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1.In most cases, these signals originate as sensory data from the real world: seismic vibrations visual images, sound waves, etc.DSP isthe mathematics, the algorithms, and the techniques used to manipulate these signals after they have been converted into a digital form.在大多數(shù)情況下,這些信號(hào)來(lái)源于人對(duì)真實(shí)世界的感覺(jué),比如地震的震動(dòng),視覺(jué)圖像,聲音波形等。數(shù)字信號(hào)處理是一種數(shù)學(xué)工具,是一種用來(lái)處理那些將上述信號(hào)轉(zhuǎn)換成數(shù)字形式后的信號(hào)的算法和技術(shù)。2.Fouriers representation of functionsas a superposition of sines and cosines has become Ubiquitous for both the analytic and numerical solution of differential equations and for the analysis and treatment of communication signals函數(shù)的傅里葉表示,即將函數(shù)表示成正弦和余弦信號(hào)的疊加,這種方法已經(jīng)廣泛用于微分方程的解析法和數(shù)值法求解過(guò)程以及通信信號(hào)的分析和處理。3.If f (t ) is a nonperiodic signal, the summation of the periodic functions ,such as sine and cosine, does not accurately represent the signal. You could artificially extend the signal to make it periodic but it would require additional continuity at the end points .如果f(t)是非周期信號(hào),那么用周期函數(shù)例如正弦和余弦的和,并不能精確的表示該信號(hào)f(t)。你可以人為的拓展這個(gè)信號(hào)使其具有周期性,但是這要求在端點(diǎn)處附加連續(xù)性4.A digital filter is a mathematical algorithm implemented in hardware, firmware, and software that operates on a digital input signal to produce a digital output signal for achieving filtering objectives.數(shù)字濾波器是一種數(shù)學(xué)算法,它可以用硬件,固件和軟件來(lái)實(shí)現(xiàn)。它作用于數(shù)字輸入信號(hào)產(chǎn)生數(shù)字輸出信號(hào)從而達(dá)到濾波目標(biāo)。5.The basic idea of Fourier series method is to design an FIR filter that approximates the desired frequency response of filter by calculating its impulse response.用傅里葉級(jí)數(shù)設(shè)計(jì)FIR濾波器的基本的理念是計(jì)算出此濾波器的單位沖激響應(yīng)來(lái)逼近所期望的濾波器的頻率響應(yīng)。6.If the signal has sharp transitions, it is necessary to window the input data, so that the sections converge to zero at the endpoints如果信號(hào)有急劇的過(guò)渡,就有必有對(duì)輸入信號(hào)加窗,這樣信號(hào)在端點(diǎn)處就會(huì)收斂于零。7.Theconceptsofsignalsandsystemsariseinawidevarietyoffields,andtheideasandtechniquesassociatedwiththeseconceptsplayanimportantroleinsuchdiverseareasofscienceandtechnologyascommunication,aeronauticsandastronautics,circuitdesign,acoustics,seismology,biomedicalengineering,energygenerationdistributionsystems,chemicalprocesscontrol,andspeechprocessing.信號(hào)與系統(tǒng)的概念出現(xiàn)在廣闊的范圍內(nèi),在科學(xué)技術(shù)的不同領(lǐng)域,如通信、航空航天、電路設(shè)計(jì)、聲學(xué)、地震學(xué)、生物學(xué)、生物醫(yī)學(xué)工程、發(fā)電和輸電系統(tǒng)、化學(xué)過(guò)程控制和語(yǔ)音處理中都離不開(kāi)這個(gè)概念的思想與技術(shù)。它在科學(xué)技術(shù)中發(fā)揮了重要作用。8.Withoutsomerestrictions,whenthecharacterizationofasystemrequiresacompleteinput-out-putrelationship,knowingtheoutputofasystemtoacertainsetofinputdoenotallowustodeterminetheoutputofthesystemtoothersetsofinputs.當(dāng)系統(tǒng)的特性描述要求完整的輸入輸出關(guān)系時(shí),如果沒(méi)有約束條件,即使知道了系統(tǒng)對(duì)某 些特定輸入產(chǎn)生的輸出時(shí),我們也并不知道系統(tǒng)對(duì)其他輸入產(chǎn)生的輸出。9.Anexampleofafinite-energysignalisasignalthattakesonthevalue1for0t1and0otherwise.舉一個(gè)有限能量信號(hào)的例子:信號(hào)在0t1,而在其他時(shí)間范圍取值為0。10.This,ofcourse,makessense,sinceifthereisanonzeroaverageenergyperunittime,thenintegratingorsummingthisoveraninfinitetimeintervalyieldsaninfiniteamountofenergy.當(dāng)然這是有意義的,因?yàn)槿绻麊挝粫r(shí)間內(nèi)存在一個(gè)非零的平均能量,那么在一個(gè)無(wú)限的時(shí)間間隔范圍內(nèi),對(duì)其積分或者求和就會(huì)產(chǎn)生一個(gè)無(wú)限的能量總和。11.Wecanbringcontinuous-timeanddiscrete-timesystemstogetherthroughtheconceptofsampling,andwecandevelopsomeinsightsintotheuseofdiscrete-timesystemstoprocesscontinuous-timesignalsthathavebeensampled.我們可以在抽樣的概念下將連續(xù)時(shí)間和離散時(shí)間系統(tǒng)放在一起考慮。我們可以將一些離散時(shí)間系統(tǒng)的概念推廣,用以處理抽樣后的連續(xù)時(shí)間系統(tǒng)。12.Oneofthemostimportantmotivationsforthedevelopmentofgeneraltoolsforanalyzinganddesigningsystemsisthat systemsfrommanydifferentapplicationshaveverysimilar mathematicaldescriptions.許多具有不同應(yīng)用的系統(tǒng)都有相類(lèi)似的數(shù)學(xué)描述,這是開(kāi)發(fā)系統(tǒng)分析和設(shè)計(jì)通用工具軟件的最重要的動(dòng)機(jī)之一。13.Electronic amplifiers are often symbolized by a simple triangle shape ,where the internal components are not individually represented.電子放大器一般都表示成三角形形狀,內(nèi)部器件并不分別表示出來(lái)。14.An increasingly positive voltage on the(+)input tends to drive the output voltage more positive,and an increasingly positive voltage on the(-)input tends to drive the output voltage more negative.增大同向輸入端的電壓,會(huì)使輸出電壓增大;增大反向輸入端的電壓,會(huì)使輸出電壓減小。15.Because we know that both inputs of the op-amp have extremely high impedance,we can safely assume they wont add or subtract any current through the divider.因?yàn)槲覀冎?,運(yùn)算放大器的兩個(gè)輸入端之間有無(wú)窮大的電阻,所以我們完全可以假設(shè)他們沒(méi)有增加或分擔(dān)任何電流。16.In other words,we can treat R1 and R2 as being in series with each other:all of the electrons flowing through R1 must flow through R2.換句話(huà)說(shuō),我們可以認(rèn)為R1和R2串聯(lián),即通過(guò)R1的電流一定會(huì)通過(guò)R2。17.FPGAs,which do not use operating sytems,minimize reliability cincerns with true parallel execution and deterministic hardware dedicated to every task.FPGA不使用操作系統(tǒng),減少了對(duì)每項(xiàng)任務(wù)并行操作和確定的硬件分配的依賴(lài)性。18.Digital communication protocols,for example,have specifications that can chang over time,and ASIC-based interfaces may cause maintenance and forward compatibility challenges.例如,數(shù)字通信協(xié)議規(guī)范可能隨時(shí)改變,基于A(yíng)SIC的接口則保持穩(wěn)定且兼容。19.VHDL is an acronym for Very high speed intergrated circuit(VHSIC)Hardware Description Language which is a programming Language that describes a logic cir cuit by function,data flow behavior,and/or structure.VHDL是甚高速集成電路硬件描述語(yǔ)言的縮寫(xiě),它是一種通過(guò)函數(shù)、數(shù)據(jù)流和(或)結(jié)構(gòu)描述邏輯電路的可編程語(yǔ)言。20.The data flow model makes use of concurrent statements that are executed in parallel as soon as data arrives at the input.數(shù)據(jù)流模式在數(shù)據(jù)到達(dá)輸入端的同事就給出相同的說(shuō)明。2.傅里葉分析Fouriers epresentation of functions as a superposition of sines and cosines has become ubiquitous for both the analytic and numerical solution of differential equations and for the analysis and treatment of communication signals.函數(shù)的傅里葉表示,即將函數(shù)表示成正弦和余弦信號(hào)的疊加,這種方法已經(jīng)廣泛用于微分方程的解析法和數(shù)值法求解過(guò)程以及通信信號(hào)的分析和處理。The Fourier transforms utility lies in its ability to analyze a signal in the time domain for its frequency content. The transform works by first translating a function in the time domain into a function in the frequency domain. The signal can then be analyzed for its frequency content because the Fourier coefficients of the transformed function represent the contribution of each sine and cosine function at each frequency. An inverse Fourier transform dose just what youd expect, transform data from the frequency domain into the time domain.傅里葉變換的效用在于它能夠在時(shí)域范圍內(nèi)分析它的頻率內(nèi)容。變換的第一步是將時(shí)域上的函數(shù)轉(zhuǎn)換為時(shí)域表示。然后就可以分析信號(hào)的頻率內(nèi)容了。因?yàn)樽儞Q函數(shù)的傅里葉系數(shù)代表各個(gè)正弦和余弦函數(shù)在各自對(duì)應(yīng)頻率區(qū)間的分配。傅里葉逆變換就會(huì)按你剛才設(shè)想的那樣,將頻域數(shù)據(jù)轉(zhuǎn)換為時(shí)域的。The discrete Fourier transform (DFT) estimates the Fourier transform of a function from a finite number of its sampled points. The sampled points are supposed to be typical of what the signal looks like at all other times離散型傅里葉變換是通過(guò)他有限的采樣點(diǎn)來(lái)評(píng)估函數(shù)的傅里葉變換。采樣點(diǎn)代表了其他時(shí)間的信號(hào)。The DFT has symmetry properties almost exactly the same as the continuous Fourier transform. In addition, the formula for the inverse discrete Fourier transform is easily calculated using the one for the discrete Fourier transform because the two formulas are almost identical.離散型傅里葉變換具有和連續(xù)型傅里葉變換幾乎完全相同的對(duì)稱(chēng)特性。此外,通過(guò)離散型傅里葉變換的公式,我們可以輕易推出離散型傅里葉變換的公式。因?yàn)檫@兩個(gè)公式幾乎相同。If f (t ) is a nonperiodic signal, the summation of the periodic functions (such as sine and cosine)does not accurately represent the signal.You could artificially extend the signal to make it periodic but it would reqiure addition continuity at the endpoints.The window Fourier transform(WFT )is one solution to the problem of better representing the nonperiodic signal. The WFT can be used to give information about signals simultaneously in the time domain and in the frequency domain 如果f(t)是非周期信號(hào),那么用周期函數(shù)例如正弦和余弦的和,并不能精確的表示該信號(hào)f(t)。你可以人為的拓展這個(gè)信號(hào)使其具有周期性,但是這要求在端點(diǎn)處附加連續(xù)性。窗口傅里葉變換能夠更好的解決關(guān)于非周期信號(hào)的表示問(wèn)題。窗口傅里葉變換同樣適用于時(shí)域和頻域上信號(hào)信息的提供。With the WFT, the input signal f(t) is chopped up into sections, and each section is analyzed for its frequency content separately, If the signal has sharp transitions, it is necessary to window the input data, so that the sections converge to zero at the endpoints. This windowing is accomplished via a weight function that places less emphasis near the intervals endpoints than in the middle. The effect of the window is to localize the signal in time.通過(guò)窗口傅里葉變換,輸入信號(hào)f(t)被分成許多小部分,每個(gè)部分都能分別分析它的頻率內(nèi)容。如果信號(hào)有急劇的過(guò)度,就有必要對(duì)輸入信號(hào)加窗,這樣信號(hào)在端點(diǎn)處就會(huì)收斂于零。通過(guò)加權(quán)函數(shù),即著眼于與中間部分而不是區(qū)間端點(diǎn)附近,這樣就完成了加窗。加窗效應(yīng)是將信號(hào)集中在同一個(gè)時(shí)間段。To approximate a function by samples, and to approximate the Fourier integral by the discrete Fourier transform, requires applying a matrix whose order is the number sample points n. Since multiplying an n*n matrix by a vector costs on the order of arithmetic operations, the problem gets quickly worse as the number of sample points increases. However, if the samples are uniformly spaced, then the Fourier matrix can be factored into a product of just a few sparse matrices, and the resulting factors can be applied to a vector in a total of order arithmetic operations. This is the so-called fast Fourier transform or FFT 通過(guò)樣本來(lái)近似函數(shù),及通過(guò)離散傅立葉傅立葉變換去逼近傅里葉積分,需要使用一個(gè)矩陣,其順序是全樣本點(diǎn)的數(shù)量。通過(guò)一個(gè)按n2算術(shù)運(yùn)算順序的向量乘以一個(gè)n*n的矩陣,當(dāng)采樣點(diǎn)的增多的時(shí)候,問(wèn)題就迅速惡化。但是,如果樣本是均勻分布的,那么傅立葉矩陣可以被分解成一個(gè)只有幾個(gè)稀疏矩陣的乘積,以及由此產(chǎn)生的因素可廣泛應(yīng)用在算術(shù)運(yùn)算順序共向量。這就是所謂的快速傅里葉變換或FFT。3. 2. Continuous-time and discrete-time systems Physical systems in the broadest sense are an interconnection of components, devices, or subsystems. In context ranging from signal processing and communications to electromechanical motors, automotive vehicles, and chemical-processing plants, a system can be viewed as a process in which input signals are transformed by the system or cause the system to respond in some way, resulting in other signals as outputs. For example, a high-fidelity system takes a recorded audio signal and generates a reproduction of that signal. If the hi-fi system has tone controls, we can change the tonal quality of the reproduced signal.Similarly, the circuit in Fig.3-1 can be viewed as a system with input voltage Vs(t) and output voltage Vc(t). An image-enhancement system transforms an input image into an output image that has some desired properties, such as improved contrast. A continuous-time system is a system in which continuous-time input signals are applied and result in continuous-time output signals. As in Figure 3-1-5(a), where x(t) is the input, y(t) is the output, and h(t) is the system impulse response.Similarly, a discrete-time systemthat is, a system that transforms discrete-time inputs into discrete-time outputsis depicted as in Figure 3-1-5 (b). Where x(n) is the input, y(n) is the output, and h(n) is the system unit sample response. We can bring continuous-time and discrete-time systems together through the concept of sampling, and we can develop some insights into the use of discrete-time systems to process continuous-time signals that have been sampled.At present, many digital signal processing methods have been widely used in science and technology fields. So we take digital signal system for example, some system properties are described in next section. 2.時(shí)間連續(xù)和時(shí)間離散系統(tǒng) 物理系統(tǒng)最直觀(guān)的感覺(jué)就是,元器件、設(shè)備和子系統(tǒng)的互連。在信號(hào)處理和通信,機(jī)電馬達(dá),電動(dòng)車(chē),化學(xué)加工廠(chǎng)中,系統(tǒng)可以視為一個(gè)處理,在這里,以某種方法,信號(hào)會(huì)被系統(tǒng)傳輸或引起系統(tǒng)相應(yīng),從而產(chǎn)生其他信號(hào)作為輸出。例如,一個(gè)高保真系統(tǒng)記錄音頻信號(hào)并重放這信號(hào)。如果這高保真系統(tǒng)有音調(diào)控制,我們可以改變所播放的聲音的質(zhì)量。同樣地,圖3-1可以視為一個(gè)帶輸入電壓Vs(t)和輸出電壓Vc(t)的系統(tǒng)。一個(gè)圖像增強(qiáng)系統(tǒng)將輸入圖像轉(zhuǎn)化成所期望的輸出圖像,例如增強(qiáng)對(duì)比度。 一個(gè)時(shí)間連續(xù)系統(tǒng)是輸入連續(xù)信號(hào)得到連續(xù)輸出信號(hào)的系統(tǒng)。例如圖3-5a所描繪的,在這里,x(t)是輸入,y(t)是輸出,h(t)是系統(tǒng)脈沖相應(yīng)。同樣地,時(shí)間離散系統(tǒng)是一個(gè)輸入離散,得到離散輸出的系統(tǒng),如圖3-5b所描繪的,在這里,x(n)是輸入,y(n)是輸出,h(n)是系統(tǒng)單位抽樣相應(yīng)。 我們可以通過(guò)抽樣定理使時(shí)間連續(xù)和時(shí)間離散系統(tǒng)相結(jié)合。我們可以開(kāi)發(fā)時(shí)間離散系統(tǒng)來(lái)處理已被抽樣的時(shí)間連續(xù)信號(hào)。目前,很多數(shù)字信號(hào)處理方法已用在科學(xué)和技術(shù)領(lǐng)域。所以,我們?nèi)?shù)字信號(hào)系統(tǒng)為例,它的一些系統(tǒng)特性將在下一部分描述。4.圖像 圖像解釋題圖2-1 Any source of voltage, including batteries, has two points for electrical contact. We can provide such a path for the battery by connecting a piece of wire from one end of the battery to the other. Forming a circuit with a loop of wire, we will initiate a continuous flow of electrons in a clockwise direction, which is shown in Fig.2-1. So long as the battery continues to produce voltage and the continuity of the electrical path isnt broken, electrons will continue to flow in the circuit. Following the metaphor of water moving through a pipe, this continuous, uniform flow of electrons through the circuit is called a current. So long as the voltage source keeps “pushing” in the same direction, the electron flow will continue to move in the same direction in the circuit. This single-direction flow of electrons is called a Direct Current, or DC. electron circuits are explored where the direction of current switches back and forth: Alternating Current, or AC. But for now, well just concern ourselves with DC circuits.圖2-2 We see that I is the only current flowing into the node. However, there are three paths for current to leave the node, and these current are represented by I , I and I . Once charge has entered into the node, it has no place to go except to leave (this is known as conservation of charge). The total charge flowing into a node must be the same as the total charge flowing out of the node. So IB+IC+ID=IA Bringing everything to the left side of the above equation, we get (IB+IC+ID)-IA=0Then, the sum of all the currents is zero. This can be generalized as follows Ii=0Note the convention we have chosen here: current flowing into the node is taken to be negative, and currents flowing out of the node are positive. 圖2-12The PNP transistor is the king of the traditional bipolar analog integrated circuits world. In fact in the most basic and most cost effective analog IC process, the chip designer has at its disposal just that; a good NPN transistor. The rest, PNPs, re

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