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 amathematical algorithm implementedin hardware, firmware, andsoftware that operates on adigital input signal to produce adigital output signal forachieving 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 seriesmethod is to design an FIR filterthat approximates the desiredfrequency response of filter bycalculating 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 sharptransitions, it is necessary towindow theinput data, so that the sectionsconverge 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 systems arise in a widevariety of fields, and the ideas and techniques associatedwith these concepts play an important role in such diverseareas of science and technology ascommunication,aeronautics and astronautics, circuit design, acoustics,seismology, biomedical engineering, energy generationdistribution systems, chemical process control, and speechprocessing. "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, when thecharacterization of a system requires a complete input-out-put relationship, knowing the output of a system to a certain set ofinput doe 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 takes on the value 1 for 0≤t≤1 and0 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, since if there is a nonzero averageenergy per unit time, then integrating or summing this over an infinite time interval yields an infinite 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 theconcept 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 motivations for the development of general tools for analyzing and designing systems is thatsystems from many different applications have very similarmathematical descriptions.许多具有不同应用的系统都有相类似的数学描h e i r be i ng ar eg oo df o rs om et h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,minimizereliability cincerns with trueparallel execution anddeterministic hardware dedicatedto 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。