资源描述
,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Introduction to Digital Signal Processing,6.1 Representation of Digital Signals数字信号的表示,Messages,sent by telegraph,are digital signals.They are written using 26,alphabetical（字母的）,characters,10,numerals,（数字）,and symbols（符号）such as,comma,s（逗号）and,periods（句号）,.These symbols certainly can be represented by different voltage levels,for example,A by 10V(volts),B by 9.5V,C by 9V,and so forth,.,电报发送的消息是数字信号。这些消息由26个英文字母，10个数字，逗号句号等符号组成。它们可以用不同的电压来表示，例如用10伏表示字母A，9.5伏表示字母B，9伏表示字母C，等等。,This type of representation,however,is not used because it,is susceptible to,（易受影响的）,noise,shifting of power supply,and any other,disturbances,.,然而并未采用这种表示法，因为它易受到噪声、电源起伏及其它,干扰,的影响。,In practice,these symbols are,coded,as sequences of,dashes（划线）and dots（点）,or,equivalently,ones and zeros.The symbol 0 can be represented by a voltage from 0 to 0.8V.The symbol 1 can be represented by a voltage from 2.0 to 5.0V.,在实际应用中，这些符号被编成一串点、划，或者1和0。符号0可以用0到0.8伏之间的电压表示；符号1可以用2.0伏到5.0伏之间的电压表示。,The,precise,voltage of each symbol is not important,but,it is critical that,its value,lies within,one of the two,allowable,ranges.If the value,lies outside,the two allowable ranges,the telegraph must make a choice of either 1 or 0,and an error may,occur,.,每个符号所表示的准确电压值并不重要，,关键是,它要落在上述任意一个允许范围之内，,否则,就必须在0，1之间作出选择而可能发生错误。,In this case,an error message can be sent,and the message,be,retransmitted(,转发,),.On the,compact disc（光盘）,1 and 0 are represented by,dimples（凹痕）,.The,leading and trailing edges,of a dimple represent a 1（凹痕的前端和后端表示1）;no change represents a 0（无变化则为0）.,在此情况下，可以发送错误信息，要求重传信号。在光盘上用凹痕来表示0和1，凹痕的前端和后端表示1，无变化则为0，,There are many types of binary coding.In this section,we discuss the simplest one,called,sign-and-magnitude coding,（符号及值编码）.Consider the following sequences of :,二进制编码的方式有很多种，本节讨论最简单的一种，,叫做符号及值编码。考虑如下序列,：,Each can,assume（,取值）only either 1 or 0 and is called a,binary digit or bit,（二进制位或比特）.There are six bits in the sequence.The,left-most,（最左边起）bit is called the,sign bit,（符号位）.The sequence represents a positive number if =0 and a negative number if =1.,每一个 称做一个二进制,位,或比特，取值只能是1或者0。该序列中有6个位，最左边的是符号位，0代表正数，1代表负数。,The,remaining,five bits represent the magnitude of the number（剩下的5个比特代表该数的大小）.For example,we have,剩下的5个比特代表该数的大小。例如，,The left-most bit,excluding,the sign bit,is the most,significant,bit(MSB)and the right-most bit is the,least significant bit,(LSB).If we use 10 bits to represent the,decimal,（小数的）part of a number,then the LSB represents=1/1024=0.0009765,which,yields(,产生,),the,quantization step,（这即是量化阶）.,除符号位外最左边的位是最高有效位，而最右边的位是最低有效位。如果用10个比特表示一个数的小数部分，最低位表示为1/1024=0.0009765,这即是量化阶。,exclude(v.):,把.排除在外,Signals,encountered,in practice are mostly,CT（continuous time）,signals.To process an analog signal digitally,it must first be,discretized in time,to yield a discrete-time signal and then,quantized in amplitude,to yield a digital signal.,Therefore,in actual digital signal processing,we,deal,exclusively,(排外地,专有地),with,digital signals.,在实际中常见的信号是连续时间信号，为了以数字的方式处理模拟信号，首先要将模拟信号进行时间离散化，产生一个离散时间信号，然后,量化,其幅度产生数字信号。因此，在实际信号处理中，我们,只,处理数字信号。,An analytical study of digital signals,however,is difficult,because quantization is not a linear process.To simplify the discussion,we use,decimal numbers,to,illustrate,this point.,Suppose,every number is to,be rounded to（四舍五入）,the nearest integer(that is,the quantization step is 1);then we have：,然而对于数字信号的分析研究却很困难，因为量化并非线性的过程。为了讨论简便，我们用十进制数来说明这一点。假设每个数值都,量化,为最近的整数（也就是量化阶为1），则有,：,where,Q,stands for quantization.Because of these nonlinear phenomena,analytical study of digital signals is,complicated,.There are,however,no such problems in studying,discrete-time,signals.,For this reason,in analysis and design,all digital signals will,be considered as,discrete-time signals.In actual processing or implementation,all discrete-time signals must,be converted into,digital signals.,这里,Q,表示量化。由于非线性的存在，数字信号的分析研究变得很,复杂,。然而，,离散时间信号,的研究就没有这种问题。,因此,，在分析与设计中，所有的数字信号都,被看作,是离散时间信号。在实际处理和实现中，所有的离散时间信号都要,转换,为数字信号。,In quantization,if the amplitude（大小）of a discrete-time signal does not,fall exactly on,a,quantization level,then the value must be,approximated,by a,quantization level,either by,truncation or rounding,in either case,errors will occur.,Such errors are called,quantization errors,.,量化时，如果离散时间信号的大小与,量化电平,不一致，那么它就必须以,截断或舍入,的方式用相应的,量化电平,来近似。两种情况下都会产生误差。这种误差叫,量化误差,。,In general,quantization errors,are studied,separately,in digital signal processing.,Such a study,is important in,specialized（专门的）,hardware,that uses,a small number of,bits such as 4 or 8 bits,.On digital computers and DSP processors,that have 16 or 32 bits,quantization errors are very small and can often be simply ignored.,通常，在数字信号处理中常对量化误差进行,专题研究,。但是，在采用很少的位数，比如4位或者8位的硬件中，量化误差的研究是非常重要的。在数字计算机和16位或者32位数字信号处理器中，量化误差很小，可以忽略不计。,For convenience,we use digital signals and discrete-time signals,interchangeably,（可交替地）,with the understanding that,（考虑到）all DT signals must be transformed into digital signals in implementation,and,all digital signals
展开阅读全文