锁相技术外文译文翻译

电影专业词典名词解释中英文对照日期：2010-07-19 10:32:49浏览次数:5629次电影专业词典名词解释中英文翻译。

影艺学院导片学院式剪接加速蒙太奇，导演用来命令演员开始表演的口头用语。

电影在表达意念时，自觉或不自觉地产生双重或多重意义。

ABERRATION 像差摄影影头因制作不精密，或人为的损害，不能将一点所发出的所有光线聚焦于底片感光膜上的同一位置，使影像变形，或失焦模糊不清。

ABSOLUTE FILM 绝对电影一种用抽象图形来诠释音乐的影片。

由德国羊肠小道前卫电影导演奥斯卡费辛格于1925-1930年首创。

ABSTRACT FILM 抽象电影一种通过影片的剪辑、视觉技巧、声音性质、色彩形状以及韵律设计等，来表达意念，给人一种自由自在、不拘形式感觉的电影。

ACADEMIC EDITING 学院式剪接一种仔细依循电影剧情发展过程的剪接方式。

其目的是在于重建一个事件的全部过程，维持电影剧情发展的流畅性。

因这种剪接方式不会引起观众对剪接本身的注意，有时也被称为“无痕迹剪接”，是好莱坞最常用的剪接方式之一。

ACADEMY APERTURE 影艺学院片门由美国影艺学院推行的一种电影片门规格，主要是用于35毫米电影摄影机和放映机。

此种规格宽高比例为1.33：1。

亦称ACADEMY FRAME。

ACADEMY AWARDS 奥斯卡金像奖美国影艺学院于1972年设立的奖项，每年颁给表现杰出的电影工作者。

每一个奖项最多有五个提名。

个人项目奖，可以提高演员或电影工作者的身价。

ACADEMY LEADER 影艺学院导片依据影艺学院所设定的标准，连接在放映拷贝首尾的一段胶片。

导片中含有一系列倒数的数字、放映记录和其他信息，便于放映师装片和换片。

导片不仅有保护影片的功能，同时可使放映机从起动到第一格画面到达放映机片门之前，达到正常的放映速度。

ACADEMY MASK 影艺学院遮片由影艺学院规画出来的一种遮掩摄影机部分片门的装置。

电子密码锁中英文对照外文翻译文献(文档含英文原文和中文翻译)2THE DESIGN OF MATRIX KEYBOARD AND LCD DISPLAY BASED ON MCUAbstractThe development of microelectronics technology and industrial measure requirement bring a good opportunity for development and research system，which makes it a broad prospects. The equipment has the advantages of small size, single power supply and a variety of output voltage leads it has a special module. Through the analysis of the hardware structure, we can summarizes each module needs.For example,we often go through the keys to realize the control of the electronic device. Small to watch mobile phone, to the TV computer, to a variety of complex instruments, all need to realize various operations through the buttons. This design is an important part of step for the further research，using buttons to control the display，include some modules like LCD 1602 liquid crystal display，4*4 matrix keyboard，STC89C52single-chip microcomputer and other bine with the Proteus software，the simulation results are displayed on the LCD in 1602 type of data.KEY WORDS: Single-chip; LCD 1602 liquid crystal display; 4*4 Matrix keyboard31 IntroductionWith the development of economy and the progress of science and technology, Microprocessors and peripheral chips have developed rapidly. The newest development of the integrated technology is the CPU chip and external. Like the program memory, data memory, parallel, serial, I/O timing / counter, interrupt controller and other control components are integrated in a chip—single chip. SCM has a manufacturing process CMOS, The smaller lithography process improves integration which make the chip space smaller, lower cost, lower working voltage, lower power consumption. Adopts double CPU structure, increasing the width of data bus, improve the speed and the ability of data processing, a pipeline structure, improve the processing and computing speed, in order to meet the needs of real-time control and processing. To increase the storage capacity, the internal EPROM EPPROM, secure program, to improve the driving capability of parallel port, in order to reduce the peripheral driving chip, increase the logic function and control the external I/O port flexibility. Peripheral in serial mode based expansion; peripheral circuit internal installation is an obvious trend to connect the internet. Reliability and application level is getting higher and higher. Some high-end microcontroller and launched in recent years also contains many special function unit, Such as A/D4converter, modem, communication controller, PLL, DMA, floating point unit etc.So,as we add some external expansion of the circuit and channel interface it can constitute a variety of computer applications, such as industrial control systems, data acquisition system, automatic test system, intelligent instrument, intelligent interface, function module etc. With MCU development and complete structure,SCM has become a powerful tool and will have a higher level and broader development.2 Design of the whole structure of systemThis design is based on single-chip, include matrix keyboard and LCD display module. Single-chip is the first model to select the appropriate target, function, reliability, cost, accuracy and speed control system. According to the actual situation of the topic selection, configuration management model different mainly from the following two aspects: First, supply chain management has strong anti-interference ability; second, SCM has a higher price. For information input module, keyboard selection can use economic benefits and meet the requirements of the 4*4 key matrix keyboard can realize multi function key requirements. As for the output module, using LCD 1602 liquid crystal display module, liquid crystal to achieve key information processing functions after the show. The circuit of the system is required by AT89C51 chip, clock circuit, reset circuit, driving circuit, scanning line5driving circuit and LCD1602 LCD screen. 4*4 matrix keyboard accessof P1.0 —P1.7,LCD 1602 screen to access P0.0—P0.7.3 System hardware circuit design3.1 Liquid crystal moduleThe principle of liquid crystal display is the use of physical properties of liquid crystal, The display control area voltage, power is displayed, it can display graphics. Liquid crystal display with thin thickness, suitable for large scale integrated circuit directly driven, easy to realize full color display characteristics, has been widely used in many fields of portable computer, digital camera, PDA mobile communication tools etc.1602 liquid crystal is also called the 1602 character LCD, which is a special used to display letters, numbers, symbols of the LCD module. It is composed of a plurality of 5X7 or 5X11 dot matrix character components, each dot matrix character who can display a character, there is a distance between the interval of each, there are intervals between each line, played the character spacing and row spacing, and because of this it is not well display graphics (with custom CGRAM, show the effect is not good). 1602 LCD refers to the display of the content for the 16X2, which can display two lines, 16 characters per line (LCD moduledisplay characters and numbers).63.2 Matrix keyboard module1. Key characteristicsThe keyboard is composed of a number of separate keys, press and release key is through the closed mechanical contact and off to achieve, because of the elastic action of mechanical contact, in the closing and the opening of the moment has a dither. Jitter must be eliminated, include software and hardware elimination.2．Scanning principleFirst determine whether a key is closed, and then one by one scan to further determine which button closure;(1) D0 ~ D3 output 0, level detection line D4 to D7. If the D4 - level D7 all high, said no key was pressed. If the D4 - level D7 is not all high, said the key was pressed.(2) If no key closure, return the scanning. If there is a button closure, in column by column scanning, closed key key number to find out. The D0=0, D1 ~ D3=1, D4 ~ D7 level, if D4=0, said the K1 key is pressed; similarly, if the D5 ~ D7=0, K5 respectively, K9, K13 key is down; if the D4 ~ D7=1, said that without a key is pressed. Then the D1=0, D0, D2, D3 was 1, the scanning of the second columns, which were carried on, until the closure of the key found.4 Software design7The software design mainly consists of keyboard scanning procedures, write instruction code program of LCD module, LCD module display data initialization code written subroutine, liquid crystal display module, liquid crystal display a character subroutine, time delay subroutine and so on. Programming for each module, software programming ended, Keil software was used for debugging, when the various parts of the program debugging is correct, according to the source sequence of calls, the parts together, compile, compile successfully downloaded to the mcu. The result is when the user presses a key, LCD display of the button is pressed after the realization of functional parameters corresponding to the. When the system power supply, P1 port scan cycle and the key button debounce, after completion of input through the SCM processing, output in the P0 port, through the liquid crystal display program content, complete system function.5 ConclusionWith the continuous development of high and new technology, the miniaturization and the miniaturization of electronic products has been achieved. And all kinds of new technology, as a single field of the new method, the development trend of new products and symbol -- intelligent significantly is one of the trends in development. The module design display microcontroller matrix keyboard and LCD, make us understand8to this technology innovation, through in-depth study on this technology, we can master the use in other areas, such as the design of electronic password lock, adjustment and control of indoor temperature and humidity, field access control system design etc.. Technological progress and economic development are the main themes of the present era, the improvement of people's living standard is bound to the requirements of electronic products increase, the design of any a small system is for a foundation, design of system innovation, the hardware, software integration, method and technology of virtual display and soft measurement artificial intelligence, I firmly believe that our life will be more colourful.9基于单片机的矩阵键盘与液晶显示的设计摘要微电子技术的发展和工业测量的需求，给系统的开发及深入研究带来了良好的契机，发展前景广阔。

锁相技术学习心得体会篇一：锁相技术锁相技术论文题目：专业班级：学生姓名：学号：任课老师：陈燕锁相技术的核心 XX级通信工程1班 XX 年 6 月13日摘要本文介绍了锁相技术的核心锁相环路：一个实现相位自动锁定的控制系统。

锁相环路有两个突出的特性：1是窄带滤波特性；2是宽带跟踪特性。

这两个特性使得锁相技术在电子技术领域得到了广泛的应用，特别是随着集成电路技术、数字技术以及通讯和计算机技术的发展，极大地推动了锁相技术的发展和应用。

现在锁相技术已经形成一门比较系统的理论科学，锁相技术的应用主要包含以下几个方面：跟踪滤波、频率合成与频率变换、模拟和数字信号的相干解调、数字通讯、调制与解调、检波、稳频和位频等。

下面来主要介绍一下锁相技术的核心，掌握核心就能运用得当。

关键字：核心，锁相环路，运用锁相环路的工作原理：锁相环路是一种反馈电路，锁相环的英文全称是Phase-Locked Loop,简称PLL。

其作用是使得电路上的时钟和某一外部时钟的相位同步。

因锁相环可以实现输出信号频率对输入信号频率的自动跟踪，所以锁相环通常用于闭环跟踪电路。

锁相环在工作的过程中，当输出信号的频率与输入信号的频率相等时，输出电压与输入电压保持固定的相位差值，即输出电压与输入电压的相位被锁住，这就是锁相环名称的由来。

在数据采集系统中，锁相环是一种非常有用的同步技术，因为通过锁相环，可以使得不同的数据采集板卡共享同一个采样时钟。

因此，所有板卡上各自的本地 80MHz和20MHz 时基的相位都是同步的，从而采样时钟也是同步的。

因为每块板卡的采样时钟都是同步的，所以都能严格地在同一时刻进行数据采集。

锁相环路是一个相位反馈自动控制系统。

它由以下三个基本部件组成：鉴相器（PD）、环路滤波器（LPF）和压控振荡器（VCO）。

锁相环的工作原理：1. 压控振荡器的输出经过采集并分频；2. 和基准信号同时输入鉴相器；3. 鉴相器通过比较上述两个信号的频率差，然后输出一个直流脉冲电压；4. 控制VCO，使它的频率改变；5. 这样经过一个很短的时间，VCO 的输出就会稳定于某一期望值。

电工翻译词汇C6carbon humidity-dependent resistor,碳湿敏电阻器card punch,卡片穿孔机card reader,卜片阅读机Carlson type strain gauge,卡尔逊应变计carrier,载波carrier gas,载气carrier ring,夹持环carrier sense,载波侦听19carrier sense multiple access with collision detection(CSMA/CD), 具有冲突检测的载波侦听多路访问carrier sync,载波同步cartridge disk,盒式磁盘cartridge disk drive,盒式磁盘机cascade control,串级控制cascade system,串级系统cascade[inductive]voltage transformer,级联式[感应式]电压互感器case,外壳casing,外壳cassette,盒式磁带；卡式磁带；暗盒catadioptric telescope,折反射望远镜catalysis element,催化元件catalytic analyzer,催化分析器catalytic chromatography,催化色谱法catalytic gas transducer[sensor],催化式气体传感器cathode,阴极cathode of electron gun,电子枪阴极cathode ray null indicator,阴极射线指零仪cavitation,空化cavitation corrosion,气蚀cavitation noise,空化噪声ceilometer,云幂仪cell,电池；传感器cell constant,电池常数cell potential transducer[sensor],细胞电位传感器Celsius,摄氏度Celsius temperature,摄氏温度Celsius temperature scale,摄氏温标center of strike,打击中心central conductor method,中心导体法；电流贯通法central principal inertia axis,中心主惯性轴central processing unit(CPU),中央处理单元central processor,中央处理器centrality,集中性centralized control,集中控制centralized intelligence,集中智能centralized management system,集中管理系统centralized network,集中式网络centralized process control computer,集中型过程控制计算机centrifugal balancing machine,离心力式平衡机centrifugal tachometer,离心式转速表ceramic microphone,陶瓷传声器ceraunograph,雷电计20ceraunometer,雷电仪certificate of conformity,合格证书certificate of control,控制证书certification,认证certification of conformity of an instrument for explosive atmosphere,防爆合格证certification system,认证体系certified standard material,有证标准物质chained list,链接表change of temperature test,温度变化试验channel,信道；通道character,字符character code,字符码character recognition,字符识别character set,字符集；字符组character-at-time printer,一次一字符打印机[印刷机]；串行打印机characteristic curve,特性曲线characteristic "fast","快"特性characteristic "impulse","脉冲"响应特性characteristic"slow","慢"特性characteristic locus,特征轨迹characteristic impedance,特性阻抗characteristic X-ray,特征X 射线charge amplifier,电荷放大器charge neutralization,电荷中和charge sensitivity,电荷灵敏度chart,记录纸chart driving mechanism,传纸机构chart lines,记录纸分度线chart scale length,记录纸标度尺长度closed loop transfer function,闭环传递函数closed loop zero,闭环零点closed position,关闭位置closed system,封闭系统closing valve time,关阀时间closure member,截流件cloud amount,云量cloud balancer,测支平衡器cloud base,云底cloud chamber,云室；云零室cloud detection radar,测云雷达cloud direction,云向cloud height indicator,云高指示器cloud height meter,云幂仪cloud searchlight,云幂灯。

锁相技术译文翻译英文原文：An On-Chip All-Digital Measurement Circuit to Characterize Phase-Locked Loop Response in 45-nm SOI译文：45纳米SOI全数字片上测量电路表征锁相环响应特性年级专业：姓名：学号：2013 年 6 月 2 日英文中文An On-Chip All-Digital Measurement Circuit to Characterize Phase-Locked Loop Response in 45-nm SOIAbstract—An all-digital measurement Circuit , built in 45-nm SOI-CMOS enabl es on-chip characterization of phase-loc ked loop (PLL) response to a self-induce d phase step.This technique allows estimationof PLL closed-loop bandwidth and jitterpeaking. The circuit canbe used to plot step-response vs.time, measure static phase error,and observe phase-lock status. INTRODUCTIONMany applications such as PCI Express ? require a PLL to produce alow-jitter cl ock at a given frequency while meeting stringent bandwidth and jitter peaking r 45纳米SOI全数字片上测量电路表征锁相环响应特性摘要---建立在45纳米的SOI-CMOS上一个全数字测量电路，它能够表征PLL对自诱导相步进的响应这项技术允许对PLL闭环带宽和抖动峰值的估计。

外文资料Phase-locked loop Technology ：A phase-locked loop or phase lock loop (PLL) is a control system that generates a signal that has a fixed relation to the phase of a "reference" signal. A phase-locked loop circuit responds to both the frequency and the phase of the input signals, automatically raising or lowering the frequency of a controlled oscillator until it is matched to the reference in both frequency and phase. A phase-locked loop is an example of a control system using negative feedback. In the order of the PLL is the way of made the frequency stability in the send up wireless,include VCO and PLL integrated circuits,VCO send up a signal,some of the signal is output,and the other through the frequency division with PLL integrated circuits generate the local signal making compared.In the order to remain the same,it’s must be remain the phase displacement same.If the phase displacement have some changes,the output of the PLL integrated circuits have some changes too,to controlle VCO until phase diffe rence to restore,make both cotrolled oscillator’s frequency and phase with input signal which is close-loop electronic circuit keep firm relationship.Phase-locked loops are widely used in radio, telecommunications, computers and other electronic applications. They may generate stable frequencies, recover a signal from a noisy communication channel, or distribute clock timing pulses in digital logic designs such as microprocessors. Since a single integrated circuit can provide a complete phase-locked-loop building block, the technique is widely used in modern electronic devices, with output frequencies from a fraction of a cycle per second up to many gigahertz.Earliest research towards what became known as the phase-locked loop goes back to 1932, when British researchers developed an alternative to Edwin Armstrong's superheterodyne receiver, the Homodyne. In the homodyne or synchrodyne system, a local oscillator was tuned to the desired input frequency and multiplied with the input signal. The resulting output signal included the original audio modulation information.The intent was to develop an alternative receiver circuit that required fewer tuned circuits than the superheterodyne receiver. Since the local oscillator would rapidly drift in frequency, an automatic correction signal was applied to the oscillator, maintaining it in the same phase and frequency as the desired signal. The technique was described in 1932, in a paper by H.de Bellescise, in the French journal Onde Electrique.In analog television receivers since at least the late 1930s, phase-locked-loop horizontal and vertical sweep circuits are locked to synchronization pulses in the broadcast signal. When Signetics introduced a line of monolithic integrated circuits that were complete phase-locked loop systems on a chip in 1969, applications for the technique multiplied. A few years later RCA introduced the "CD4046" CMOS Micropower Phase-Locked Loop, which became a popular integrated circuit. Applications：Phase-locked loops are widely used for synchronization purposes; in space communications for coherent carrier tracking and threshold extension, bit synchronization, and symbol synchronization. Phase-locked loops can also be used to demodulate frequency-modulated signals. In radio transmitters, a PLL is used to synthesize new frequencies which are a multiple of a reference frequency, with the same stability as the reference frequency.Clock recovery ：Some data streams, especially high-speed serial data streams (such as the raw stream of data from the magnetic head of a disk drive), are sent without an accompanying clock. The receiver generates a clock from an approximate frequency reference, and then phase-aligns to the transitions in the data stream with a PLL. This process is referred to as clock recovery. In order for this scheme to work, the data stream must have a transition frequently enough to correct any drift in the PLL's oscillator. Typically, some sort of redundant encoding is used; 8B10B is very common.Deskewing ：If a clock is sent in parallel with data, that clock can be used to sample the data.Because the clock must be received and amplified before it can drive the flip-flops which sample the data, there will be a finite, and process-, temperature-, and voltage-dependent delay between the detected clock edge and the received data window. This delay limits the frequency at which data can be sent. One way of eliminating this delay is to include a deskew PLL on the receive side, so that the clock at each data flip-flop is phase-matched to the received clock. In that type of application, a special form of a PLL called a Delay-Locked Loop (DLL) is frequently used.Clock generation：Many electronic systems include processors of various sorts that operate at hundreds of megahertz. Typically, the clocks supplied to these processors come from clock generator PLLs, which multiply a lower-frequency reference clock (usually 50 or 100 MHz) up to the operating frequency of the processor. The multiplication factor can be quite large in cases where the operating frequency is multiple gigahertz and the reference crystal is just tens or hundreds of megahertz.Spread spectrum：All electronic systems emit some unwanted radio frequency energy. Various regulatory agencies (such as the FCC in the United States) put limits on the emitted energy and any interference caused by it. The emitted noise generally appears at sharp spectral peaks (usually at the operating frequency of the device, and a few harmonics).A system designer can use a spread-spectrum PLL to reduce interference with high-Q receivers by spreading the energy over a larger portion of the spectrum. For example, by changing the operating frequency up and down by a small amount (about 1%), a device running at hundreds of megahertz can spread its interference evenly over a few megahertz of spectrum, which drastically reduces the amount of noise seen by FM receivers which have a bandwidth of tens of kilohertz.中文翻译锁相环技术：锁相环或锁相回路（PLL）是一个信号控制系统，即用来锁定一系列的“参考”信号。

专业英语考试资料翻译，共享出来，望大伙儿消化吸收，取得好成绩。

因本人水平所限，确信会有翻译的不行的或错误的地址，请大伙儿踊跃拍砖（跟我联系也能够），谢谢。

——守贝1. 名词翻译VLSI（超大规模集成电路）, impedance（阻抗）, diode（二极管）, transistor（三极管）, MOSFET（金属氧化物半导体场效应晶体管）, OP-AMP（放大器）, bandwidth（带宽）, gain（增益）, frequency response（频率响应）, rectifier（整流器）, distortion（失真，畸变）, filter（滤波器）, oscilloscope（示波器）, harmonics（谐波）, function-generator（函数发生器）, spectrum（频谱）, current density（电流密度）, power supply（电源，电源供给器）, node（节点）, compiler （编译器）, wafer（晶片）, memory（存储器，内存）, microprocessor（微处置器）, RISC（精简指令集计算）, laptop（笔记本电脑）, transient（瞬态）, steady （稳态）, servo（伺服，随动）, overshoot（超调量）, algorithm（算法）, FIR（有限脉冲响应）, capacity（电容）, RAM（随机存取存储器）, ROM（只读存储器）, embedded system（嵌入式系统）, data acquistion （数据搜集）2. 段落翻译In general, all materials may be classified in three major categories —conductors, semiconductors, and insulators-depending upon their ability to conduct an electric current. The materials most often used in semiconductor devices are germanium and silicon.通常，依照材料导电性能的不同，可分为三种类型—导体，半导体和绝缘体。

Compressive Radar ImagingRichard Baraniuk Department of Electrical and Computer EngineeringRice University Philippe Steeghs E.P.Wigner Institute Bucharest,RomaniaAbstract—We introduce a new approach to radar imag-ing based on the concept of compressive sensing(CS).In CS,a low-dimensional,nonadaptive,linear projection is used to acquire an efficient representation of a compress-ible signal directly using just a few measurements.The signal is then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit. We demonstrate that CS has the potential to make two significant improvements to radar systems:(i)eliminating the need for the pulse compression matchedfilter at the receiver,and(ii)reducing the required receiver analog-to-digital conversion bandwidth so that it need operate only at the radar reflectivity’s potentially low“information rate”rather than at its potentially high Nyquist rate.These ideas could enable the design of new,simplified radar systems, shifting the emphasis from expensive receiver hardware to smart signal recovery algorithms.I.I NTRODUCTIONA typical radar system transmits a wideband pulse (linear chirp,coded pulse,pseudonoise(PN)se-quence,etc.)and then correlates the received signal with that same pulse in a matchedfilter(effecting pulse compression)[1].A traditional radar receiver consists of either an analog pulse compression sys-tem followed by a high-rate analog-to-digital(A/D) converter or a high-rate A/D converter followed by pulse compression in a digital computer(see Figs.1and2);both approaches are complicated and expensive.Achieving adequate A/D conversion of a wide-band PN/chirp radar signal(which is compressed into a short duration pulse by the matchedfilter) requires both a high sampling frequency and a large dynamic range.Currently available A/D conversion technology is a limiting factor in the design of ultrawideband(high resolution)radar systems,be-cause in many cases the required performance is either beyond what is technologically possible or too expensive.In this paper,we introduce a new approach to radar imaging based on the concept of compres-sive sensing(CS)[2],[3].In CS,an incoherent linear projection is used to acquire an efficient representation of a compressible signal directly us-ing just a few measurements.Interestingly,random projections play a major role.The signal is then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit.We demonstrate that when the CS theory applies, significantly fewer samples/measurements of the radar signal need to be acquired in order to obtain an accurate representation for further processing.The potential impacts on radar hardware are promising; we will show that CS can:(i)eliminate the need for the matchedfilter in the radar receiver,and(ii) reduce the required receiver A/D conversion band-width so that it need operate only at the reflectivity’s potentially low“information rate”rather than at its potentially high Nyquist rate(see Fig.3).II.C OMPRESSIVE S ENSING Consider a length-N discrete-time signal x of any dimension(without loss of generality,we will fo-cus on one-dimensional(1D)signals for notational simplicity)indexed as x(n),n=1,...,N.We can interpret x as an N×1column vector.The signal x is sparsely representable if there exists a sparsity basis{ψi}that provides a K-sparse representationof x;that isx=Ni=1θiψi=K=1θ(i )ψi,(1)where x is a linear combination of K basis vec-tors chosen from{ψi},{i }are the indices of those vectors,and{θi}are the weighting coeffi-cients.Alternatively,by stacking the basis vectorsIEEE Radar Conference, Waltham, MA, April 2007pulsegenerator−→s T(t)to transmit antenna Fig.1.Prototypical radar transmitter.(a)s R(t)from receive antenna−→analogmatchedfilter−→high-rateA/D−→processing(b)s R(t)from receive antenna−→high-rateA/D −→digitalmatchedfilter−→processingFig.2.Prototypical digital radar receivers for the transmitter in Fig.1perform matchedfiltering either in the(a)analog or(b)digital domain.s R(t)from receive antenna−→low-rateA/D−→y−→processingpressive radar receiver for the transmitter in Fig.1performs neither matchedfiltering nor high-rate analog-to-digital conversion.as columns into the N×N sparsity basis matrix Ψ=[ψ1|...|ψN],we can write in matrix notationx=Ψθ,(2) whereθis an N×1column vector with K nonzero elements.Various expansions,including wavelets, the DCT,and Gabor frames[4],are widely used for the representation and compression of natural signals,images,and other data.Using · p to denote the p norm,we can write that θ 0=K;that is,the 0“norm” θ 0 merely counts the number of nonzero entries in the vectorθ.The signal x is compressible if the sorted magnitudes of the coefficients{|θi|}decay rapidly to zero;this is the case,for example,ifθ∈ p for p≤pressible signals are well-approximated as sparse.The standard procedure for compressing sparse signals,known as transform coding,is to(i)acquire the full N-point signal x via Nyquist-rate sampling; (ii)compute the complete set of transform coeffi-cients{θi};(iii)locate the K largest,significant co-efficients and discard the(many)small coefficients; (iv)encode the values and locations of the largest coefficients.This procedure has three inherent inefficiencies. First,for a wideband signal,we must start with a large number of Nyquist-rate samples N.Second,the encoder must compute all of the N transform coefficients{θi},even though it will discard all but K of them.Third,the encoder must encode the locations of the large coefficients since the locations change with each signal.In compressive sensing(CS),we do not measure or encode the K significantθi directly.Rather,we measure and encode M<N linear projections y(m)= x,φT m of the signal onto a second set of vectors{φm},m=1,...,M,whereφT m denotes the transpose ofφm and ·,· denotes the inner product. In matrix notation,we measurey=Φx,(3) where y is an M×1column vector and the measurement matrixΦis M×N with each row a measurement vectorφT m.Since M<N,recovery of the signal x from the measurements y is ill-posed in general.How-ever,the CS theory tells us that when the matrix ΦΨhas the Restricted Isometry Property(RIP) [2],[3],[5],then it is indeed possible to recover the K largestθi’s from a similarly sized set of M=O(K log(N/K))measurements y.The RIP is closely related to an incoherency property between ΦandΨ,where the rows ofΦdo not provide a sparse representation of the columns ofΨand vice versa.The RIP and incoherency hold for many pairsof bases,including for example,delta spikes and Fourier sinusoids,or sinusoids and wavelets.An interesting,powerful,and somewhat surpris-ing choice for the measurement matrixΦis a (pseudo)random,noise-like matrix.For example, we may select its MN entries as iid Bernoulli or Gaussian random variables(see Fig.4).It can be shown that many random measurement matrices are universal in the sense that they are incoherent with anyfixed basisΨ(spikes,sinusoids,wavelets, Gabor functions,curvelets,and so on)with high probability[2],[3],[5].1When the RIP/incoherency holds,the signal x (via its coefficentsθ)can be recovered exactly from y by solving an 1minimization problem[2],[3] θ=arg min θ1such that y=ΦΨθ.(4) This optimization problem,also known as Basis Pursuit[6],can be solved with traditional linear programming techniques.At the expense of slightly more measurements,iterative greedy algorithms such as Matching Pursuit and Orthogonal Match-ing Pursuit(OMP)[7]can recover the signal x from the measurements y.The same CS framework of incoherent measurements and optimization-based reconstruction also applies to recovering a close approximation to a compressible signal.Another choice for the measurement matrixΦthat offers good performance in many cases is a causal,quasi-Toeplitz matrix where each row is an N/M -place right-shift of the row immediately above it;that is,φm,n=p( N/M m−n)for some vector p.In this case,y=Φx can be implemented in a streaming fashion as a linear time-invariantfilter followed by decimation by D= N/M [8]y(m)=Nn=1p(Dm−n)x(n)(5)for m=1,...,M.When p is a PN sequence,we dub this approach randomfiltering(see Fig.5).1We note that it is critical that the measurement matrixΦbe known to both the encoder and decoder,so in practice it is sufficient to use a pair of pseudo-random number generators at both the encoder and decoder with a common seed known to both.III.CS-BASED R ADARIn order to illustrate our CS-based radar concept, consider a simplified1D range imaging model ofa target described by u(r)with range variable r.If we let the transmitted radar pulse s T(t)interact with the target by means of a linear convolution[1],then the received radar signal s R(t)is given bys R(t)=As T(t−τ)u(τ)dτ,(6) where we have converted the range variable r totime t using t=2rc,with c the propagation velocity of light,and where A represents attenuation due to propagation and reflection.If the transmitted signal has the property that s T(t)∗s T(−t)≈δ(t)(which is true for PN and chirp signals),then a band-limited measurement of the radar reflectivity u(t) can be obtained by pulse compression,that is,by correlating s R(t)with s T(t)in a matchedfilter (recall Fig.2)[1].A/D conversion occurs either before or after the matchedfiltering,resulting in N Nyquist-rate samples.Our CS-based radar approach is based on two key observations.First,the target reflectivity func-tions u(t)that we wish to obtain through the radar process are often sparse or compressible in some basis.For example,a set of K point targets corresponds to a sparse sum of delta functions as in u(t)=Ki=1a iδ(t−κi);smooth targets are sparse in the Fourier or wavelet domain;and range-Doppler reflectivities are often sparse in the joint time-frequency(or ambiguity)domain[1].Such target reflectivity functions u(t)are good candidates for acquisition via CS techniques.Second,time-translated and frequency-modulated versions of the PN or chirp signals transmitted as radar waveforms s T(t)form a dictionary(the extension of a basis or frame)that is incoherent with the time,frequency,and time-frequency bases that sparsify or compress the above mentioned classes of target reflectivity functions u(t)[8].This means that PN or chirp signals are good candidates for the rows of a CS acquisition matrixΦas a“random filter”(recall(5)).By combining these observations we can both eliminate the matchedfilter in the radar receiver and lower the receiver A/D converter bandwidth using CS principles.Consider a new design for a radar(a)(b)Fig.4.Theoretical compressive sensing(CS)measurement matricesΦof size N=64and M=16:(a)iid Bernoulli(±1)measurements and(b)iid Gaussian measurements.In the color map,blue corresponds to large negative,green to zero,and red to largepositive.(a)(b)Fig.5.“Randomfilter”measurement matricesΦof size N=64and M=16based on(a)PN signal and(b)chirp pare to Fig.4 and note the causal,quasi-Toeplitz,yet“rich”structure.Same color map as Fig.4.system that consists of the following components.The transmitter is the same as in a classical radar;the transmit antenna emits a PN or chirp signals T(t)(recall Fig.1).However,the receiver doesnot consist of a matchedfilter and high-rate A/Dconverter but rather only a low-rate A/D converterthat operates not at the Nyquist rate but at a rate pro-portional to the target reflectivity’s compressibility(see Fig.3).We make the connection explicit for a PN-basedCS radar with a simple sampling model.Considera target reflectivity generated from N Nyquist-ratesamples x(n)via u(t)=x( t/∆ ),n=1,...,N,on the time interval of interest0≤t<N∆.Theradar transmits a PN signal generated from a length-N random Bernoulli±1vector p(n)via s T(t)=p( t/∆ ).The received radar signal s R(t)is givenby(6);we sample it not every∆seconds but ratherevery D∆seconds,where D= N/M and M<N,to obtain the M samples,m=1,...,M,y(m)=s R(t)|t=mD∆=AN∆s T(mD∆−τ)u(τ)dτ=ANn=1p(mD−n)n∆(n−1)∆u(τ)dτ=ANn=1p(mD−n)x(n),(7)which are precisely a scaled version of(5).In words,a PN sequence radar implements a randomfilter inthe sense of[8],and hence the low-rate samplesy contain sufficient information to reconstruct thesignal x corresponding to the Nyquist-rate samplesof the reflectivity u(t)via linear programming or agreedy algorithm.Chirp pulses yield similar results.Figure6illustrates the scheme in action.A radarreflectivity profile is probed with a PN pulse se-quence,measured at one-half the Nyquist samplingrate,and subsequently recovered exactly using anOMP greedy algorithm and a sparsity frameΨcombining delta spikes and Haar wavelets.Additional gains can be expected for2D CS radarimaging.We illustrate this with a simple simulationof SAR data acquisition and imaging.Figure7(a)shows the reflectivity function that is to be recoveredfrom the SAR data.We simulated a SAR data ac-quisition using the method described in[9].Figure7(b)shows the result of a2D CS implementationwith four times undersampling,which gives an exactrecovery of the reflectivity function.The traditionalSAR image(Fig.7(c))shows artifacts of the limitedaperture of the imaging operator,which are absentin the CS image.The result is similar to what is ob-tained with the feature-enhanced imaging approachof[10].However,the CS-based approach has someadvantages,such as an almost infinite number ofsparse representations to choose from as well asmore efficient signal recovery algorithms.Fig.6.CS radar example.(a)Transmitted PN pulse s T(t),(b)low-rate measurement y,and(c)true and recovered reflectivity profiles u(t).x cross−range cross−rangeFig.7.CS synthetic aperture radar(SAR)example.(a)2D reflectivity,(b)CS SAR image,and(c)traditional SAR image.IV.D ISCUSSION AND C ONCLUSIONS Using compressive sensing(CS)ideas,we have proposed two potential improvements to a wide class of radar systems:(i)we can eliminate the matchedfilter in the radar receiver,and(ii)we can reduce the required sampling rate of the re-ceiver A/D converter so that it need only operate at the target reflectivity’s potentially low“information rate”rather than at its potentially high Nyquist rate. For example,for a scene consisting of K point targets,just M=O(K log(N/K))rather than N measurements will suffice.These ideas could enable the design of new,simplified radar systems,shifting the emphasis from expensive hardware(A/D con-version,matchedfiltering)to smart signal recovery algorithms.Reconstruction,estimation,detection, and so on are performed using a digital algorithm and can even be performed off-line.CS techniques are appropriate for monostatic, bistatic,and multiscatic(many receivers and trans-mitters)scenarios.Since the radar receiver is greatly simplified,CS provides a powerful yet inexpensive framework for multistatic sensor network radars, where the radar signals resulting from one trans-mitting antenna are received at many receiving antennas that,by virtue of our simplifications,canbe made very simply and inexpensively.Our results can also be combined with the theory of distributed compressed sensing(DCS)[11],[12]for array processing and beamforming type applications.The CS-based imaging framework introduced here also applies directly to other modalities such as sonar and synthetic aperture sonar imaging.While the CS literature has focused almost ex-clusively on problems in signal reconstruction,ap-proximation,and estimation,CS is information scal-able to a much wider range of statistical inference tasks.Detection,classification,and recognition do not require a reconstruction of the signal,but only require estimates of the relevant sufficient statistic for the problem at hand[13].A key point is that it is possible to directly extract these statistics from a small number of random measurements without ever reconstructing the signal.The two upshots are that significantly fewer measurements can be required for signal detection than for signal reconstruction and that the computational complexity of detection can be much reduced compared to reconstruction. Both of these bode well for radar applications, since if we are merely interested in detecting targets rather than reconstructing images of them,then we can use an even lower sampling rate for the CS-based receiver.Moreover,in many radar applica-tions,target detection,classification,and recognition decisions are often made based on the result of some kind of matchedfiltering or correlation with a set of rmation scalability enables us to compute close approximations to these matched filter results directly from incoherent measurements without having to perform expensive reconstruction or approximation computations[14].There are a number of challenges to be overcome before an actual CS-based radar system will become a reality.First,the target reflectivity being probed must be compressible in some basis,frame,or dictionary.Second,the signal recovery algorithms must be able to handle real-world radar acquisition scenarios with sufficient computational efficiency and robust performance for noisy data.Third,there is a subtle tradeoff to optimize between the reduc-tion in sampling rate N/M and the dynamic range of the resulting CS system[15].These are areas of active research for both our team and the broader CS community.In particular,there could be links with recent work onfinite rate of innovation sampling for ultrawideband communication systems[16].Acknowledgements:This work was supported by the grants DARPA/ONR N66001-06-1-2011and N00014-06-1-0610,NSF CCF-0431150,ONR N00014-06-1-0769and N00014-06-1-0829,AFOSR FA9550-04-1-0148,and the Texas Instruments Leadership University Program.Website: /cs.Email:richb@,philippe@.R EFERENCES[1]M.Skolnik,Radar Handbook.New York,NY,USA:McGrawHill,1970.[2] E.Cand`e s,J.Romberg,and T.Tao,“Robust uncertaintyprinciples:Exact signal reconstruction from highly incomplete frequency information,”IEEE Trans.on Information Theory, vol.52,no.2,pp.489–509,2006.[3] D.Donoho,“Compressed sensing,”IEEE Trans.on InformationTheory,vol.52,no.4,pp.5406–5425,2006.[4]S.Mallat,A Wavelet Tour of Signal Processing.San Diego:Academic Press,1999.[5]R.G.Baraniuk,M.Davenport,R. A.DeV ore,and M. B.Wakin,“A simplied proof of the restricted isometry property for random matrices(aka the Johnson-Lindenstrauss lemma meets compressed sensing),”Constructive Approximation,2007. [6]S.Chen,D.Donoho,and M.Saunders,“Atomic decompositionby basis pursuit,”SIAM J.on p.,vol.20,no.1,pp.33–61,1998.[7]J.Tropp and A.C.Gilbert,“Signal recovery from partial infor-mation via orthogonal matching pursuit,”Apr.2005.Preprint.[8]J.Tropp,M.Wakin,M.Duarte,D.Baron,and R.G.Baraniuk,“Randomfilters for compressive sampling and reconstruction,”Proc.IEEE ICASSP,2005.[9]M.Cetin,Feature-Enhanced Synthetic Aperture Radar Imaging.Ph.D.Thesis Boston University,College of Engineering,2001.[10]M.Cetin and W.C.Karl,“Feature-enhanced synthetic apertureradar image formation based on non-quadratic regularization,”IEEE Trans.Image Processing,vol.10,pp.623–631,2001. [11] D.Baron,M.B.Wakin,M.F.Duarte,S.Sarvotham,and R.G.Baraniuk,“Distributed compressed sensing,”2005.preprint.[12]M.F.Duarte,M.B.Wakin,D.Baron,and R.G.Baraniuk,“Universal distributed sensing via random projections,”in Proc.Information Processing in Sensor Networks(IPSN),2006. [13]M.Duarte,M.Davenport,M.Wakin,and R.G.Baraniuk,“Sparse signal detection from incoherent projections,”Proc.IEEE ICASSP,2005.[14]M.Davenport,M.Duarte,M.Wakin,D.Takhar,K.K.Kelly,and R.G.Baraniuk,“The smashedfilter for compressive classi-fication and target recognition,”in Proc.IS&T/SPIE Symposium on Electronic Imaging:Computational Imaging,Jan.2007. [15]ska,S.Kirolos,M.F.Duarte,T.S.Ragheb,R.G.Baraniuk,and Y.Massoud,“Theory and implementation of an analog-to-information converter using random demodulation,”in IEEE ISCAS,2007.[16]I.Maravic,J.Kusuma,and M.Vetterli,“Low-sampling rateUWB channel characterization and synchronization,”m.and Networks,vol.5,Dec.2003.。