CH7 - Properties of Convolution.rar

  • Altair Computer
    了解作者
  • PDF
    开发工具
  • 233KB
    文件大小
  • rar
    文件格式
  • 0
    收藏次数
  • 1 积分
    下载积分
  • 0
    下载次数
  • 2020-05-01 16:23
    上传日期
DSP Guide to DSP Chapter 7
CH7 - Properties of Convolution.rar
  • CH7 - Properties of Convolution.pdf
    278.7KB
内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6256d9eabd8c6f2306a92910/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6256d9eabd8c6f2306a92910/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">123</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws0">CHAPTER</div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls2 ws0">7</div><div class="t m0 x4 h5 y4 ff1 fs3 fc0 sc0 ls3 ws1">EQUATION 7-1</div><div class="t m0 x4 h5 y5 ff1 fs3 fc0 sc0 ls4 ws2">The delta function is the identity for</div><div class="t m0 x4 h5 y6 ff1 fs3 fc0 sc0 ls5 ws3">convolution. Any signal convolved with</div><div class="t m0 x4 h5 y7 ff1 fs3 fc0 sc0 ls6 ws4">a delta function is left unchanged.</div><div class="t m0 x5 h6 y8 ff2 fs4 fc0 sc0 ls7 ws0">x<span class="_ _0"></span><span class="ff1 ls8">[</span><span class="ls9">n<span class="_ _0"></span><span class="ff1 ls8">]<span class="_ _0"></span><span class="ff3 lsa">(<span class="_ _1"> </span><span class="ff4 lsb">*<span class="_ _0"></span></span></span>[</span>n<span class="_ _0"></span><span class="ff1 ls8">]<span class="_ _2"> </span><span class="ff3 lsa">'<span class="_ _2"> </span></span></span></span>x<span class="_ _0"></span><span class="ff1 ls8">[</span><span class="ls9">n<span class="_ _0"></span><span class="ff1 ls8">]</span></span></div><div class="t m0 x6 h7 y9 ff5 fs5 fc0 sc0 lsc ws5">Properties of Convolution</div><div class="t m0 x4 h8 ya ff1 fs6 fc0 sc0 lsd ws6">A linear system's characteristics are completely specified by the system's impulse response, as</div><div class="t m0 x4 h8 yb ff1 fs6 fc0 sc0 lse ws7">governed by the mathematics of convolution. This is the basis of many signal processing</div><div class="t m0 x4 h8 yc ff1 fs6 fc0 sc0 lsf ws8">techniques. For example: Digital filters are created by <span class="ff2 ls10 ws0">designing</span><span class="ls11 ws9"> an appropriate impulse</span></div><div class="t m0 x4 h8 yd ff1 fs6 fc0 sc0 ls12 wsa">response. Enemy aircraft are detected with radar by <span class="ff2 ls13 ws0">analyzing</span><span class="ls14 wsb"> a measured impulse response.</span></div><div class="t m0 x4 h8 ye ff1 fs6 fc0 sc0 ls15 wsc">Echo suppression in long distance telephone calls is accomplished by creating an impulse</div><div class="t m0 x4 h8 yf ff1 fs6 fc0 sc0 ls16 wsd">response that <span class="ff2 ls17 ws0">counteracts</span><span class="ls18 wse"> the impulse response of the reverberation. The list goes on and on.</span></div><div class="t m0 x4 h8 y10 ff1 fs6 fc0 sc0 ls19 wsf">This chapter expands on the properties and usage of convolution in several areas. First, several</div><div class="t m0 x4 h8 y11 ff1 fs6 fc0 sc0 ls1a ws10">common impulse responses are discussed. Second, methods are presented for dealing with</div><div class="t m0 x4 h8 y12 ff1 fs6 fc0 sc0 ls1b ws11">cascade and parallel combinations of linear systems. Third, the technique of <span class="ff2 ls1c ws0">correlation</span><span class="ls1d ws12"> is</span></div><div class="t m0 x4 h8 y13 ff1 fs6 fc0 sc0 ls1e ws13">introduced. Fourth, a nasty problem with convolution is examined, the computation time can be</div><div class="t m0 x4 h8 y14 ff1 fs6 fc0 sc0 ls1f ws14">unacceptably long using conventional algorithms and computers<span class="fs7 ls20 ws15">. </span></div><div class="t m0 x4 h9 y15 ff5 fs8 fc0 sc0 ls21 ws16">Common Impulse Responses</div><div class="t m0 x7 ha y16 ff6 fs7 fc0 sc0 ls22 ws17">Delta Function </div><div class="t m0 x7 hb y17 ff1 fs7 fc0 sc0 ls23 ws18">The simplest impulse response is nothing more that a delta function, as shown</div><div class="t m0 x7 hb y18 ff1 fs7 fc0 sc0 ls24 ws19">in Fig. 7-1a. That is, an impulse on the input produces an identical impulse on</div><div class="t m0 x7 hb y19 ff1 fs7 fc0 sc0 ls25 ws1a">the output. This means that <span class="ff2 ls26 ws0">all</span><span class="ls27 ws1b"> signals are passed through the system <span class="ff2 ls28 ws0">without</span></span></div><div class="t m0 x7 hb y1a ff2 fs7 fc0 sc0 ls29 ws0">change<span class="ff1 ls2a ws1c">. Convolving any signal with a delta function results in exactly the</span></div><div class="t m0 x7 hb y1b ff1 fs7 fc0 sc0 ls2b ws1d">same signal. Mathematically, this is written:</div><div class="t m0 x7 ha y1c ff1 fs7 fc0 sc0 ls2c ws1e">This property makes the delta function the <span class="ff6 ls2d ws0">identity</span><span class="ls2e ws1f"> for convolution. This is</span></div><div class="t m0 x7 hb y1d ff1 fs7 fc0 sc0 ls2f ws20">analogous to <span class="ff2 ls30 ws0">zero</span><span class="ls31 ws21"> being the identity for addition <span class="_ _3"> </span><span class="ls32 ws22">, and <span class="ff2 ls29 ws0">one</span><span class="ls30 ws23"> being the<span class="_ _4"></span><span class="fs0 ls33 ws0">(<span class="_ _0"></span><span class="ff2 ls0">a<span class="_ _0"></span><span class="ff3 ls34">%<span class="_ _0"></span></span><span class="ff1">0<span class="_ _1"> </span><span class="ff3 ls34">'<span class="_ _5"> </span></span></span>a<span class="_ _0"></span></span>)</span></span></span></span></div><div class="t m0 x7 hb y1e ff1 fs7 fc0 sc0 ls35 ws24">identity for multiplication <span class="_ _6"> </span><span class="ls36 ws25">. At first glance, this type of system<span class="_ _7"></span><span class="fs0 ls33 ws0">(<span class="_ _0"></span><span class="ff2 ls0">a<span class="_ _0"></span></span><span class="ls37">&#215;<span class="_ _0"></span><span class="ls0">1<span class="_ _1"> </span><span class="ff3 ls34">'<span class="_ _5"> </span></span><span class="ff2">a<span class="_ _0"></span></span></span></span>)</span></span></div></div><div class="pi" data-data='{"ctm":[1.839080,0.000000,0.000000,1.839080,0.000000,0.000000]}'></div></div> </body> </html>
评论
    相关推荐
    • DSP精华问答
      此文档收集了很多关于DSP开发中遇到的问题以及解决办法,实用性很强!
    • DSP培训讲义
      DSP培训讲义。非常全面、系统的介绍了DSP开发的过程以及需要注意的问题。
    • dsp学习教程
      关于dsp学习的资料,包括一些教程,DSP芯片原理及应用,DSP的指令系统,基于DSP5402的音频处理设计与实现。
    • DSP调试工具
      DSP调试工具,非常实用,包括bushound5.0完美版,DSP汇编指令速查软件,网络抓包软件,字模提取软件。
    • DSPDSP例程
      DSP中的各种例程,CCS程序的各种代码,适合初学者 DSP中的各种例程,CCS程序的各种代码,适合初学者
    • DSPBuilder
      DSPBuilder-讲义,DSP Builder设计初步
    • DSP_MATLAB
      本光盘共包含三个子目录,分别是DSP_FORTRAN, DSP_C和DSP_MATLAB。DSP_FORTRAN和DSP_C各含有约40个信号处理的子程序,概括了书中所涉及到的绝大部分算法。程序分别由FORTRAN语言和C语言编写(MA模型、ARMA模型及最小...
    • DSP实验指导书
      DSP 是一门理论与实践并重的技术,在学习了DSP 的结构体系与基本原理以 后,必须配合通过一些典型的DSP 实验,以加深对DSP 软、硬件的理解与掌握, 同时学会DSP 的开发工具的使用,了解DSP 应用系统的开发环境...
    • dsp 课件 编程 软件
      进入21世纪之后,数字化浪潮正在席卷全球,数字信号处理器DSP(Digital Signal Processor)正是这场数字化革命的核心,无论在其应用的广度还是深度方面,都在以前所未有的速度向前发展。本章主要对数字信号处理进行...
    • Altera DSP Builder开发资料
      DSP Builder7.2 Release Notes and Errata (PDF).pdf DSP Builder7.2 参考手册 (PDF).pdf DSP Builder7.2 用户指南(PDF).pdf DSP Builder经验.doc DSP Builder设计论文// Matlab_simulink在FPGA设计中的应用...