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1.a2-b2=(a+b)(a-b)a squared minus b squared equals open parenthesis a plus b close parenthesis times open parenthesis a minus b close parenthesis2.x+1/x2(x3-4)2/3X plue one over the quantity x squared times the quantity x cubed minus four to the two-third power.3.lim1/n2(1+2+n) The limit as n approaches infinity of the quantity one over n squared times one plus two plus to plus n.4.1/2ab+(c-d)One half open brace ,a open bracket b plus open parenthesis c minus d close parenthesis close bracket close brace.5.max(a1,a2,.,an),min(a1,a2,.an)Maximum/minimum value of the series a sub one to a sub n.6.lim(1+1/n)n=eLimit as n approaches infinity of the quantity of one plus one over n to the nth power equals e.7.lim squ an,lim inf anUpper/lower limit of a sub n as n approaches/tends to infinity.8.y=-1/xnY prime equals minus one over x to the nth power.9.d2y/dx2=a2e-axThe second derivative of y with respect to x equals a squared times e to the power of minus a times x.10.a-m/n=1/(a0,m,n均为正整数)a to the minus m over n power equals one over the nth root of a to the mth power ,where a is greater than zero,and both m and n are positive numbers.11.f(x)=1+ln(x-2)The function of x equals one plus log the quantity x minus 2 to the base e.12.sin3x=3sinx-4sin3xThe sine of three x is equivalent to three times sine of x minus four times the quantity sine x cubed.句子翻译1So 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.(只要电池持续供电,并且导线没有断开,电子将始终在回路中流动)2.If a condenser is connected to a battery,the electrons will flow out of the negative terminal of the battery and accumulate on the condenser plate connected to that side .thus the condenser is said to be charged.当电容与电池相连,电子将从电池的负极流出,并聚集在电容与该端相联的极板上,称电容被充电。3.whenever electrons flow through a conductor,a magnetic field will develop around that conductor.只要电子束流过导体,就将在这个导体周围产生磁场。4. glass ,for instance, is a very good insulator at room temperature,but becomes a conductor when heated to a very high temperature.(例如,玻璃在室温下是一个非常好的绝缘体,但当把它加热到相当高的温度时它就变成一个导体。)5. whenever an electric voltage exists between two separated conductors,an electric field is present within the space between those conductors. (只要在两个独立的导体间存在电压,则他们之间会产生一个电场。)6. while the normal motion of “free”electrons in a conductor is random ,with no particular direction or speed ,electrons can be influenced to move in a coordinated fashion through a conductive material.通常导体里的自由电子是随机运动的,没有确定的方向和速度,但是电子受力后可沿相同的方向通过导体。7.many so-called “linear”circuits are quite nonlinear in their behavior ,either by necessity of physics or by design.许多线性电路在工作时呈非线性,或者是由于物理结构造成的,或者是由于电路设计的问题。8.simply stated ,the transistor conducts a collector current Ic which is a copy of the base current Ib amplified by a factor of .(简单地说,晶体管集电极电流Ic较基极电流Ib放大倍。)9. AND gateproduces a 1 output if both of its inputs are 1.(与门全1出1.)10.A combinational logic circuit may contain an arbitrary number of logic gates and inverters but no feedback loops.(组合逻辑电路可能包括许多逻辑门和反向器,但不包含反馈电路。)11.It simplifies a logic function by combining pairs of adjacent 1 cells into a Sum-Of-Products terms that covers all of the 1 cells .(卡诺图通过合并相邻项简化逻辑函数,把所有的1项合并成积和式。)12.the concepts of signals and systems arise in a wide variety of fields, and the ideas and techniques associated with these concepts play an important role in such diverse areas of science and technology as communications, aeronautics and astronautics, circuit design, acoustics, seismology, biomedical engineering, energy generation and distribution systems, chemical process control, and speech processing.(信号与系统的概念出现在广阔的范围内,在科学技术的不同领域,如通信,航空航天,电路设计,声学,地震学,生物医学工程,发电和输电系统,化学过程控制和语音处理中都离不开这个概念的思想与技术。它在科学技术中发挥了重要作用。)13.without some restrictions, when the characterization of a system requires a complete input-output relationship, knowing the output of a system to a certain set of input does not allow us to determine the output of the system to other sets of inputs. (当系统的特性描述要求完整的输入输出关系时,如果没有约束条件,即使知道了系统对某些特定输入产生输出时,我们也并不知道系统对其他输入产生的输出。)14.an example of a finite-energy signal is a signal that takes on the value 1 for 0t1 and 0 otherwise.(举一个有限能量信号的例子:信号在0t1内其值为1,而在其他时间范围内取值为015.this,of course, make sense, since if there is a nonzero average energy per unit time, then integrating or summing this over an infinite time interval yields an infinite amount of energy.(当然这是由意义的,因为如果单位时间内存在一个非零的平均能量,那么在一个无限的时间间隔范围内,对其积分或者求和就会产生一个无限的能量总和)16,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.(我们可在抽样的概念下将连续时间和离散时间系统放在一起考虑。我们可以将一些离散时间系统的概念推广,用以处理抽样后的连续时间系统)17.one of the most important motivations for the development of general tools for analyzing and designing systems is that systems from many different applications have very similar mathematical descriptions.(许多具有不同应用的系统都有相类似的数学描述,这是开发系统分析和设计通用工具软件的重要的动机之一)18.In most cases,these signals originate as sensory data from the real world:seismic vibrations,visual images,sound waves,etc.DSP is the mathematics,the algorithms,and the techniques used to manipulate these signals after they have been converted into a digital form.(在大多数情况下,这些信号来源于人对真实世界的感觉,比如地震的震动,视觉图像,声音波形等。数字信号处理是一种数学工具,是一种用来处理那些将上述信号转换成数字形式后的信号的算法和技术)19.Fouriers representation 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.(函数的傅里叶表示,即将函数表示成正弦和余弦信号的叠加,这种方法已经广泛用于微分方程的解析法和数值法求解过程以及通信信号的分析和处理)20.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 endpoints.(如果f(t)是非周期信号,那么用周期函数例如正弦与余弦的和,并不能精确地表示信号f(t)。你可以认为的拓展这个信号使其具有周期性,但是这个要求在端点处附加连续性)21If the signal has sharp transitions,it is necessary to window the input data,so that the sections converge to zero at the endpoints.(如果信号有急剧的过渡,就有必要对输入信号加窗,这样信号在端点处附加连续性。)22.A digital filter is a mathematical algorithm implemented in hardware,firmware,and/or software that operates on a digital input signal to produce a digital output signal for achieving filtering objectives.(数字滤波器是一种数学算法,它可以用硬件,固件以及软件来实现。它作用于数字输入信号产生数字输出信号从而达到滤波目标)23.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.(用傅里叶级数设计FIR滤波器的基本思想是计算出此滤波器的单位冲激响应来逼近所期望的滤波器的频率响应) RADAR: (Radio Detection And Ranging) RFID(Radio Frequency Identification)VLSI: (very-large-scale integration) VOIP(Voice over Internet Protocol)PLC (Programmable Logic Controller) UWB(Ultra Wide Band )CMOS (Complementary Metal Oxide Semiconductor) WiFi(Wireless Fidelity)AC (Alternate Current)DSP (digital signal processing)CDPD (Cellular Digital Packet Data)EDGE (Enhanced Datarate for GSM Evolution)GPRS (General Packet Radio ServiceHSDPA (High Speed Downlink Package Access)NFC (Near Field Communication)OFDM (Orthogonal Frequency Division Multiplexing)PCS (Personal Communications Service)PDA (Personal Digita

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