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精品文档 1欢迎下载 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 2 Fourier s 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 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 是非周期信号 那么用周期函 数例如正弦和余弦的和 并不能精确的 表示该信号 f t 你可以人为的拓展 这个信号使其具有周期性 但是这要求 在端点处附加连续性 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 数 字滤波器是一种数学算法 它可以用硬 件 固件和软件来实现 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 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 用傅里叶级数设计 FIR 滤波器的 基本的理念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 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 如果信号有急剧的过渡 就有必有 对输入信号加窗 这样信号在端点处就 会收敛于零 7 The concepts of signals and sy stems arise in a wide variety of fields and the ideas a nd techniques associated with these concepts play an import ant role in such diverse areas of science and technology as communication aeronautics and astronautics cir cuit design acoustics seismology biomedical engineerin g energy generation distribution systems chemical pro cess 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 8 Without some restrictions whe n the characterization of a system requi 精品文档 2欢迎下载 res a complete input out put relationship knowing the outp ut of a system to a certain set of input doe not allow us to determi ne the output of the system to oth er 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 特定输入产生的输出时 我们也并不知 道系统对其他输入产生的输出 9 An example of a finite energy signal is a signal that tak es on the value 1 for 0 t 1 and 0 otherwise 举一个有限能量信号 的例子 信号在 0 t 1 而在其他时 间范围取值为 0 10 This of course makes sense s ince if there is a nonzero average energy per unit time then integr ating or summing this over an infi nite time interval yields an infin ite amount of energy 当然这是有 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 11 We can bring continuous time and discrete time systems together through the concept of sampling and we can de velop some insights into the use o f discrete time systems to process continuous time signals that have been sample d 我们可以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 12 One of the most important motiv ations for the development of gene ral tools for analyzing and design ing systems is that systems from many different applic ations 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 软件的最重要的动机之一 13 Electronic amplifiers are often symbolized by a simple triangle shape where the internal components are not individually represented 电子放大器一般都表 示成三角形形状 内部器件并不分别表 示出来 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 增大同向输入端的电 压 会使输出电压增大 增大反向输入 端的电压 会使输出电压减小 15 Because we know that both inputs of the op amp have extremely high impedance we can safely assume they won t add or subtract any current through the divider 因为我们知道 运算放大 器的两个输入端之间有无穷大的电阻 所以我们完全可以假设他们没有增加或 分担任何电流 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 换句话说 我们可以认为 R1 和 R2 串联 即通过 R1 的电流一定 会通过 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 统 减少了对每项任务并行操作和确定 的硬件分配的依赖性 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 数字通信协议规范可能随时改变 基于 ASIC 的接口则保持稳定且兼容 19 VHDL is an acronym for Very 精品文档 3欢迎下载 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 是甚高速集成电路硬件描述语言的缩写 它是一种通过函数 数据流和 或 结 构描述逻辑电路的可编程语言 20 The data flow model makes use of concurrent statements that are executed in parallel as soon as data arrives at the input 数据流 模式在数据到达输入端的同事就给出相 同的说明 2 傅里叶分析 Fourier s 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 The Fourier transform s 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 you d expect transform data from the frequency domain into the time domain 傅里叶变换的效用在于它能够在 时域范围内分析它的频率内容 变换 的第一步是将时域上的函数转换为时 域表示 然后就可以分析信号的频率 内容了 因为变换函数的傅里叶系数 代表各个正弦和余弦函数在各自对应 频率区间的分配 傅里叶逆变换就会 按你刚才设想的那样 将频域数据转 换为时域的 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 离散型傅里叶变换是通过他有限 的采样点来评估函数的傅里叶变换 采样点代表了其 他时间的信号 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 离散型傅里叶变换具有和连续型 傅里叶变换几乎完全相同的对称特性 此外 通过离散型傅里叶变换的公式 我们可以轻易推出离散型傅里叶变换 的公式 因为这两个公式几乎相同 If f t is a nonperiodic signal t h e summation of t h e 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 精品文档 4欢迎下载 the problem of better representing the nonperiodic signal The W F T can be used to give information about signals simultaneously in the time domain and in the frequency domain 如果 f t 是非周期信号 那么用周 期函数例如正弦和余弦的和 并不能精 确的表示该信号 f t 你可以人为的拓 展这个信号使其具有周期性 但是这要 求在端点处附加连续性 窗口傅里叶变 换能够更好的解决关于非周期信号的 表示问题 窗口傅里叶变换同样适用 于时 域和频域上信号信息的提供 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 interval s endpoints than in the middle The effect of the window is to localize the signal in time 通过窗口傅里叶变换 输入信号 f t 被 分成许多小部分 每个部分都能分别分 析它的频率内容 如果信号有急剧的过 度 就有必要对输入信号加窗 这样信 号在端点处就会收敛于零 通过加权函 数 即着眼于与中间部分而不是区间端 点附近 这样就完成了加窗 加窗效应 是将信号集中在同一个时间段 To approximate a function by samples a n d 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 通过样本来近似函数 及通过离散 傅立叶傅立叶变换去逼近傅里叶积分 需要使用一个矩阵 其顺序是全样本点 的数量 通过一个按 n2算术运算顺序 的向量乘以一个 n n 的矩阵 当采样点 的增多的时候 问题就迅速恶化 但是 如果样本是均匀分布的 那么傅立 叶矩阵可以被分解成一个只有几个稀疏 矩阵的乘积 以及由此产生的因素可广 泛应用在算术运算顺序共向量 这就是 所谓的快速傅里叶变换或 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 精品文档 5欢迎下载 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 system that is a system that transforms discrete time inputs into discrete time outputs is 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 时间连续和时间离散系统 物理系统最直观的感觉就是 元器件 设备和子系统的互连 在信号处理和通 信 机电马达 电动车 化学加工厂中 系统可以视为一个处理 在这里 以某 种方法 信号会被系统传输或引起系统 相应 从而产生其他信号作为输出 例 如 一个高保真系统记录音频信号并重 放这信号 如果这高保真系统有音调控 制 我们可以改变所播放的声音的质量 同样地 图 3 1 可以视为一个带输入电 压 Vs t 和输出电压 Vc t 的系统 一个图像增强系统将输入图像转化成所 期望的输出图像 例如增强对比度 一个时间连续系统是输入连续信号 得到连续输出信号的系统 例如图 3 5a 所描绘的 在这里 x t 是输入 y t 是输出 h t 是系统脉冲相应 同 样地 时间离散系统是一个输入离散 得到离散输出的系统 如图 3 5b 所描 绘的 在这里 x n 是输入 y n 是输 出 h n 是系统单位抽样相应 我们可以通过抽样定理使时间连续 和时间离散系统相结合 我们可以开发 时间离散系统来处理已被抽样的时间连 续信号 目前 很多数字信号处理方法 已用在科学和技术领域 所以 我们取 数字信号系统为例 它的一些系统特性 将在下一部分描述 4 图像 图像解释题 图 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 isn t 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 精品文档 6欢迎下载 circuits are explored where the direction of current switches back and forth Alternating Current or AC But for now we ll just concern ourselves with DC circuits 图 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 0 Then the sum of all the currents is zero This can be generalized as follows Ii 0 Note 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 图 2 12 The 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 resistors and capacitors

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