基于MATLAB的雷达数字信号处理_目标检测_matlab_其他

<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/6271ab8ed973ef42a459a9a6/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/6271ab8ed973ef42a459a9a6/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1 </div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0"> <span class="_"> </span><span class="ff3 sc1 ls1">基于<span class="_ _0"> </span></span>MA<span class="_ _1"></span>TLAB<span class="_"> </span><span class="ff3 sc1">的雷达<span class="_ _2"></span>数字信号处理<span class="_ _2"></span></span> </div><div class="t m0 x3 h4 y3 ff2 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x4 h5 y4 ff3 fs2 fc0 sc0 ls0 ws0">本教程目的为：利用<span class="_ _3"> </span><span class="ff1">MA<span class="_ _1"></span>TL<span class="_ _4"></span>AB<span class="_ _3"> </span><span class="ff3">设计经典的雷达数字信号处理。该系统具备对雷</span></span></div><div class="t m0 x5 h6 y5 ff3 fs2 fc0 sc0 ls0 ws0">达目标回波的处理能力，能够从噪声中将目标检测出来，并提取目标的距离、速度、</div><div class="t m0 x5 h5 y6 ff3 fs2 fc0 sc0 ls0 ws0">角度信息。教程分五节完成，主要包括：<span class="ff1"> </span></div><div class="t m0 x4 h5 y7 ff3 fs2 fc0 sc0 ls0 ws0">第一节，雷达<span class="_ _5"> </span><span class="ff1">L<span class="ls2">FM<span class="_"> </span></span></span>信号分析；<span class="ff1"> </span></div><div class="t m0 x4 h5 y8 ff3 fs2 fc0 sc0 ls0 ws0">第二节，脉冲压缩处理；<span class="ff1"> </span></div><div class="t m0 x4 h5 y9 ff3 fs2 fc0 sc0 ls0 ws0">第三节，相参积累处理；<span class="ff1"> <span class="_"> </span> </span></div><div class="t m0 x4 h5 ya ff3 fs2 fc0 sc0 ls0 ws0">第四节，恒虚警<span class="_ _5"> </span><span class="ff1">CF<span class="_ _1"></span>AR<span class="_"> </span><span class="ff3">处理；</span> </span></div><div class="t m0 x4 h5 yb ff3 fs2 fc0 sc0 ls0 ws0">第五节，目标信息提取处理。<span class="ff1"> </span></div><div class="t m0 x4 h5 yc ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h7 yd ff2 fs3 fc0 sc0 ls3 ws0">1.<span class="ff4 ls0"> <span class="_ _6"> </span><span class="ff3 sc1 ls1">雷达<span class="_ _5"> </span></span><span class="ff2">L<span class="ls4">FM<span class="_"> </span></span><span class="ff3 sc1">信号分<span class="_ _2"></span>析</span> </span></span></div><div class="t m0 x4 h5 ye ff3 fs2 fc0 sc0 ls0 ws0">脉冲压缩雷达最常见的调制信号是线性调频<span class="_ _7"></span>（<span class="ff1">Linear Frequency Modulation</span>）<span class="_ _7"></span>信号<span class="ff1">,</span></div><div class="t m0 x5 h5 yf ff3 fs2 fc0 sc0 ls0 ws0">接收时采用匹配滤波器<span class="_ _4"></span>（<span class="ff1 ls5">Ma<span class="ls0">tched Filter</span></span>）<span class="_ _4"></span>压缩脉冲。<span class="_ _4"></span>脉冲压缩雷达能同时提高雷达的</div><div class="t m0 x5 h6 y10 ff3 fs2 fc0 sc0 ls0 ws0">作用距离和距离分辨率。<span class="_ _1"></span>这种体制采用宽脉冲发射以提高发射的平均功率，<span class="_ _8"></span>保证足够</div><div class="t m0 x5 h6 y11 ff3 fs2 fc0 sc0 ls0 ws0">大的作用距离；而接受时采用相应的脉冲压缩算法获得窄脉冲，以提高距离分辨率，</div><div class="t m0 x5 h5 y12 ff3 fs2 fc0 sc0 ls0 ws0">较好的解决雷达作用距离与距离分辨率之间的矛盾。<span class="ff1"> </span></div><div class="t m0 x6 h5 y13 ff1 fs2 fc0 sc0 ls0 ws0">LFM<span class="_"> </span><span class="ff3">信号的数学表达式为：</span> </div><div class="t m0 x6 h5 y14 ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x7 y15 w2 h8"><div class="t m1 x8 h9 y16 ff1 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m1 x9 ha y17 ff1 fs5 fc0 sc0 ls0 ws0">2<span class="_ _9"> </span>(<span class="_ _a"> </span>)</div><div class="t m1 xa ha y18 ff1 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m1 xb hb y19 ff1 fs6 fc0 sc0 ls0 ws0">(<span class="_ _3"> </span>)<span class="_ _b"> </span>(<span class="_ _c"> </span>)</div><div class="t m1 x6 hc y1a ff5 fs4 fc0 sc0 ls0 ws0">c</div><div class="t m1 xa hd y1b ff5 fs5 fc0 sc0 ls0 ws0">k</div><div class="t m1 xc hd y1c ff5 fs5 fc0 sc0 ls0 ws0">j<span class="_ _d"> </span>f<span class="_ _5"> </span>t<span class="_ _c"> </span>t</div><div class="t m1 xd he y1d ff5 fs6 fc0 sc0 ls0 ws0">t</div><div class="t m1 xe he y1e ff5 fs6 fc0 sc0 ls0 ws0">s<span class="_ _e"> </span>t<span class="_ _f"> </span>re<span class="_ _4"></span>ct<span class="_ _10"> </span>e</div><div class="t m1 xf he y1f ff5 fs6 fc0 sc0 ls0 ws0">T</div><div class="t m2 x10 hf y20 ff6 fs7 fc0 sc0 ls0 ws0"></div><div class="t m1 x11 h10 y21 ff6 fs5 fc0 sc0 ls0 ws0"></div><div class="t m1 x12 h11 y22 ff6 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x13 h5 y14 ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _11"> </span>(0.1) </div><div class="t m0 x5 h6 y23 ff3 fs2 fc0 sc0 ls0 ws0">式中</div><div class="c x4 y24 w3 h12"><div class="t m3 xb h13 y25 ff5 fs8 fc0 sc0 ls0 ws0">c</div><div class="t m3 x14 h14 y26 ff5 fs9 fc0 sc0 ls0 ws0">f</div></div><div class="t m0 x15 h6 y23 ff3 fs2 fc0 sc0 ls0 ws0">为载波频率，</div><div class="c x16 y27 w4 h15"><div class="t m4 x17 h16 y28 ff1 fsa fc0 sc0 ls6 ws0">()</div><div class="t m4 x18 h17 y29 ff5 fsa fc0 sc0 ls0 ws0">t</div><div class="t m4 xe h17 y2a ff5 fsa fc0 sc0 ls0 ws0">rec<span class="_ _4"></span>t</div><div class="t m4 x19 h17 y2b ff5 fsa fc0 sc0 ls0 ws0">T</div></div><div class="t m0 x1a h5 y23 ff3 fs2 fc0 sc0 ls0 ws0">为矩形信号，<span class="ff1"> </span></div><div class="t m0 x6 h5 y2c ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x7 y2d w5 h18"><div class="t m5 x1b h19 y2e ff1 fsb fc0 sc0 ls7 ws0">11</div><div class="t m5 x17 h19 y2f ff1 fsb fc0 sc0 ls8 ws0">()</div><div class="t m5 x1c h19 y30 ff1 fsb fc0 sc0 ls9 ws0">0,</div><div class="t m5 x1d h1a y31 ff5 fsb fc0 sc0 ls0 ws0">t</div><div class="t m5 x18 h1a y32 ff5 fsb fc0 sc0 ls0 ws0">t</div><div class="t m5 xe h1a y2f ff5 fsb fc0 sc0 ls0 ws0">rec<span class="_ _4"></span>t</div><div class="t m5 x1e h1a y33 ff5 fsb fc0 sc0 ls0 ws0">T</div><div class="t m5 x19 h1a y34 ff5 fsb fc0 sc0 ls0 ws0">T</div><div class="t m5 x1f h1a y30 ff5 fsb fc0 sc0 ls0 ws0">else<span class="_ _4"></span>wise</div><div class="t m5 x20 h1b y31 ff6 fsb fc0 sc0 ls0 ws0"></div><div class="t m5 x21 h1b y2e ff6 fsb fc0 sc0 ls0 ws0"><span class="_ _1"></span><span class="_ _4"></span><span class="_ _d"> </span></div><div class="t m5 x20 h1b y35 ff6 fsb fc0 sc0 ls0 ws0"></div><div class="t m5 x22 h1b y2f ff6 fsb fc0 sc0 ls0 ws0"></div><div class="t m5 x20 h1b y36 ff6 fsb fc0 sc0 ls0 ws0"></div><div class="t m5 x20 h1b y37 ff6 fsb fc0 sc0 ls0 ws0"></div><div class="t m5 xf h1b y30 ff6 fsb fc0 sc0 ls0 ws0"><span class="_ _12"> </span></div><div class="t m5 x20 h1b y38 ff6 fsb fc0 sc0 ls0 ws0"></div></div><div class="t m0 x13 h5 y2c ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _11"> </span>(0.2)<span class="_ _2"></span> </div><div class="c x5 y39 w6 h1c"><div class="t m6 x19 h1d y3a ff5 fsc fc0 sc0 ls0 ws0">B</div><div class="t m6 xe h1d y3b ff5 fsc fc0 sc0 ls0 ws0">K</div><div class="t m6 x12 h1d y3c ff5 fsc fc0 sc0 ls0 ws0">T</div><div class="t m6 x23 h1e y3d ff6 fsc fc0 sc0 ls0 ws0"></div></div><div class="t m0 x24 h6 y3e ff3 fs2 fc0 sc0 ls0 ws0">，<span class="_ _1"></span>是调频斜率，<span class="_ _8"></span>于是，<span class="_ _1"></span>信号的瞬时频率为</div><div class="c x25 y3f w7 h1f"><div class="t m7 x26 h20 y40 ff1 fsd fc0 sc0 lsa ws0">()</div><div class="t m7 xf h20 y41 ff1 fsd fc0 sc0 lsb ws0">22</div><div class="t m7 xb h21 y42 ff5 fse fc0 sc0 ls0 ws0">c</div><div class="t m7 x27 h22 y43 ff5 fsd fc0 sc0 lsc ws0">TT</div><div class="t m7 x14 h22 y44 ff5 fsd fc0 sc0 ls0 ws0">f<span class="_ _13"> </span>Kt<span class="_ _14"> </span>t<span class="_ _15"></span><span class="ff6"><span class="_ _16"> </span><span class="_ _0"> </span><span class="_ _f"> </span><span class="_ _17"> </span></span></div></div><div class="t m0 x28 h5 y3e ff3 fs2 fc0 sc0 ls0 ws0">，<span class="_ _1"></span>如图<span class="_ _5"> </span><span class="ff1">1<span class="_"> </span></span>所示：<span class="_ _18"></span><span class="ff1"> </span></div><div class="t m0 x29 h5 y45 ff1 fs2 fc0 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.613554,0.000000,0.000000,1.613554,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6271ab8ed973ef42a459a9a6/bg2.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">2 </div><div class="t m0 x2a h5 y46 ff1 fs2 fc0 sc0 lsd ws0"> <span class="ls0"> </span></div><div class="t m0 x2b h5 y47 ff1 fs2 fc0 sc0 ls0 ws0">up-chirp (K>0) <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span>down-chirp (K<0) <span class="_"> </span> </div><div class="t m0 x2c h5 y48 ff3 fs2 fc0 sc0 ls0 ws0">图<span class="_ _5"> </span><span class="ff1">1<span class="_"> </span></span>典型的<span class="_ _19"> </span><span class="ff1">chirp<span class="_"> </span></span>信号<span class="ff1"> </span></div><div class="t m0 x2d h5 y49 ff3 fs2 fc0 sc0 ls0 ws0">将<span class="_ _19"> </span><span class="ff1">1.1<span class="_"> </span></span>式中的<span class="_ _5"> </span><span class="ff1">up-chirp<span class="_"> </span></span>信号重写为：<span class="ff1"> </span></div><div class="t m0 x6 h5 y4a ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x2e y4b w8 h23"><div class="t m8 x2f h24 y4c ff1 fsf fc0 sc0 ls0 ws0">2</div><div class="t m8 xb h25 y4d ff1 fs10 fc0 sc0 ls0 ws0">(<span class="_ _3"> </span>)<span class="_ _1a"> </span>(<span class="_ _3"> </span>)</div><div class="t m8 x30 h26 y4e ff5 fs11 fc0 sc0 ls0 ws0">c</div><div class="t m8 x31 h27 y4f ff5 fsf fc0 sc0 ls0 ws0">j<span class="_ _1b"> </span>f<span class="_ _5"> </span>t</div><div class="t m8 xe h28 y50 ff5 fs10 fc0 sc0 ls0 ws0">s<span class="_ _e"> </span>t<span class="_ _10"> </span>S<span class="_ _9"> </span>t<span class="_ _1c"> </span>e</div><div class="t m9 x32 h29 y51 ff6 fs12 fc0 sc0 ls0 ws0"></div><div class="t m8 x33 h2a y52 ff6 fs10 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x34 h5 y4a ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _1d"> </span>(0.3) </div><div class="t m0 x5 h5 y53 ff3 fs2 fc0 sc0 ls0 ws0">式中，<span class="ff1"> </span></div><div class="t m0 x6 h5 y54 ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x35 y55 w9 h2b"><div class="t ma x36 h2c y56 ff1 fs13 fc0 sc0 ls0 ws0">2</div><div class="t ma x37 h2d y57 ff1 fs14 fc0 sc0 ls0 ws0">(<span class="_ _3"> </span>)<span class="_ _b"> </span>(<span class="_ _c"> </span>)</div><div class="t ma x30 h2e y58 ff5 fs15 fc0 sc0 ls0 ws0">j<span class="_ _1c"> </span>K<span class="_ _4"></span>t</div><div class="t ma x38 h2f y59 ff5 fs14 fc0 sc0 ls0 ws0">t</div><div class="t ma xe h2f y5a ff5 fs14 fc0 sc0 ls0 ws0">S<span class="_ _1c"> </span>t<span class="_ _f"> </span>re<span class="_ _4"></span>c<span class="_ _4"></span>t<span class="_ _10"> </span>e</div><div class="t ma xd h2f y5b ff5 fs14 fc0 sc0 ls0 ws0">T</div><div class="t mb x39 h30 y58 ff6 fs16 fc0 sc0 ls0 ws0"></div><div class="t ma x33 h31 y5c ff6 fs14 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x3a h5 y54 ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _1e"> </span>(0.4) </div><div class="t m0 x5 h5 y5d ff3 fs2 fc0 sc0 ls0 ws0">是信号<span class="_ _1f"> </span><span class="ff1">s(t)</span>的复包络。由傅立叶变换性质，<span class="ff1">S(t)</span>与<span class="_ _1f"> </span><span class="ff1">s(t)</span>具有相同的幅频特性，只是中心</div><div class="t m0 x5 h5 y5e ff3 fs2 fc0 sc0 ls0 ws0">频率不同而以，<span class="_ _1"></span>因此，<span class="_ _1"></span><span class="ff1 ls5">MA<span class="_ _20"></span><span class="ls0">TLAB<span class="_"> </span><span class="ff3">仿真时，<span class="_ _20"></span>只需考虑<span class="_ _5"> </span><span class="ff1">S(t)</span>。<span class="_ _20"></span>以下<span class="_ _5"> </span><span class="ff1">MA<span class="_ _20"></span>TLAB<span class="_"> </span><span class="ff3">程序产生<span class="_ _19"> </span></span>1.4</span></span></span></span></div><div class="t m0 x5 h5 y5f ff3 fs2 fc0 sc0 ls0 ws0">式的<span class="_ _19"> </span><span class="ff1">chirp<span class="_"> </span></span>信号，并作出其时域波形和幅频特性，如图<span class="_ _5"> </span><span class="ff1">2<span class="_"> </span></span>所示。<span class="ff7 fs17"> </span></div></div><div class="pi" data-data='{"ctm":[1.613554,0.000000,0.000000,1.613554,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6271ab8ed973ef42a459a9a6/bg3.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">3 </div><div class="c x3b y60 wa h32"><div class="t mc x3c h33 y61 ff8 fs18 fc0 sc0 lse ws0">-5<span class="_ _21"> </span>-4<span class="_ _21"> </span>-3<span class="_ _22"> </span>-2<span class="_ _21"> </span>-1<span class="_ _23"> </span><span class="ls0">0<span class="_ _24"> </span>1<span class="_ _24"> </span>2<span class="_ _a"> </span>3<span class="_ _24"> </span>4<span class="_ _23"> </span>5</span></div><div class="t mc x3d h33 y62 ff8 fs18 fc0 sc0 lse ws0">-1</div><div class="t mc x3e h33 y63 ff8 fs18 fc0 sc0 ls0 ws0">-<span class="_ _4"></span>0.5</div><div class="t mc x3f h33 y64 ff8 fs18 fc0 sc0 ls0 ws0">0</div><div class="t mc x40 h33 y65 ff8 fs18 fc0 sc0 ls0 ws0">0.5</div><div class="t mc x41 h33 y66 ff8 fs18 fc0 sc0 ls0 ws0">T<span class="_ _8"></span>im<span class="_ _2"></span>e in u <span class="_ _2"></span>s<span class="_ _2"></span>ec</div><div class="t mc x42 h34 y67 ff9 fs18 fc0 sc0 lsf ws0">线性调频信号</div><div class="t mc x3f h33 y68 ff8 fs18 fc0 sc0 ls0 ws0">-<span class="_ _4"></span>30<span class="_ _25"> </span>-<span class="_ _4"></span>20<span class="_ _25"> </span>-1<span class="_ _4"></span>0<span class="_ _26"> </span>0<span class="_ _27"> </span><span class="ls10">10<span class="_ _28"> </span>20<span class="_ _29"> </span>30</span></div><div class="t mc x26 h33 y69 ff8 fs18 fc0 sc0 ls10 ws0">10</div><div class="t mc x26 h33 y6a ff8 fs18 fc0 sc0 ls10 ws0">20</div><div class="t mc x26 h33 y6b ff8 fs18 fc0 sc0 ls10 ws0">30</div><div class="t mc x26 h33 y6c ff8 fs18 fc0 sc0 ls10 ws0">40</div><div class="t mc x43 h33 y6d ff8 fs18 fc0 sc0 ls0 ws0">Fre<span class="_ _4"></span>qu<span class="_ _4"></span>en<span class="_ _4"></span>c<span class="_ _2"></span>y<span class="_ _2"></span> <span class="_ _2"></span>in M<span class="_ _2"></span>H<span class="_ _4"></span>z</div><div class="t mc x44 h34 y6e ff9 fs18 fc0 sc0 lsf ws0">线性调频信号的幅频特性</div></div><div class="t m0 x45 h5 y6f ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x46 h5 y70 ff3 fs2 fc0 sc0 ls0 ws0">图<span class="_ _19"> </span><span class="ff1">2<span class="lsd"> </span>LFM<span class="_"> </span></span>信号的时域波形和幅频特性<span class="ff1"> </span></div><div class="t m0 x5 h5 y71 ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h7 y72 ff2 fs3 fc0 sc0 ls3 ws0">2.<span class="ff4 ls0"> <span class="_ _6"> </span><span class="ff3 sc1">脉冲压缩处理</span><span class="ff2"> </span></span></div><div class="t m0 x4 h6 y73 ff3 fs2 fc0 sc0 ls0 ws0">脉冲压缩指雷达在发射时采用宽脉冲信号，<span class="_ _1"></span>接收和处理回波后输出窄脉冲。<span class="_ _8"></span>脉冲</div><div class="t m0 x5 h6 y74 ff3 fs2 fc0 sc0 ls0 ws0">压缩技术是匹配滤波理论和相关接收理论的一个很好的实际应用。<span class="_ _2a"></span>很好地解决了这样</div><div class="t m0 x5 h6 y75 ff3 fs2 fc0 sc0 ls0 ws0">的一个问题：<span class="_ _2a"></span>在发射端发射大时宽、<span class="_ _2a"></span>带宽信号，<span class="_ _2a"></span>以提高信号的发射能量，<span class="_ _2a"></span>而在接收端，</div><div class="t m0 x5 h6 y76 ff3 fs2 fc0 sc0 ls0 ws0">将宽脉冲信号压缩为窄脉冲，<span class="_ _1"></span>以提高雷达对目标的距离分辨精度和距离分辨力。<span class="_ _8"></span>该技</div><div class="t m0 x5 h6 y77 ff3 fs2 fc0 sc0 ls0 ws0">术解决了雷达远距离探测与高精度测距性能不可兼顾的问题，<span class="_ _2a"></span>是现代雷达中不可缺少</div><div class="t m0 x5 h5 y78 ff3 fs2 fc0 sc0 ls0 ws0">的关键技术。<span class="ff1"> </span></div><div class="t m0 x4 h5 y79 ff3 fs2 fc0 sc0 ls0 ws0">脉冲压缩的<span class="_ _9"> </span><span class="ff1">DSP<span class="_ _6"> </span></span>处理<span class="_ _4"></span>方法有时域相关或频域相乘。对于点数较多的回波信号，</div><div class="t m0 x5 h5 y7a ff3 fs2 fc0 sc0 ls0 ws0">采用频域相乘方法可以获得较快的运算速度。频域脉冲压缩的原图如下图所示。<span class="ff1"> </span></div><div class="c x47 y7b wb h35"><div class="t md xd h36 y7c ff3 fs19 fc0 sc0 ls0 ws0">采样</div><div class="t md x48 h37 y7d ff1 fs19 fc0 sc0 ls0 ws0">FFT</div><div class="t md x49 h37 y7c ff3 fs19 fc0 sc0 ls0 ws0">复数乘法器<span class="ff1">1</span></div><div class="t md x4a h36 y7e ff3 fs19 fc0 sc0 ls0 ws0">匹配滤波器</div><div class="t md x4b h36 y7f ff3 fs19 fc0 sc0 ls0 ws0">频谱</div><div class="t md x3a h37 y80 ff1 fs19 fc0 sc0 ls0 ws0">IFFT</div><div class="t md x23 h36 y81 ff3 fs19 fc0 sc0 ls0 ws0">基带回</div><div class="t md x23 h36 y82 ff3 fs19 fc0 sc0 ls0 ws0">波数据</div><div class="t md x4c h36 y83 ff3 fs19 fc0 sc0 ls0 ws0">压缩后的</div><div class="t md x4d h36 y84 ff3 fs19 fc0 sc0 ls0 ws0">数据</div><div class="t md x4e h37 y85 ff3 fs19 fc0 sc0 ls0 ws0">复数乘法器<span class="ff1">2</span></div></div><div class="c x4f y86 wc h38"><div class="t me x50 h39 y87 ff1 fs1a fc0 sc0 ls0 ws0">2</div><div class="t me x51 h39 y88 ff1 fs1a fc0 sc0 ls0 ws0">exp<span class="_ _6"> </span>j2<span class="ffa">π</span></div><div class="t me x52 h3a y87 ff5 fs1a fc0 sc0 ls0 ws0">ivT</div><div class="t me x53 h3a y89 ff5 fs1a fc0 sc0 ls0 ws0">c</div><div class="t me x54 h3b y8a ff6 fs1a fc0 sc0 ls11 ws0"></div><div class="t me x54 h3b y8b ff6 fs1a fc0 sc0 ls11 ws0"></div><div class="t me x54 h3b y8c ff6 fs1a fc0 sc0 ls11 ws0"></div></div><div class="t m0 x55 h3c y8d ff1 fs1b fc0 sc0 ls0 ws0"> </div><div class="t m0 x35 h5 y8e ff3 fs2 fc0 sc0 ls0 ws0">图<span class="_ _19"> </span><span class="ff1">3 <span class="_"> </span></span>脉冲压缩处理流程图<span class="ff1"> </span></div><a class="l" rel='nofollow' onclick='return false;'><div class="d mf"></div></a></div><div class="pi" data-data='{"ctm":[1.613554,0.000000,0.000000,1.613554,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6271ab8ed973ef42a459a9a6/bg4.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">4 </div><div class="t m0 x4 h5 y8f ff1 fs2 fc0 sc0 ls0 ws0">DSP<span class="_"> </span><span class="ff3">对采样后的数据进行<span class="_ _19"> </span></span><span class="ls2">FFT<span class="_ _5"> </span></span><span class="ff3">变换，<span class="_ _7"></span>变换至频域后，<span class="_ _2b"></span>与其匹配滤波器频率数据进</span></div><div class="t m0 x5 h6 y90 ff3 fs2 fc0 sc0 ls0 ws0">行复数相乘，<span class="_ _8"></span>相乘后，<span class="_ _4"></span>再与复数补偿因子进行相乘解决脉冲间距离走动问题，<span class="_ _8"></span>最后将</div><div class="t m0 x5 h5 y91 ff3 fs2 fc0 sc0 ls0 ws0">结果做<span class="_ _19"> </span><span class="ff1">IFFT</span>，<span class="_ _7"></span>重新变换<span class="_ _2"></span>回时域。<span class="_ _7"></span>其中，<span class="_ _2a"></span><span class="ff1 ls2">FFT<span class="_"> </span><span class="ff3 ls0">点数、<span class="_ _7"></span>复数相乘点数、<span class="_ _2a"></span><span class="ff1">I<span class="_ _4"></span>FFT<span class="_"> </span><span class="ff3">点数均为<span class="_ _5"> </span></span>1024</span></span></span></div><div class="t m0 x5 h5 y92 ff3 fs2 fc0 sc0 ls0 ws0">点。<span class="ff1"> </span></div><div class="t m0 x4 h6 y93 ff3 fs2 fc0 sc0 ls0 ws0">信号</div><div class="c x56 y94 wd h3d"><div class="t m10 x57 h3e y95 ff1 fs1c fc0 sc0 ls12 ws0">()<span class="_ _2c"></span><span class="ff5 ls13">st</span></div></div><div class="t m0 x58 h5 y93 ff3 fs2 fc0 sc0 ls0 ws0">的匹配滤波器的时域脉冲响应为：<span class="ff1"> </span></div><div class="t m0 x6 h5 y96 ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x59 y97 we h3f"><div class="t m11 x40 h40 y98 ff1 fs1d fc0 sc0 ls0 ws0">*</div><div class="t m11 x3c h40 y99 ff1 fs1d fc0 sc0 ls0 ws0">0</div><div class="t m11 xb h41 y9a ff1 fs1e fc0 sc0 ls0 ws0">(<span class="_ _0"> </span>)<span class="_ _10"> </span>(<span class="_ _2d"> </span>)<span class="_ _2e"></span><span class="ff5">h<span class="_ _0"> </span>t<span class="_ _2f"> </span>s<span class="_ _30"> </span>t<span class="_ _31"> </span>t<span class="_ _32"></span><span class="ff6 ls14"></span></span></div></div><div class="t m0 x5a h5 y96 ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _33"> </span>(1.1) </div><div class="c x5 y9b wf h42"><div class="t m12 x5b h43 y9c ff1 fs1f fc0 sc0 ls0 ws0">0</div><div class="t m12 x51 h44 y9d ff5 fs20 fc0 sc0 ls0 ws0">t</div></div><div class="t m0 x1d h6 y9e ff3 fs2 fc0 sc0 ls0 ws0">是使滤波器物理可实现所附加的时延。理论分析时，可令</div><div class="c x5c y9b w10 h42"><div class="t m13 x5b h43 y9c ff1 fs1f fc0 sc0 ls0 ws0">0</div><div class="t m13 x51 h44 y9d ff5 fs20 fc0 sc0 ls0 ws0">t</div></div><div class="t m0 x5d h5 y9e ff3 fs2 fc0 sc0 ls0 ws0">＝<span class="ff1">0</span>，重写<span class="_ _19"> </span><span class="ff1">2.1<span class="_"> </span></span>式，<span class="ff1"> </span></div><div class="t m0 x6 h5 y9f ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x5e ya0 w11 h45"><div class="t m14 x40 h43 ya1 ff1 fs1f fc0 sc0 ls0 ws0">*</div><div class="t m14 xb h46 ya2 ff1 fs20 fc0 sc0 ls0 ws0">(<span class="_ _0"> </span>)<span class="_ _2d"> </span>(<span class="_ _34"> </span>)<span class="_ _35"></span><span class="ff5">h<span class="_ _0"> </span>t<span class="_ _36"> </span>s<span class="_ _37"> </span>t<span class="_ _38"></span><span class="ff6 ls15"></span></span></div></div><div class="t m0 x5f h5 y9f ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _39"> </span>(1.2) </div><div class="t m0 x5 h5 ya3 ff3 fs2 fc0 sc0 ls0 ws0">将<span class="_ _19"> </span><span class="ff1">2.1<span class="_"> </span></span>式代入<span class="_ _5"> </span><span class="ff1">2.2<span class="_"> </span></span>式得<span class="ff1">: </span></div><div class="t m0 x6 h5 ya4 ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x60 ya5 w12 h47"><div class="t m15 x3b h48 ya6 ff1 fs21 fc0 sc0 ls0 ws0">2</div><div class="t m15 x61 h49 ya7 ff1 fs22 fc0 sc0 ls0 ws0">2</div><div class="t m15 xb h4a ya8 ff1 fs23 fc0 sc0 ls0 ws0">(<span class="_ _0"> </span>)<span class="_ _3a"> </span>(<span class="_ _3b"> </span>)</div><div class="t m15 x48 h4b ya9 ff5 fs21 fc0 sc0 ls0 ws0">c</div><div class="t m15 x24 h4c yaa ff5 fs22 fc0 sc0 ls0 ws0">j<span class="_ _34"> </span>f<span class="_ _19"> </span>t</div><div class="t m15 x5 h4c yab ff5 fs22 fc0 sc0 ls0 ws0">j<span class="_ _e"> </span>Kt</div><div class="t m15 x21 h4d yac ff5 fs23 fc0 sc0 ls0 ws0">t</div><div class="t m15 xe h4d yad ff5 fs23 fc0 sc0 ls0 ws0">h<span class="_ _0"> </span>t<span class="_ _3c"> </span>re<span class="_ _4"></span>ct<span class="_ _3d"> </span>e<span class="_ _3e"> </span>e</div><div class="t m15 x62 h4d yae ff5 fs23 fc0 sc0 ls0 ws0">T</div><div class="t m16 x63 h4e yaf ff6 fs24 fc0 sc0 ls0 ws0"></div><div class="t m16 xc h4e yb0 ff6 fs24 fc0 sc0 ls0 ws0"></div><div class="t m15 x32 h4f yb1 ff6 fs22 fc0 sc0 ls0 ws0"></div><div class="t m15 x64 h50 yb2 ff6 fs23 fc0 sc0 ls16 ws0"></div></div><div class="t m0 x65 h5 ya4 ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _3f"> </span>(1.3) </div><div class="t m0 x5 h5 yb3 ff1 fs2 fc0 sc0 lsd ws0"> <span class="_ _40"> </span><span class="ls0"> </span></div><div class="t m0 x66 h5 yb4 ff3 fs2 fc0 sc0 ls0 ws0">图<span class="_ _19"> </span><span class="ff1">4<span class="lsd"> </span>LFM<span class="_"> </span></span>信号的匹配滤波<span class="ff1"> </span></div><div class="t m0 x4 h5 yb5 ff3 fs2 fc0 sc0 ls0 ws0">如上图<span class="ff1">,</span></div><div class="c x67 yb6 wd h51"><div class="t m17 x57 h3e yb7 ff1 fs1c fc0 sc0 ls12 ws0">()<span class="_ _2c"></span><span class="ff5 ls13">st</span></div></div><div class="t m0 x68 h6 yb5 ff3 fs2 fc0 sc0 ls0 ws0">经过系统</div><div class="c x69 yb6 w13 h51"><div class="t m18 xb h52 yb8 ff1 fs25 fc0 sc0 ls17 ws0">()<span class="_ _41"></span><span class="ff5 ls18">ht</span></div></div><div class="t m0 x6a h6 yb5 ff3 fs2 fc0 sc0 ls0 ws0">得输出信号</div><div class="c x6b yb9 w14 h53"><div class="t m19 x6c h46 yba ff1 fs20 fc0 sc0 ls19 ws0">()</div><div class="t m19 x6d h54 ybb ff5 fs1f fc0 sc0 ls0 ws0">o</div><div class="t m19 xe h44 ybc ff5 fs20 fc0 sc0 ls1a ws0">st</div></div><div class="t m0 x6e h6 yb5 ff3 fs2 fc0 sc0 ls0 ws0">，当</div><div class="c x6f ybd w15 h55"><div class="t m1a x51 h56 ybe ff1 fs26 fc0 sc0 ls0 ws0">0<span class="_ _c"> </span><span class="ff5 ls1b">tT<span class="_ _42"></span><span class="ff6 ls1c"></span></span></div></div><div class="t m0 x4d h5 yb5 ff3 fs2 fc0 sc0 ls0 ws0">时<span class="ff1">, </span></div><div class="t m0 x6 h5 ybf ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x70 yc0 w16 h57"><div class="t m1b x3c h58 yc1 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1b x71 h58 yc2 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1b x27 h58 yc3 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1b x72 h58 yc4 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1b x73 h59 yc5 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1b x57 h59 yc6 ff1 fs28 fc0 sc0 ls0 ws0">0</div><div class="t m1b x47 h59 yc7 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1b x74 h59 yc8 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1b x68 h59 yc9 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1b x75 h59 yca ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1b x76 h59 ycb ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1b x54 h5a ycc ff1 fs29 fc0 sc0 ls1d ws0">()</div><div class="t m1b x77 h5a ycd ff1 fs29 fc0 sc0 ls0 ws0">2</div><div class="t m1b x26 h5a yce ff1 fs29 fc0 sc0 ls0 ws0">sin<span class="_ _43"> </span>(<span class="_ _44"> </span>)</div><div class="t m1b x78 h5b ycf ff5 fs27 fc0 sc0 ls0 ws0">T</div><div class="t m1b x79 h5b yd0 ff5 fs27 fc0 sc0 ls0 ws0">T</div><div class="t m1b x2 h5b yd1 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m1b x75 h5b yd2 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m1b xd h5c yd3 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _1c"> </span>Kt<span class="_ _45"> </span>j<span class="_ _c"> </span>Ktu</div><div class="t m1b x26 h5c yd4 ff5 fs28 fc0 sc0 ls0 ws0">t</div><div class="t m1b x30 h5c yc7 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _c"> </span>Ktu</div><div class="t m1b x15 h5c yd5 ff5 fs28 fc0 sc0 ls0 ws0">T</div><div class="t m1b x7a h5c yc9 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _46"> </span>f<span class="_ _5"> </span>t</div><div class="t m1b x79 h5c yd6 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _1c"> </span>Kt</div><div class="t m1b x7b h5c yd7 ff5 fs28 fc0 sc0 ls0 ws0">T</div><div class="t m1b x74 h5c ycb ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _46"> </span>f<span class="_ _5"> </span>t</div><div class="t m1b xe h5d yd8 ff5 fs29 fc0 sc0 ls0 ws0">s<span class="_ _47"> </span>t<span class="_ _48"> </span>e<span class="_ _43"> </span>e<span class="_ _49"> </span>du</div><div class="t m1b x7c h5d yd9 ff5 fs29 fc0 sc0 ls0 ws0">e</div><div class="t m1b x7d h5d yda ff5 fs29 fc0 sc0 ls1e ws0">ee</div><div class="t m1b x15 h5d ydb ff5 fs29 fc0 sc0 ls0 ws0">t</div><div class="t m1b x7e h5d ydc ff5 fs29 fc0 sc0 ls0 ws0">j<span class="_ _3c"> </span>Kt</div><div class="t m1b x38 h5d ydd ff5 fs29 fc0 sc0 ls0 ws0">K<span class="_ _1c"> </span>T<span class="_ _4a"> </span>t<span class="_ _1c"> </span>t</div><div class="t m1b x24 h5d yde ff5 fs29 fc0 sc0 ls0 ws0">e</div><div class="t m1b x7f h5d ydf ff5 fs29 fc0 sc0 ls1f ws0">Kt</div><div class="t m1c x38 h5e yd3 ff6 fs2a fc0 sc0 ls20 ws0"></div><div class="t m1c x1e h5e yc7 ff6 fs2a fc0 sc0 ls0 ws0"></div><div class="t m1c x80 h5e yc9 ff6 fs2a fc0 sc0 ls0 ws0"></div><div class="t m1c x3c h5e yd6 ff6 fs2a fc0 sc0 ls0 ws0"></div><div class="t m1c x81 h5e ycb ff6 fs2a fc0 sc0 ls0 ws0"></div><div class="t m1c x10 h5f ye0 ff6 fs2b fc0 sc0 ls0 ws0"></div><div class="t m1c x62 h5f ye1 ff6 fs2b fc0 sc0 ls0 ws0"></div><div class="t m1c x38 h5f ye2 ff6 fs2b fc0 sc0 ls0 ws0"></div><div class="t m1b x82 h60 ye3 ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1b x3d h60 yd4 ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1b x71 h60 ye4 ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1b x83 h61 ye5 ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1b xe h61 ye6 ff6 fs29 fc0 sc0 ls21 ws0"><span class="_ _4b"> </span></div><div class="t m1b x74 h61 ye7 ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1b x84 h61 ye8 ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1b x1e h61 ye9 ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1b xe h61 yea ff6 fs29 fc0 sc0 ls21 ws0"></div><div class="t m1b x85 h62 yeb ff6 fs2c fc0 sc0 ls0 ws0"></div></div><div class="t m0 x86 h5 ybf ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _4c"> </span>(1.4) </div><div class="t m0 x5 h6 yec ff3 fs2 fc0 sc0 ls0 ws0">当</div><div class="c x1d yed w17 h55"><div class="t m1d x78 h56 yee ff1 fs26 fc0 sc0 ls0 ws0">0<span class="_ _4d"></span><span class="ff5 ls22">Tt<span class="_ _4e"></span><span class="ff6 ls0"><span class="_ _3b"> </span><span class="_ _30"> </span></span></span></div></div><div class="t m0 x67 h5 yec ff3 fs2 fc0 sc0 ls0 ws0">时<span class="ff1">, </span></div><div class="t m0 x6 h5 yef ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x70 yf0 w18 h63"><div class="t m1e x27 h58 yf1 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1e x71 h58 yf2 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1e x20 h58 yf3 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1e x72 h58 yf4 ff1 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m1e x73 h59 yf5 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1e x57 h59 yf6 ff1 fs28 fc0 sc0 ls0 ws0">0</div><div class="t m1e x39 h59 yf7 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1e x75 h59 yf8 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1e x68 h59 yf9 ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1e x7b h59 yfa ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1e x76 h59 yfb ff1 fs28 fc0 sc0 ls0 ws0">2</div><div class="t m1e x54 h5a yfc ff1 fs29 fc0 sc0 ls1d ws0">()</div><div class="t m1e x77 h5a yfd ff1 fs29 fc0 sc0 ls0 ws0">2</div><div class="t m1e x26 h5a yfe ff1 fs29 fc0 sc0 ls0 ws0">sin<span class="_ _43"> </span>(<span class="_ _44"> </span>)</div><div class="t m1e x79 h5b yff ff5 fs27 fc0 sc0 ls0 ws0">T</div><div class="t m1e x3f h5b y100 ff5 fs27 fc0 sc0 ls0 ws0">T</div><div class="t m1e x2 h5b y101 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m1e x75 h5b y102 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m1e x7d h5c y103 ff5 fs28 fc0 sc0 ls0 ws0">t</div><div class="t m1e xd h5c yf5 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _1c"> </span>Kt<span class="_ _45"> </span>j<span class="_ _c"> </span>Ktu</div><div class="t m1e x77 h5c yf7 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _c"> </span>Ktu</div><div class="t m1e x7b h5c y104 ff5 fs28 fc0 sc0 ls0 ws0">T</div><div class="t m1e x7a h5c yf9 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _46"> </span>f<span class="_ _5"> </span>t</div><div class="t m1e x79 h5c y105 ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _1c"> </span>Kt</div><div class="t m1e x87 h5c y106 ff5 fs28 fc0 sc0 ls0 ws0">T</div><div class="t m1e x74 h5c yfb ff5 fs28 fc0 sc0 ls0 ws0">j<span class="_ _46"> </span>f<span class="_ _5"> </span>t</div><div class="t m1e xe h5d yfc ff5 fs29 fc0 sc0 ls0 ws0">s<span class="_ _47"> </span>t<span class="_ _48"> </span>e<span class="_ _43"> </span>e<span class="_ _49"> </span>du</div><div class="t m1e x15 h5d y107 ff5 fs29 fc0 sc0 ls0 ws0">t</div><div class="t m1e x2f h5d y108 ff5 fs29 fc0 sc0 ls0 ws0">e</div><div class="t m1e x7d h5d y109 ff5 fs29 fc0 sc0 ls23 ws0">ee</div><div class="t m1e x7e h5d yfd ff5 fs29 fc0 sc0 ls0 ws0">j<span class="_ _3c"> </span>Kt</div><div class="t m1e x38 h5d yfe ff5 fs29 fc0 sc0 ls0 ws0">K<span class="_ _1c"> </span>T<span class="_ _4a"> </span>t<span class="_ _1c"> </span>t</div><div class="t m1e x24 h5d y10a ff5 fs29 fc0 sc0 ls0 ws0">e</div><div class="t m1e x7f h5d y10b ff5 fs29 fc0 sc0 ls1f ws0">Kt</div><div class="t m1f x38 h64 yf5 ff6 fs2d fc0 sc0 ls24 ws0"></div><div class="t m1f x1e h64 yf7 ff6 fs2d fc0 sc0 ls0 ws0"></div><div class="t m1f x80 h64 yf9 ff6 fs2d fc0 sc0 ls0 ws0"></div><div class="t m1f x3c h64 y105 ff6 fs2d fc0 sc0 ls0 ws0"></div><div class="t m1f x81 h64 yfb ff6 fs2d fc0 sc0 ls0 ws0"></div><div class="t m1f x10 h65 yfd ff6 fs2e fc0 sc0 ls0 ws0"></div><div class="t m1f x62 h65 yfe ff6 fs2e fc0 sc0 ls0 ws0"></div><div class="t m1f x38 h65 y10b ff6 fs2e fc0 sc0 ls0 ws0"></div><div class="t m1e x3d h60 y103 ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1e x1f h60 yf5 ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1e x22 h60 y10c ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1e x71 h60 yf7 ff6 fs28 fc0 sc0 ls0 ws0"></div><div class="t m1e x83 h61 yfc ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1e x63 h61 y107 ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1e xe h61 y109 ff6 fs29 fc0 sc0 ls21 ws0"><span class="_ _4b"> </span></div><div class="t m1e x15 h61 y10d ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1e x84 h61 yfd ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1e x1e h61 yfe ff6 fs29 fc0 sc0 ls0 ws0"></div><div class="t m1e xe h61 y10a ff6 fs29 fc0 sc0 ls21 ws0"></div><div class="t m1e x85 h62 y10e ff6 fs2c fc0 sc0 ls0 ws0"></div></div><div class="t m0 x86 h5 yef ff1 fs2 fc0 sc0 ls0 ws0"> <span class="_ _4c"> </span>(1.5)<span class="_ _2"></span> </div><div class="t m0 x5 h5 y10f ff3 fs2 fc0 sc0 ls0 ws0">合并<span class="_ _19"> </span><span class="ff1">2.4<span class="_"> </span></span>和<span class="_ _5"> </span><span class="ff1">2.5<span class="_"> </span></span>两式：<span class="ff1"> </span></div></div><div class="pi" data-data='{"ctm":[1.613554,0.000000,0.000000,1.613554,0.000000,0.000000]}'></div></div>