、IPTV、可视电话、音乐合成、音调控制、玩具与游戏等。

SCUT

SCUT

SCUT

第 17页

Digital Signal Processing, 2014, Y.Zeng

第 18页

1.1 BackgroundThroughout human history, engineering has driven the advance of civilization.

1.1 Background

SCUT

How about the future, 14 Challenges in engineering byNAE of USAMake solar energy economical Manage the nitrogen cycle Advance health informatics Prevent nuclear terror Advance personalized learning Provide energy from fusion Provide access to clean water Engineer better medicines

SCUTDevelop carbon sequestration methods Restore and improve urban infrastructure Reverse-engineer the brain Enhance virtual reality

In the modern era, the Industrial Revolution brought engineering’s influence to every niche of life, as machines supplemented and replaced human labor for countless tasks, improved systems for sanitation enhanced health, and the steam engine facilitated mining, powered trains and ships, and provided energy for factories.

How about the future October 2010, The 2010 NAE (National Academy of Engineering) Grand Challenges National Summit brings together leading scientists and engineers, educators, policy leader

s, innovators and corporate executives to address the 14 Challenges, which represent key societal issues of the 21st Century, articulated by the National Academy of Engineering.

Secure cyberspace Engineer the tools of scientific discovery

SCUT

/第 19页

SCUT

/第 20页

Digital Signal Processing, 2014, Y.Zeng

Digital Signal Processing, 2014, Y.Zeng

1.2 Aim and Motivation More and more signals are gathered, communicated, shown, and be used for analysis or control everyday in engineering, industry and society life. More precision(精度) and stable and reliable More general and cheaper devices Less and more compact devices High integration (集成) and more functions More dynamic (动态) balance& adaptive Easier to be operated and debuged (调试)

1.3 What is DSP

SCUT

Digital signal processing (DSP) is concerned with the representation of signals by a sequence of numbers or symbols and the processing of these signals. The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. DSP algorithms have long been run on standard computers, on specialized processors called digital signal processor on purpose-built hardware such as application-specific integrated circuit (ASICs).

SCUT

?第 21页

Digital Processing !

SCUT

信息化的基础是数字化。数字化的核心技术之一是数字信号处理。

SCUT

- /wiki/Digital_signal_processing

Digital Signal Processing, 2014, Y.Zeng

Digital Signal Processing, 2014, Y.Zeng

第 22页

1.3 What is DSP 1.数字信号处理(DSP, Digital signal processing): 信号处理是研究系统对含有信息的信号进行处理方法，以获得人们所希望的信号，从而达到提取信息、便于利用的一门学科。 DSP是20世纪60年代，随着信息学科和计算机学科的高速发展而迅速发展起来的一门新兴学科。 研究利用离散系统和数字方法进行信号的处理分析,将信号通过采样量化为数字信号,用数字或符号表示成序列，通过计算机或通用(专用)信号处理设备，用数字的数值计算方法(算法, algorithm)处理，达到提取或辨识有用信息,用于人类或机器的识别及响应。例如：滤波、变换、增强、检测、估计、压缩、识别、参数提取、频谱分析等。x(t) System/ Operator y(t) x(t) A/D x(n) System/ y(n) D/A Operator y(t)

1.3 What is DSP

SCUT

2. What is signal?Signal and information

SCUT

More and more signals are gathered, communicated, displayed, and are utilized for analysis or control of modern industry and society life everyday. We get information from signal . Signals: Signals are variations that carry information from one place to another.信号是信息的载体,信号是一种物理体现,是变化的物理量.信息是信号的内容.Question:Gave us some

signal examples.

Continuous Signal Processing System

SCUT

Digital Signal Processing System

y(n)第 23页

SCUTDigital Signal Processing, 2014, Y.Zeng第 24页

Digital Signal Processing, 2014, Y.Zeng

1.3 What is DSP 3. The basic parameters of a signal:幅度(amplitude) .频率(frequency) . Question相位(phase) .

1.3 What is DSP

SCUT

A question occurs: There are so many kinds of signals.How can we processing them?

SCUT

Some Signals电磁波：3-30kHz:Very low frequency VLF(潜水艇导航)甚低频 30-300kHz:Low frequency LF(潜水艇通信)低频 300~3000kHz:Medium frequency(调幅广播)中频 3-30MHz:High frequency(HF)(无线电爱好者，国际广播，军事通信，无线电话，电报，传真)高频 30-300MHz:Very High frequency(VHF)(调频FM,甚高频电视) 0.3~3GHz:Ultra high frequency(UHF)(UHF电视，蜂窝电话，雷达，微波，个人通信)超高频

What common characteristics and features they have? How do they change when they go through a system? Can we extract some general methods and ways to analize and process them all?

声波：

SCUT

频率低20Hz范围，称为次声波，它不能被听到，当强度足够大，能被感觉到。 (处于VLF Very low frequency)甚低频频率20Hz~20KHz称为声波，Low frequency (处于LF)低频频率>20KHz称为超声波，具有方向性，可以成束(处于LF) Digital Signal Processing, 2014, Y.Zeng第 25页

抽象是从众多的事物中抽取出共同的、本质性的特征，而舍弃其非本质的特征。

SCUTDigital Signal Processing, 2014, Y.Zeng第 26页

1.3 What is DSP 4. Discrete-time Signals& Digital Signals Continuous-time signals are defined along a continuum of times and thus are represented by a continuous independent variable(自变量). Discrete-time signals are defined at discrete times and thus the independent variable has discrete values. Analog signals are those for which both time and amplitude are continuous. Digital signals are those for which both time and amplitude are discrete. Continuous-time signal will be sampled into set of its values at definite time. If duration(持续时间) of each sampling time is fixed in equal period called sampling period, T. Thus nth value of sampled signal is equal to the value of the continuous-time signal xc(t) at time nT. Representation of sampled values will be shown in a sequence of numbers x={x[n]}. 1/T is called the sampling frequency.

1.3 What is DSP

SCUT

4. Discrete-time Signals& Digital Signals

由模拟信号产生数字信号(一个二进制流)。其有两个过程：抽样(sample)和保持(hold)。抽样(sample):每隔T秒(抽样周期)取出一次xa(t)的幅度，此信号称为离散信号离散信号。它只表示时间点0,T,2T…,nT,…上的值xa(0),xa(T),xa(2T)…,xa(nT)…..。保持(hold):在保持电路中将抽样信号变换成数字信号，因为一般采用

有限位二进制码，所以它所表示的信号幅度就是有一定限制的。如4位码，只能表示24=16种不同的信号幅度，这些幅度称为量化电平量化电平。经过A/D变换器后，不但时间离散化了，幅度也量化了，这种信号称为数字信号或序列(Sequences Sequences),用x[n]表示。当离散时间信号幅度与量化电平不相同时，就要以最接近的一个量化电平来近似它,即产生了量化误差。

SCUT

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第 28页

Digital Signal Processing, 2014, Y.Zeng

第 27页

1.3 What is DSP 4. Discrete-time Signals& Digital Signalsxa(t)

1.3 What is DSP

SCUTContinuoustime signal

5. Digital Systems

0 xa(nT)

t Sampled

处理数字信号的系统即数字系统. 1.采用大、小型计算机或微机(非实时/实时,计算量大,灵活/可调整,估计/预测). 2.用单片机或单板机(实时,复杂,灵活/可调整,工业信号). 3.利用通用DSP芯片(实时,简捷,工业信号). 4.利用特殊用途的DSP芯片(实时).

SCUT

也有另一种分法： 1.软件实现法:算法+通用计算机. 2.硬件实现法:专门的芯片或专门设计的系统. 3.用通用的可编程的数字信号处理器实现法—是目前重要的数字信号处理实现方法，它即有硬件实现法实时的优点，又具有软件实现的灵活性优点。

0 x[n]

t Quantized n第 29页

SCUTDigital Signal Processing, 2014, Y.Zeng

SCUTDigital Signal Processing, 2014, Y.Zeng第 30页

1.3 What is DSP 5. Digital Systems DSP芯片较之单片机有着更为突出优点。 -如内部带有乘法器，累加器，采用流水线工作方式及并行结构，多总线速度快。配有适于信号处理的指令(如FFT指令)等。目前市场上的DSP芯片有： -美国德州仪器公司Texas Instrument(TI):TMS320C2000、TMS320C5X、 TMS320C6X占有70% - Analog Devices的ADSP-21xx、TigerSharc DSP、SHARC DSP - Lucent的DSP-16xx、DSP 16000 - Motorola的DSP-56800、DSP 563xx -还有AT&T公司dsp16,dsp32系列，AD公司的ADSP21X,ADSP210X系列市场上推出专门用于FFT,FIR滤波器，卷积、相关等专用数字芯片。如：BB公司：DF17XX系列 MAXIM公司：MAXIM27X,MAXIM28X National公司：National-SEMI系列：MF系列。其软件算法已在芯片内部用硬件电路实现，使用者只需给出输入数据，可在输出端直接得到数据。

1.3 What is DSP

SCUT

6. Time-Domain Signal Operation Basic operations Scaling: gain– Amplification– Attenuation(衰减)

Delay/ Advance Addition

Elementary operations Integration(积分)/ Summation Differentiation/ Difference Production Convolution

SCUT

SCUT

近年来的一个趋势:嵌入式(ARM)系统的广泛应用第 31页

SCUTDigital Signal Processing, 2014, Y.Zeng第 32页

Digital Signal Processing, 2014, Y.

Zeng

1.3 What is DSP 7. Typical Sampling Rates and System Latencies(保持) for Selected ApplicationsApplicationInstrumentation Control Voice Audio Video

1.3 What is DSP

SCUT

8. Classification of Signals& Systems Based on all kinds of properties One-dimensional signal (time) Multidimensional signal (spatial coordinate) Real-valued function Complex-valued function Analog signal/system Continuous-time signal/system Quantized signal/system Discrete-time signal/system Digital signal/system

SCUT

I/O Sampling Rate1 Hz> 0.1 kHz 8 kHz 44.1 kHz 1~14 MHz

Latency (Delay)System dependent* System dependent*< 50 ms< 50 ms*< 50 ms*

Time-invariant system Time-varying system Causal Non-causal Deterministic signal– Periodic– Non-periodic Random signal– Stochastic signal– Noise or interference Stationary signal Non-stationary signal第 34页

* Many times, a signal may not need to be concerned with latency: for example, a TV signal is more dependent on synchronization(同步) with audio than the latency. In each of these cases, the latency is dependent on the application.

SCUT

Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000, Prentice Hall, 2001.

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 33页

Digital Signal Processing, 2014, Y.Zeng

1.4 Characteristics of DSP1.精度高(higher precision) 在模拟系统中，它的精度是由元件决定，模拟元器件的精度很难达到10-3以上。而数字系统中，17位字长就可达10-5精度，所以在高精度系统中，有时只能采用数字系统。

1.4 Characteristics of DSP

SCUT

4.易于大规模集成(easier to be integrated)

2.可靠性强(higher reliability) 数字系统：只有两个信号电平0,1受噪声及环境条件等影响小。模拟系统：各参数都有一定的温度系数，易受环境条件，如温度、振动、电磁感应等影响，产生杂散效应甚至振荡等.且数字系统采用大规模集成电路，其故障率远远小于采用众多分立元件构成的模拟系统。

数字部件：高度规范性，便于大规模集成，大规模生产，对电路参数要求不严，故产品成品率高。例：(尤其)在低频信号：如地震波分析，需要过滤几Hz~几十Hz的信号，用模拟系统处理时，其电感器、电容器的数值，体积，重量非常大，且性能亦不能达到要求，而数字信号处理系统在这个频率处却非常优越，显示出体积，重量和性能的优点。例：对信号进行频谱分析模拟频谱仪在频率低端只能分析到10Hz以上频率，且难于做到高分辨率 (也即足够窄的带宽)。但在数字的谱分析中，已能做到10-3Hz的谱分析。又例：有限长冲激响应数字滤波器，则可实现准确的线性相位特性，这在模拟系统中是很难达到的。

SCUT

5.

高性能(higher performance)

3.灵活性强(higher agility)

SCUT

数字系统的性能主要决定于乘法器的各系数，且系数存放于系数存储器内，只需改变存储的系数，就可得到不同的系统，比改变模拟系统方便得多。

SCUTDigital Signal Processing, 2014, Y.Zeng第 36页

Digital Signal Processing, 2014, Y.Zeng

第 35页

1.4 Characteristics of DSP6.时分复用(Time Division Multiplex, TDM) 利用DSP同时处理几个通道的信号。某一路信号的相邻两抽样值之间存在很大的空隙时间，因而在同步器的控制下，在此时间空隙中送入其他路的信号，而各路信号则利用同一DSP,后者在同步器的控制下，算完一路信号后，再算另一路信号，因而处理器运算速度越高，能处理的信道数目也就越多。1 2 3 n多路器 DSP分路器 1 2 3 n

1.4 Characteristics of DSP

SCUT

8.局限性(Limitation)

数字系统的速度有限，因而对于很高频率的信号代价较大。 (因为抽样频率要满足奈奎斯特准则定理)。 另外，数字系统的设计和结构复杂，价格较高，对一些要求不高、批量不大的应用来说，代价也较大。

SCUT

同步

7.二维与多维处理(easier on 2-dimensional or n-dimensional processing)利用庞大的存储单元，可以存储一帧或数帧图象信号，实现二维甚至多维信号包括二维或多维滤波，二维及多维谱分析等。

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第 38页

Digital Signal Processing, 2014, Y.Zeng

第 37页

1.5 Basic Framework of DSP 1. Beginning 在国际上一般把1965年由Cooley-Turkey提出快速付里叶变换(FFT)的问世，作为数字信号处理这一学科的开端。

1.5 Basic Framework of DSP 4. Main Subjects 数字信号处理学科包含有 (1)信号的采集，包括A/D,D/A技术，采样，量化噪声理论等。 (2)离散时间信号与系统的时域及频域分析 (3) Difference Equation, z-Transform (4)离散付里叶变换(DFT)理论,快速付里叶变换(FFT ),谱分析基础。 (5)数字滤波技术(结构与设计) (6)信号的压缩，包括语音信号与图象信号的压缩 (7)随机信号分析与模型 (8)谱估计(现代谱分析) (9)时频分析与小波变换 (10)自适应信号处理 (11)多维信号分析与处理 (12)信号识别(模式识别)与系统辨识

SCUT

SCUT

2. Foundations 数字信号处理的基本工具：微积分，高等代数，概率统计，随机过程，数理统计，数字电路,计算机理论。数字信号处理的理论基础：信号与系统。

3. Expanding 在学科发展上，数字信号处理又和最优控制，通信理论，故障诊断等紧紧相连，成为人工智能，模式识别，神经网络，数字通信等新兴学科的理论基础。

SCUT

一般将前5项归为经典数字信号处理的

课题,后7项归为现代信号处理的课题.第 39页

SCUT

Digital Signal Processing, 2014, Y.Zeng

Digital Signal Processing, 2014, Y.Zeng

第 40页

1.5 Basic Framework of DSP数字信号处理的应用大致可分为：数字滤波(Digital Filtering)、信号分析 (Signal Analysis)、信号识别(Signal Recognition)等。数字滤波(Digital Filtering):就是在形形色色的信号中提取所需要的信号,抑制不需要的信号或干扰信号。应用于(1)消除信息在传输过程中由于信道不理想所引起的失真, (2)滤除不需要的背景噪声，(3)去除干扰、(4)频带分割，信号谱的成形。广泛应用于数字通信，雷达，遥感，声纳，语音合成，图象处理，测量与控制，高清晰度电视，多媒体，生物医学，机器人等。信号分析(Signal Analysis):主要是信号特性参量的测量。主要应用于：谱(频率和/或相位)分析、语音分析、目标检测。如(1)对环境噪声的谱分析,可确定主要频率成分,了解噪声的成因,找出降低噪声的对策;(2)对振动信号的谱分析,可了解振动物体的特性,为设计或故障诊断提供资料和数据；(3)变换编码等。信号识别(Signal Recognition):语音识别，模式识别，机器视觉等。

1.6 Course OutlineWe'll make an intensive and thorough study on the theory and technology of digital signal processing. Introduction(1,4) Discrete-Time Signals and Systems(2) Difference Equations The zTransform(2,3) Transform Analysis of Linear Time-Invariant Systems(5) Digital Signal Spectra, The Discrete Fourier Transform, Fourier Analysis of Signals Using the Discrete Fourier Transform(2, 4, 8)

SCUT

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第 41页

SCUT

Computation of the Discrete Fourier Transform (FFT)(9) Fourier Analysis of Signals using DFT (10) Structures for Discrete-Time Systems (FIR,IIR) (6) Filter Design Techniques (FIR,IIR) (7) Introduction to Wavelet Transform&MRA(additional ) Introduction to DSP Hardware(additional )

Digital Signal Processing, 2014, Y.Zeng

第 42页

1.7取样和量化 1.采样(Sampling)将连续信号变成离散信号有各种取样方法，其中最常用的是等间隔周期取样(Periodic Sampling ),即每隔固定时间T取一个信号值，如图所示。其中T称为取样周期，T的倒数称为取样频率(Sampling Frequency)或取样率。记为 fS=1/T. Converting a continuously changing waveform (analog) into a series of discrete levels (digital). The device that does the conversion is called an Analog to Digital Converter (ADC)

1.7取样和量化

SCUT

模拟信号x(t)用周期为Ts的采样保持器进行采样。假定采集时间(模拟开关的闭合时间)忽略不计。可以得到阶梯状的采样保持信号。

SCUT

f(t)

T f(n)

nT

t

SCUTDigital Signal Processing, 2014, Y.Zeng第 43页

SCUT

1

n

n第 44页

Digital Signal Processing, 2014, Y.Zeng

1.7取样和量化f(n)

1.7取样和量化

SCUTn Digital SignalRead also pp. 142 (Figure 4.2)

3. Nyquist sampling theorem— or Shannon theorem

SCUT

任一连续信号xa(t),设其频谱的最高频率分量为fm,则当对它进行取样时，只要选择取样率大于或等于2fm,就可以(才可以)由这个取样序列xa (nT)来唯一准确地恢复xa (t)。设有一限带信号xa(t)。当|Ω|≤Ω max,它的付氏变换为Xa(Ω)。将xa(t)乘一取样函数p(t)就得到xa(t),如图所示。 The theorem is commonly called the Nyquist sampling theorem

1

n

2.取样函数定义

p (t )

1 t comb( ) T T n

(t nT ) SCUTDigital Signal Processing, 2014, Y.Zeng第 45页

SCUT

Question: What problem does it resolve?第 46页

Digital Signal Processing, 2014, Y.Zeng

1.7取样和量化 3. Nyquist sampling theorem— or Shannon theorem

1.7取样和量化

Please skim pp.140~147"4.1 Periodic Sampling"

SCUT

4. Quantization(量化)SW-8

SCUTV-high V-7 V-6 V-5

"4.2 Frequency-domain representation of sampling"

x[n] xc (nT ) X ( e j ) T n

(4.17) j n

x[n]e

(4.18)

2 f Fs

The simplest form of ADC uses a resistance(电阻，阻抗) ladder to switch in the appropriate number of resistors in series to create the desired voltage that is compared to the input (unknown) voltage.

SW-7

SW-6

SW-5 Output SW-4 V-4 SW-3 V-3 SW-2 V-2 SW-1 V-1

In my opinion, sampling is the first step of the process of abstracting the world of signals.

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng

V-low

Digital Signal Processing, 2014, Y.Zeng

第 47页

第 48页

1.7取样和量化 4. Quantization The output of the resistance ladder is compared to the analog voltage in a comparator. When there is a match, the digital equivalent (switch configuration) is captured.Analog Voltage Comparator Output Higher Equal Lower

1.7取样和量化input

Reference

SCUT

4. Quantization Initial conditions–––– Expected high 5-volts Expected low 0-volts 5-volts 256-binary 0-volts 0-binary Analog 5-volts 3.42-volts 2.5-volts

Question

SCUTDigital 255 Unknown 128

Voltage to be converted– 3.42-volts– Equates to? binary全并行ADC结构图第 49页

0-volts

0

SCUTResistance Ladder Voltage

SCUTDigital Signal Processing, 2014, Y.Zeng第 50页

Digital Signal Processing, 2014, Y.Zeng

1.7取样和量化 4. Quantization Initial conditions–––– Expected high 5-volts Expected low 0-volts 5-volts 256-binary 0-volts 0-binary Analog 5-volts 3.42-volts 2.5-volts

1.7取样和量化

SCUTDigital 256 175 128

5. Quantization ErrorAnalog 5-volts 3.42-volts 2.5-volts Digital 255 176? 175 174? 128

SCUTError 3.4375 3.41796875 3.3984375 0.0175 0.00203125 0.0215625

Voltage to be conv

erted

SCUT

– 3.42-volts– Equates to 175 binary

0-volts

0

0-volts

0

Question: Any error?第 51页

SCUTDigital Signal Processing, 2014, Y.Zeng第 52页

Digital Signal Processing, 2014, Y.Zeng

1.7取样和量化 5. Quantization ErrorVFSR= Full Scale Input Voltage, Continuous input signal digitized into 2N levels.111 3 2 1 0 -4 -3 -2 -1 -1 010 -2 001 -3 000 -4 0 1 2 3 4

1.7取样和量化

SCUT2Nq= 244.1 V

5. Quantization Error0.3 0.2

Uniform, bipolar transfer function (N=3)

Voltage[V]

0.1 0 0 -0.1 -0.2 2 4 6 8 10

Quantisation Error eq in[-0.5 q,+0.5 q].

SCUT

Quantisation step q=V

V FSR

eq limits ability to resolve small signal. Higher resolution means lower eq.

Ex: VFSR= 1V, N= 12

time[ms]

2 10-4

|e q|[V]

VFSR1

least significant bitq/2

Voltage (= q) Scale factor (= 1/ 2N ) Percentage (= 100/ 2N )10-4

(LSB) LSB)2 3 4

0.5

QE for N= 12 VFS= 10 2 4 6 8 10 Sampling time, tk

SCUT0

-4

-3

-2

-1

0

1

-0.5

-q/2

Quantisation error第 53页

-1

SCUT

Digital Signal Processing, 2014, Y.Zeng

Digital Signal Processing, 2014, Y.Zeng

第 54页

1.7取样和量化 6. ADC的分类与指标ADC一般有：积分型、逐次逼近型、并行比较型/串并行型、Σ-Δ调制型、电容阵列逐次比较型及压频变换型。 1)积分型(如TLC7135)积分型AD工作原理是将输入电压转换成时间(脉冲宽度信号)或频率(脉冲频率),然后由定时器/计数器获得数字值。其优点是用简单电路就能获得高分辨率，但缺点是由于转换精度依赖于积分时间，因此转换速率极低。初期的单片AD转换器大多采用积分型，现在逐次比较型已逐步成为主流。具体参考双积分TLC7135芯片资料。 2)逐次比较型(如TLC0831)逐次比较型AD由一个比较器和DA转换器通过逐次比较逻辑构成，从MSB开始，顺序地对每一位将输入电压与内置DA转换器输出进行比较，经n次比较而输出数字值。其电路规模属于中等。其优点是速度较高、功耗低，在低分辩率(<12位)时价格便宜，但高精度(>12位)时价格很高。 TLC0831芯片资料(德州仪器公司(TI)推出的 TLC0831/2是广泛应用的8位A/D转换器。 TLC0831是单通道输入；TLC0832是双通道输入，并且可以软件配置成单端或差分输入。串行输出可以方便的和标准的移位寄存器及微处理器接口) TLC0831可以外接高精度基准以提高转换精度，TLC0832的基准输入在片内与VCC连接。TLC0831/2的操作非常类似TLC0834/8(更多输入通道),为以后升级提供便利。

1.7取样和量化

SCUT

6. ADC的分类与指标

SCUT

3)并行比较型/串并行比较型(如TLC5510)并行比较型AD采用多个比较器，仅作一次比较而实行转换，又称FLash(快速)型。由于转换速率极高，n位的转换需要2n-1个比较器，因此电路规模

也极大，价格也高，只适用于视频AD转换器等速度特别高的领域。串并行比较型AD结构上介于并行型和逐次比较型之间，最典型的是由2个n/2位的并行型AD转换器配合DA转换器组成，用两次比较实行转换，所以称为 Half flash(半快速)型。还有分成三步或多步实现AD转换的叫做分级(Multistep/Subrangling)型 AD,而从转换时序角度又可称为流水线(Pipelined)型AD,现代的分级型AD中还加入了对多次转换结果作数字运算而修正特性等功能。这类AD速度比逐次比较型高，电路规模比并行型小。 TLC5510芯片资料 (TLC5510是CMOS、8位、20MSPS模拟量转数字量的转换器 (ADC),它采用半闪速结构(semi-flash architecture)。单5V工作电源且功耗只有 100mW(典型值)的功率。内含采样和保持电路，具有高阻抗方式的并行接口和内部基准电阻。与闪速转换器(flash converters)相比，半闪速结构减少了功率损耗和晶片尺寸。通过在2步过程(2-step process)中实现转换，可以极大地减少比较器的数目。转换数据的等待时间为2.5个时钟。内部基准电阻使用VDDA可产生标准的2V满度转换范围。为了实现此选项仅需外部跳线器，这样减小了对外部基准或电阻的需求。差分线性度在25℃温度下为 0.5LSB,在整个工作温度范围内的最大值是0.75LSB。用差分增益1%和差分相位为 0.7%可以规定动态特性范围。

SCUT

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 55页

Digital Signal Processing, 2014, Y.Zeng

第 56页

1.7取样和量化 6. ADC的分类与指标4)Σ-Δ(Delta-Sigma)调制型(如AD7705)Σ-Δ型AD由积分器、比较器、1位DA转换器和数字滤波器等组成。原理上近似于积分型，将输入电压转换成时间(脉冲宽度)信号，用数字滤波器处理后得到数字值。电路的数字部分基本上容易单片化，因此容易做到高分辨率。主要用于音频和测量。

1.7取样和量化

SCUT

5)电容阵列逐次比较型电容阵列逐次比较型AD在内置DA转换器中采用电容矩阵方式，也可称为电荷再分配型。一般的电阻阵列DA转换器中多数电阻的值必须一致，在单芯片上生成高精度的电阻并不容易。如果用电容阵列取代电阻阵列，可以用低廉成本制成高精度单片 AD转换器。最近的逐次比较型 AD转换器大多为电容阵列式的。 6)压频变换型(如AD650)压频变换型(Voltage-Frequency Converter)是通过间接转换方式实现模数转换的。其原理是首先将输入的模拟信号转换成频率，然后用计数器将频率转换成数字量。从理论上讲这种AD的分辨率几乎可以无限增加，只要采样的时间能够满足输出频率分辨率要求的累积脉冲个数的宽度。其优点是分辩率高、功耗低、价格低，但是需

要外部计数电路共同完成AD转换。

SCUT

Digital Signal Processing, 2014, Y.Zeng

第 57页

6. ADC的分类与指标 AD转换器的主要技术指标 1)分辩率(Resolution)指数字量变化一个最小量时模拟信号的变化量，定义为满刻度与2n的比值。分辩率又称精度，通常以数字信号的位数来表示。 2)转换速率(Conversion Rate)是指完成一次从模拟转换到数字的AD转换所需的时间的倒数。积分型AD的转换时间是毫秒级属低速AD,逐次比较型AD是微秒级属中速AD,全并行/串并行型AD可达到纳秒级。采样时间则是另外一个概念，是指两次转换的间隔。为了保证转换的正确完成，采样速率 (Sample Rate)必须小于或等于转换速率。因此有人习惯上将转换速率在数值上等同于采样速率也是可以接受的。常用单位是ksps和 Msps,表示每秒采样千/百万次(kilo/ Million Samples per Second)。 3)量化误差 (Quantizing Error)由于AD的有限分辩率而引起的误差，即有限分辩率AD的阶梯状转移特性曲线与无限分辩率AD(理想AD)的转移特性曲线(直线)之间的最大偏差。通常是1个或半个最小数字量的模拟变化量，表示为1LSB、1/2LSB。 4)偏移误差(Offset Error)输入信号为零时输出信号不为零的值，可外接电位器调至最小。 5)满刻度误差(Full Scale Error)满度输出时对应的输入信号与理想输入信号值之差。 6)线性度(Linearity)实际转换器的转移函数与理想直线的最大偏移，不包括以上三种误差。其他指标还有：绝对精度(Absolute Accuracy),相对精度(Relative Accuracy),微分非线性，单调性和无错码，总谐波失真(Total Harmonic Distotortion缩写THD)和积分非线性。第 58页 Digital Signal Processing, 2014, Y.Zeng

SCUT

SCUT

1.8内插 数字信号恢复模拟信号(Reconstruction of a Bandlimited Signal from its samples) 数字信号x(n)通过理想低通滤波器，只要其截止频率Ωc满足 Ωmax≤Ωc≤(Ωs-Ωmax)时，就可以恢复出原来信号

1.8内插

SCUT

数字信号恢复模拟信号(Reconstruction of a Bandlimited Signal from its samples)

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第 59页

SCUTDigital Signal Processing, 2014, Y.Zeng第 60页

Further Reading, Report and Exercises Report or Comment:题目一：在测量与控制、通信、生物医学工程、机器视觉、高清晰度电视、数字音频等任意一个领域，做一个较为具体的研究，找到近五年这个领域在利用数字信号处理技术方面的具体应用成就。题目二：对各类科学和工程领域中的线性和非线性问题及其处理方法进行一个较为具体的研究。针对题目一或者题目二，写一篇超过五百字的感想或评论，可以提出问题，也可对相关技术或者你的探求过

程进行介绍。请同时提交原文和你的感想和评论。欢迎电子文档(email to scutoptics@,邮件名：班号-座位号-姓名-report01,如：光1101-01-xx-report01 ),也欢迎打印的或手写版本。 Write it by yourself ! You can do it here, you can do it anywhere.

Contents of the Next LessonDiscrete-time signals and system

SCUT

SCUT

Discrete Signal Discrete Linear Time - Invariant System (DLTIS) Representation of A DLTIS and Impulse Response h(n) Discrete Convolution it’ it’s Calculating Method Properties of LTIS

Homeworks: (要求准备两个作业本) pp.214~216( 4.3,4.8(a),4.30)

Read 4.2 Frequency-domain representation of samplingDigital Signal Processing, 2014, Y.Zeng第 61页

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第 62页

Acknowledgment Some text and images and in the lectures of the course were excerpted from textbooks, references or internet websites, such as Wikipedia ( /wiki/Main_Page), and they could not be indexed. Thanks a lot!

SCUT

SCUTDigital Signal Processing, 2014, Y.Zeng第 63页

本文来源：https://www.bwwdw.com/article/ec24.html