1、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
2、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.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函数的傅里叶表
3、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 con
4、tinuity 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
5、 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
6、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.”Theconceptsofsignalsandsystemsariseinawidevarietyoffields,andtheideasandtechniquesassociatedwiththeseconceptsplayanimportantroleinsuchdivers
7、eareasofscienceandtechnologyascommunication,aeronauticsandastronautics,circuitdesign,acoustics,seismology,biomedicalengineering,energygenerationdistributionsystems,chemicalprocesscontrol,andspeechprocessing。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
8、技术。它在科学技术中发挥了重要作用。8。”Withoutsomerestrictions,whenthecharacterizationofasystemrequiresacompleteinputoutputrelationship,knowingtheoutputofasystemtoacertainsetofinputdoenotallowustodeterminetheoutputofthesystemtoothersetsofinputs.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
9、。Anexampleofafinite-energysignalisasignalthattakesonthevalue1for0t1and0otherwise。举一个有限能量信号的例子:信号在0t1,而在其他时间范围取值为0.10。This,ofcourse,makessense,sinceifthereisanonzeroaverageenergyperunittime,thenintegratingorsummingthisoveraninfinitetimeintervalyieldsaninfiniteamountofenergy。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
10、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。Wecanbringcontinuoustimeanddiscretetimesystemstogetherthroughtheconceptofsampling,andwecandevelopsomeinsightsintotheuseofdiscrete-timesystemstoprocesscontinuous-timesignalsthathavebeensampled。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
11、。12。Oneofthemostimportantmotivationsforthedevelopmentofgeneraltoolsforanalyzinganddesigningsystemsisthat systemsfrommanydifferentapplicationshaveverysimilar mathematicaldescriptions。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 sh
12、ape ,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
13、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 wont 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 i
14、n 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
15、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 high speed intergrated circuit(VHSIC)Hardware
16、 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 a
17、t 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.函数的傅里叶表示,即将函数表示成正弦和余弦信号的叠加,
18、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 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
19、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。傅里叶变换的效用在于它能够在时
20、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 th
21、e 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 Fouri
22、er 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, the summation of the periodic functions (such as sine and cosine)does not accurately represent the signal。You could artificial
23、ly 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 a
24、nd 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
25、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
26、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, and to approximate the Fourier integral by the discrete Fourier transform, requires applying a matrix whose orde
27、r is the number sample points n. Since multiplying an nn 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 ju
28、st a few sparse matrices, and the resulting factors can be applied to a vector in a total of order arithmetic operations。 This is the socalled 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
29、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, autom
30、otive 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
31、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
32、output image that has some desired properties, such as improved contrast。 A continuous-time system is a system in which continuoustime input signals are applied and result in continuoustime output signals. As in Figure 31-5(a), where x(t) is the input, y(t) is the output, and h(t) is the system impu
33、lse response.Similarly, a discrete-time systemthat is, a system that transforms discrete-time inputs into discretetime 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 continuoustime and discretetime sys
34、tems together through the concept of sampling, and we can develop some insights into the use of discrete-time systems to process continuoustime 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
35、 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
36、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35b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21 Any source
37、 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,
38、 which is shown in Fig.21。 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
39、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 singledirection flow of electrons is called a Direct Current, or DC. electron circuits are explored where the direction of curr
40、ent switches back and forth: Alternating Current, or AC. But for now, well 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 charg
41、e 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
42、)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。图2-12The PNP transistor is the king of the traditional bipolar anal
43、og 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 are just byproducts , a notch better than parasites。 For intuitive, back-ofthe-envelope
44、type analysis, it is sufficient to model the transistor mostly in DC (Direct Current), keeping in mind that the bandwidth of such an element is finite.When complexity, like smallsignal AC (Alternate Current) behavior, is added to the model, computing simulations should be used since the math quickly
45、 becomes hopeless。 In Fig。212 the NPN transistor is shown with its symbol and its DC model. In this component the current flow enters the collector and base and exits the emitter。 Simply stated, the transistor conducts a collector current IC which is a copy of the base current IB amplified by a fact
46、or of beta . It follows that the emitter current IE is one plus beta times the base current. A typical value for the amplification factor is 100。 NPNs have excellent dynamic performance, or bandwidth, measured by their cutoff frequency; easily above 1GHz。图2-13 The PNP transistor is complementary to
47、the NPN, with the current flow entering the emitter and exiting the collector and base, the opposite of what happens in the NPN, which is shown in Fig.2-13. Simplicity dictates that PNPs are a by-product of the NPN construction, hence they often have less beta current gain and are slower than NPNs. A typical value for their amplification factor is 50 their cutoff frequency (fT), is generally above 1 MHz.