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<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/626311c84f8811599e09e67c/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">2013 <span class="ff2">年</span> 9 <span class="ff2">月</span></div><div class="t m0 x1 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">第<span class="ff1"> 9 </span>期<span class="ff1"> <span class="_ _0"> </span></span>总第<span class="ff1"> 483 </span>期</div><div class="t m0 x2 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0">水运工程</div><div class="t m0 x3 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">Port & Waterway <span class="_ _0"> </span>Engineering</div><div class="t m0 x4 h3 y5 ff1 fs0 fc0 sc0 ls0 ws0">Sep. 2013</div><div class="t m0 x5 h3 y6 ff1 fs0 fc0 sc0 ls0 ws0">No. 9 <span class="_ _0"> </span>Serial No. 483</div><div class="t m0 x6 h4 y7 ff3 fs1 fc0 sc0 ls0 ws0">实<span class="_ _1"></span>际<span class="_ _1"></span>的<span class="_ _1"></span>海<span class="_ _1"></span>浪<span class="_ _1"></span>是<span class="_ _1"></span>三<span class="_ _1"></span>维<span class="_ _1"></span>的<span class="_ _1"></span>，<span class="_ _1"></span>海<span class="_ _1"></span>浪<span class="_ _1"></span>能<span class="_ _1"></span>量<span class="_ _1"></span>是<span class="_ _1"></span>随<span class="_ _1"></span>频<span class="_ _1"></span>率<span class="_ _1"></span>和</div><div class="t m0 x1 h4 y8 ff3 fs1 fc0 sc0 ls0 ws0">方<span class="_ _1"></span>向<span class="_ _1"></span>分<span class="_ _1"></span>布<span class="_ _1"></span>的<span class="_ _2"></span>函<span class="_ _1"></span>数<span class="_ _1"></span>，<span class="_ _1"></span>亦<span class="_ _1"></span>即<span class="_ _2"></span>方<span class="_ _1"></span>向<span class="_ _1"></span>谱<span class="_ _1"></span>。<span class="_ _1"></span>方<span class="_ _2"></span>向<span class="_ _1"></span>谱<span class="_ _1"></span>为<span class="_ _1"></span>海<span class="_ _1"></span>洋<span class="_ _2"></span>预</div><div class="t m0 x1 h4 y9 ff3 fs1 fc0 sc0 ls0 ws0">报<span class="_ _1"></span>、<span class="_ _1"></span>海<span class="_ _1"></span>洋<span class="_ _1"></span>遥<span class="_ _2"></span>感<span class="_ _1"></span>、<span class="_ _1"></span>上<span class="_ _1"></span>层<span class="_ _1"></span>海<span class="_ _2"></span>洋<span class="_ _1"></span>动<span class="_ _1"></span>力<span class="_ _1"></span>学<span class="_ _1"></span>、<span class="_ _2"></span>海<span class="_ _1"></span>洋<span class="_ _1"></span>工<span class="_ _1"></span>程<span class="_ _1"></span>以<span class="_ _2"></span>及</div><div class="t m0 x1 h4 ya ff3 fs1 fc0 sc0 ls0 ws0">近<span class="_ _1"></span>岸<span class="_ _1"></span>泥<span class="_ _1"></span>沙<span class="_ _1"></span>运<span class="_ _2"></span>动<span class="_ _1"></span>等<span class="_ _1"></span>领<span class="_ _1"></span>域<span class="_ _1"></span>的<span class="_ _2"></span>研<span class="_ _1"></span>究<span class="_ _1"></span>提<span class="_ _1"></span>供<span class="_ _1"></span>了<span class="_ _2"></span>重<span class="_ _1"></span>要<span class="_ _1"></span>依<span class="_ _1"></span>据<span class="_ _1"></span>，<span class="_ _2"></span>因</div><div class="t m0 x1 h4 yb ff3 fs1 fc0 sc0 ls0 ws0">此<span class="_ _1"></span>海<span class="_ _1"></span>浪<span class="_ _1"></span>方<span class="_ _1"></span>向<span class="_ _2"></span>谱<span class="_ _1"></span>的<span class="_ _1"></span>研<span class="_ _1"></span>究<span class="_ _1"></span>具<span class="_ _2"></span>有<span class="_ _1"></span>十<span class="_ _1"></span>分<span class="_ _1"></span>重<span class="_ _1"></span>要<span class="_ _2"></span>的<span class="_ _1"></span>理<span class="_ _1"></span>论<span class="_ _1"></span>意<span class="_ _1"></span>义<span class="_ _2"></span>和</div><div class="t m0 x1 h4 yc ff3 fs1 fc0 sc0 ls0 ws0">工程价值。</div><div class="t m0 x6 h4 yd ff3 fs1 fc0 sc0 ls0 ws0">目<span class="_ _3"> </span>前<span class="_ _3"> </span>，<span class="_ _3"> </span>有<span class="_ _3"> </span>多<span class="_ _3"> </span>种<span class="_ _3"> </span>方<span class="_ _3"> </span>向<span class="_ _3"> </span>谱<span class="_ _3"> </span>的<span class="_ _3"> </span>估<span class="_ _3"> </span>计<span class="_ _3"> </span>方<span class="_ _3"> </span>法<span class="_ _3"> </span>，<span class="_ _3"> </span>如<span class="_ _3"> </span>改</div><div class="t m0 x1 h4 ye ff3 fs1 fc0 sc0 ls0 ws0">进<span class="_ _4"></span>的<span class="_ _4"></span>最<span class="_ _4"></span>大<span class="_ _4"></span>似<span class="_ _4"></span>然<span class="_ _4"></span>法<span class="_ _4"></span>（<span class="_ _4"></span><span class="ff1">M<span class="_ _4"></span>M<span class="_ _4"></span>L<span class="_ _4"></span>M<span class="_ _4"></span></span>）<span class="_ _4"></span>、<span class="_ _4"></span>改<span class="_ _4"></span>进<span class="_ _4"></span>的<span class="_ _4"></span>贝<span class="_ _4"></span>叶<span class="_ _4"></span>斯<span class="_ _4"></span>法</div><div class="t m0 x1 h4 yf ff3 fs1 fc0 sc0 ls0 ws0">（<span class="_ _1"></span><span class="ff1">M<span class="_ _1"></span>B<span class="_ _2"></span>D<span class="_ _1"></span>M<span class="_ _2"></span></span>）<span class="_ _1"></span>、<span class="_ _2"></span>最<span class="_ _1"></span>大<span class="_ _2"></span>熵<span class="_ _1"></span>法<span class="_ _1"></span>（<span class="_ _2"></span><span class="ff1">M<span class="_ _1"></span>E<span class="_ _2"></span>P<span class="_ _1"></span></span>）<span class="_ _2"></span>和<span class="_ _1"></span>直<span class="_ _1"></span>接<span class="_ _2"></span>基<span class="_ _1"></span>于<span class="_ _2"></span>傅<span class="_ _1"></span>里</div><div class="t m0 x1 h4 y10 ff3 fs1 fc0 sc0 ls0 ws0">叶<span class="_ _2"></span>变<span class="_ _4"></span>换<span class="_ _4"></span>（<span class="_ _2"></span><span class="ff1">D<span class="_ _4"></span>F<span class="_ _4"></span>T<span class="_ _2"></span></span>）<span class="_ _4"></span>的<span class="_ _2"></span>方<span class="_ _4"></span>法<span class="_ _4"></span>等</div><div class="t m0 x7 h5 y11 ff1 fs2 fc0 sc0 ls0 ws0">[<span class="_ _1"></span>1<span class="_ _2"></span>-<span class="_ _1"></span>2<span class="_ _2"></span>]</div><div class="t m0 x8 h4 y12 ff3 fs1 fc0 sc0 ls0 ws0">，<span class="_ _2"></span>传<span class="_ _4"></span>统<span class="_ _4"></span>的<span class="_ _2"></span>估<span class="_ _4"></span>计<span class="_ _4"></span>方<span class="_ _2"></span>法</div><div class="t m0 x1 h4 y13 ff3 fs1 fc0 sc0 ls0 ws0">都<span class="_ _4"></span>是<span class="_ _4"></span>在<span class="_ _4"></span>假<span class="_ _4"></span>定<span class="_ _4"></span>波<span class="_ _4"></span>浪<span class="_ _4"></span>场<span class="_ _4"></span>为<span class="_ _4"></span>平<span class="_ _4"></span>稳<span class="_ _4"></span>的<span class="_ _2"></span>基<span class="_ _4"></span>础<span class="_ _4"></span>上<span class="_ _4"></span>进<span class="_ _4"></span>行<span class="_ _4"></span>的<span class="_ _4"></span>。<span class="_ _4"></span>然</div><div class="t m0 x1 h4 y14 ff3 fs1 fc0 sc0 ls0 ws0">而<span class="_ _4"></span>实<span class="_ _4"></span>际<span class="_ _4"></span>的<span class="_ _4"></span>海<span class="_ _4"></span>浪<span class="_ _4"></span>是<span class="_ _4"></span>非<span class="_ _4"></span>平<span class="_ _4"></span>稳<span class="_ _4"></span>的<span class="_ _4"></span>，<span class="_ _2"></span>因<span class="_ _4"></span>此<span class="_ _4"></span>采<span class="_ _4"></span>用<span class="_ _4"></span>非<span class="_ _4"></span>平<span class="_ _4"></span>稳<span class="_ _4"></span>分</div><div class="t m0 x1 h4 y15 ff3 fs1 fc0 sc0 ls0 ws0">析<span class="_ _4"></span>方<span class="_ _4"></span>法<span class="_ _4"></span>估<span class="_ _4"></span>计<span class="_ _4"></span>海<span class="_ _4"></span>浪<span class="_ _4"></span>方<span class="_ _4"></span>向<span class="_ _4"></span>谱<span class="_ _4"></span>更<span class="_ _4"></span>为<span class="_ _2"></span>准<span class="_ _4"></span>确<span class="_ _4"></span>。<span class="_ _4"></span>小<span class="_ _4"></span>波<span class="_ _4"></span>变<span class="_ _4"></span>换<span class="_ _4"></span>是</div><div class="t m0 x9 h6 y16 ff4 fs3 fc0 sc0 ls0 ws0">基于小波变换的海浪方向谱估计方法研究</div><div class="t m0 xa h7 y17 ff5 fs4 fc0 sc0 ls0 ws0">*</div><div class="t m0 xb h8 y18 ff2 fs5 fc0 sc0 ls0 ws0">张<span class="ff1"> <span class="_ _5"> </span></span>乐，马玉祥，董国海</div><div class="t m0 xc h2 y19 ff1 fs0 fc0 sc0 ls0 ws0">(<span class="ff2">大连理工大学</span> <span class="ff2">海岸和近海工程国家重点实验室，辽宁</span> <span class="ff2">大连</span> 116023)</div><div class="t m0 xd h2 y1a ff6 fs0 fc0 sc0 ls1 ws0">摘要：<span class="ff2 ls0">利用<span class="_ _1"></span>数<span class="_ _1"></span>值模<span class="_ _1"></span>拟方<span class="_ _1"></span>法<span class="_ _1"></span>分析<span class="_ _1"></span>了<span class="_ _1"></span>基于<span class="_ _1"></span>小波<span class="_ _1"></span>变<span class="_ _1"></span>换的<span class="_ _1"></span>方向<span class="_ _1"></span>谱<span class="_ _1"></span>估计<span class="_ _1"></span>分<span class="_ _1"></span>析方<span class="_ _1"></span>法的<span class="_ _1"></span>适<span class="_ _1"></span>用性<span class="_ _1"></span><span class="ff1">,</span>测<span class="_ _1"></span>波<span class="_ _1"></span>阵列<span class="_ _1"></span>类<span class="_ _1"></span>型、<span class="_ _1"></span>波浪<span class="_ _1"></span>入<span class="_ _1"></span>射方<span class="_ _1"></span>向、<span class="_ _1"></span>方<span class="_ _1"></span>向</span></div><div class="t m0 x1 h2 y1b ff2 fs0 fc0 sc0 ls0 ws0">集<span class="_ _1"></span>中度<span class="_ _1"></span>以<span class="_ _1"></span>及<span class="_ _1"></span>采<span class="_ _1"></span>用长<span class="_ _1"></span>度<span class="_ _1"></span>对<span class="_ _1"></span>小<span class="_ _1"></span>波方<span class="_ _1"></span>向<span class="_ _1"></span>谱<span class="_ _1"></span>估<span class="_ _1"></span>计分<span class="_ _1"></span>析<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _1"></span>分析<span class="_ _1"></span>结<span class="_ _1"></span>果<span class="_ _1"></span>的<span class="_ _1"></span>影响<span class="_ _1"></span>。<span class="_ _1"></span>结<span class="_ _1"></span>果<span class="_ _1"></span>表明<span class="_ _1"></span>：<span class="_ _1"></span>小<span class="_ _1"></span>波<span class="_ _1"></span>方向<span class="_ _1"></span>谱<span class="_ _1"></span>的<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _1"></span>适用<span class="_ _1"></span>条<span class="_ _1"></span>件<span class="_ _1"></span>较<span class="_ _1"></span>广泛<span class="_ _1"></span>，<span class="_ _1"></span>实<span class="_ _1"></span>用</div><div class="t m0 x1 h2 y1c ff2 fs0 fc0 sc0 ls0 ws0">性更<span class="_ _1"></span>强。</div><div class="t m0 xd h2 y1d ff6 fs0 fc0 sc0 ls0 ws0">关键词：<span class="ff2">方向谱；小波变换；阵列类型；时间序列长度</span></div><div class="t m0 xd h9 y1e ff6 fs0 fc0 sc0 ls0 ws0">中图分类号：</div><div class="t m0 xe h2 y1f ff1 fs0 fc0 sc0 ls0 ws0">P 731.2<span class="ff2">；</span>TV 139.2 <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span><span class="ff6">文献标志码：</span>A <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span> <span class="_ _0"> </span><span class="ff6">文章编号：</span>1002-4972</div><div class="t m0 xf h3 y20 ff1 fs0 fc0 sc0 ls0 ws0">(</div><div class="t m0 x10 h3 y1f ff1 fs0 fc0 sc0 ls0 ws0">2013</div><div class="t m0 x11 h3 y20 ff1 fs0 fc0 sc0 ls0 ws0">)</div><div class="t m0 x12 ha y21 ff7 fs0 fc0 sc0 ls0 ws0">09<span class="ff1">-0024-07</span></div><div class="t m0 x13 hb y22 ff8 fs5 fc0 sc0 ls0 ws0">Directional spectrum estimation of random wave based on wavelet transform</div><div class="t m0 x14 h3 y23 ff1 fs0 fc0 sc0 ls0 ws0">ZHANG Le, MA Yu-xiang, DONG Guo-hai</div><div class="t m0 x15 h3 y24 ff1 fs0 fc0 sc0 ls0 ws0">(State Key Laboratory of Coastal and Offshare Engineering, Dalian University of Technology, Dalian 116023, China)</div><div class="t m0 x6 hb y25 ff8 fs5 fc0 sc0 ls2 ws0">Abstract:</div><div class="t m0 x16 hc y26 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _4"></span>Th<span class="_ _1"></span>e <span class="_ _6"> </span>ap<span class="_ _1"></span>pl<span class="_ _1"></span>ic<span class="_ _1"></span>ab<span class="_ _1"></span>il<span class="_ _1"></span>it<span class="_ _1"></span>y <span class="_ _4"></span>o<span class="_ _1"></span>f <span class="_ _6"> </span>th<span class="_ _1"></span>e <span class="_ _4"></span>e<span class="_ _1"></span>st<span class="_ _1"></span>im<span class="_ _1"></span>at<span class="_ _1"></span>io<span class="_ _1"></span>n <span class="_ _6"> </span>of<span class="_ _1"></span> <span class="_ _4"></span>th<span class="_ _1"></span>e <span class="_ _6"> </span>di<span class="_ _1"></span>re<span class="_ _1"></span>ct<span class="_ _1"></span>io<span class="_ _1"></span>na<span class="_ _1"></span>l <span class="_ _4"></span>s<span class="_ _1"></span>pe<span class="_ _1"></span>ct<span class="_ _1"></span>ru<span class="_ _1"></span>m <span class="_ _6"> </span>ba<span class="_ _1"></span>se<span class="_ _1"></span>d <span class="_ _4"></span>o<span class="_ _1"></span>n <span class="_ _6"> </span>wa<span class="_ _1"></span>ve<span class="_ _1"></span>le<span class="_ _1"></span>t <span class="_ _4"></span>t<span class="_ _1"></span>ra<span class="_ _1"></span>ns<span class="_ _1"></span>fo<span class="_ _1"></span>rm<span class="_ _1"></span> <span class="_ _4"></span>i<span class="_ _1"></span>s </div><div class="t m0 x1 hc y27 ff1 fs1 fc0 sc0 ls0 ws0">di<span class="_ _1"></span>sc<span class="_ _1"></span>us<span class="_ _1"></span>se<span class="_ _1"></span>d <span class="_ _4"></span>u<span class="_ _1"></span>si<span class="_ _1"></span>ng<span class="_ _1"></span> <span class="_ _4"></span>th<span class="_ _1"></span>e <span class="_ _4"></span>d<span class="_ _1"></span>at<span class="_ _1"></span>a <span class="_ _6"> </span>ge<span class="_ _1"></span>ner<span class="_ _1"></span>at<span class="_ _1"></span>ed<span class="_ _1"></span> <span class="_ _4"></span>fr<span class="_ _1"></span>om<span class="_ _1"></span> <span class="_ _4"></span>t<span class="_ _1"></span>he <span class="_ _6"> </span>nu<span class="_ _1"></span>me<span class="_ _1"></span>ri<span class="_ _1"></span>ca<span class="_ _1"></span>l <span class="_ _4"></span>s<span class="_ _1"></span>im<span class="_ _1"></span>ul<span class="_ _1"></span>ati<span class="_ _1"></span>on<span class="_ _1"></span>s.<span class="_ _1"></span> <span class="_ _4"></span>T<span class="_ _1"></span>he <span class="_ _6"> </span>an<span class="_ _1"></span>al<span class="_ _1"></span>ys<span class="_ _1"></span>is<span class="_ _1"></span> <span class="_ _4"></span>fo<span class="_ _1"></span>cu<span class="_ _1"></span>si<span class="_ _1"></span>ng <span class="_ _6"> </span>on<span class="_ _1"></span> <span class="_ _4"></span>th<span class="_ _1"></span>e <span class="_ _4"></span>i<span class="_ _1"></span>nf<span class="_ _1"></span>lu<span class="_ _1"></span>en<span class="_ _1"></span>ce<span class="_ _1"></span>s <span class="_ _4"></span>o<span class="_ _1"></span>f </div><div class="t m0 x1 hc y28 ff1 fs1 fc0 sc0 ls0 ws0">meas<span class="_ _1"></span>ured<span class="_ _1"></span> <span class="_ _4"></span>array<span class="_ _1"></span> <span class="_ _4"></span>types<span class="_ _1"></span>, <span class="_ _4"></span>wave<span class="_ _1"></span> <span class="_ _4"></span>incid<span class="_ _1"></span>ent <span class="_ _4"></span>di<span class="_ _1"></span>rect<span class="_ _1"></span>ion, <span class="_ _4"></span>d<span class="_ _1"></span>irect<span class="_ _1"></span>iona<span class="_ _1"></span>l <span class="_ _4"></span>conc<span class="_ _1"></span>entra<span class="_ _1"></span>tion<span class="_ _1"></span> <span class="_ _4"></span>and <span class="_ _4"></span>sa<span class="_ _1"></span>mplin<span class="_ _1"></span>g <span class="_ _4"></span>leng<span class="_ _1"></span>ths <span class="_ _4"></span>on<span class="_ _1"></span> <span class="_ _4"></span>the <span class="_ _4"></span>di<span class="_ _1"></span>rect<span class="_ _1"></span>ional </div><div class="t m0 x1 hc y29 ff1 fs1 fc0 sc0 ls0 ws0">spectrum <span class="_ _1"></span>based <span class="_ _1"></span>on <span class="_ _1"></span>wavelet <span class="_ _1"></span>transform <span class="_ _1"></span>is <span class="_ _2"></span>carried <span class="_ _1"></span>out, <span class="_ _1"></span>which <span class="_ _1"></span>shows <span class="_ _1"></span>that <span class="_ _2"></span>the <span class="_ _1"></span>wavelet <span class="_ _1"></span>direction <span class="_ _1"></span>spectrum <span class="_ _1"></span>is <span class="_ _2"></span>more <span class="_ _1"></span>widely </div><div class="t m0 x1 hc y2a ff1 fs1 fc0 sc0 ls0 ws0">applicable.</div><div class="t m0 x6 hb y2b ff8 fs5 fc0 sc0 ls0 ws0">Key words: </div><div class="t m0 x17 hc y2c ff1 fs1 fc0 sc0 ls0 ws0">directional spectrum; wavelet transform; type of array; length of time series </div><div class="t m0 x6 h9 y2d ff6 fs0 fc0 sc0 ls0 ws0">收稿日期：<span class="ff1">2013-01-28</span></div><div class="t m0 x6 hd y2e ff5 fs0 fc0 sc0 ls3 ws0"> *</div><div class="t m0 x6 h2 y2f ff6 fs0 fc0 sc0 ls0 ws0">基金项目：<span class="ff2">国家自然科学基金（<span class="ff1">11172058</span>）</span></div><div class="t m0 x6 h2 y30 ff6 fs0 fc0 sc0 ls0 ws0">作者简介：<span class="ff2">张乐（<span class="ff1">1987</span>—），女，硕士研究生，从事基于小波变换的波浪非线性研究。</span></div><div class="t m0 x18 h4 y7 ff3 fs1 fc0 sc0 ls0 ws0">分<span class="_ _4"></span>析<span class="_ _4"></span>非<span class="_ _4"></span>平<span class="_ _4"></span>稳<span class="_ _4"></span>信<span class="_ _4"></span>号<span class="_ _4"></span>的<span class="_ _4"></span>有<span class="_ _4"></span>力<span class="_ _4"></span>工<span class="_ _4"></span>具<span class="_ _2"></span>，<span class="_ _4"></span>近<span class="_ _4"></span>些<span class="_ _4"></span>年<span class="_ _4"></span>来<span class="_ _4"></span>在<span class="_ _4"></span>海<span class="_ _4"></span>浪</div><div class="t m0 x18 h4 y8 ff3 fs1 fc0 sc0 ls0 ws0">分<span class="_ _2"></span>析<span class="_ _4"></span>方<span class="_ _4"></span>面<span class="_ _2"></span>得<span class="_ _4"></span>到<span class="_ _2"></span>了<span class="_ _4"></span>广<span class="_ _2"></span>泛<span class="_ _4"></span>的<span class="_ _4"></span>应<span class="_ _2"></span>用<span class="_ _4"></span>。<span class="_ _2"></span><span class="ff1">D<span class="_ _4"></span>o<span class="_ _2"></span>n<span class="_ _4"></span>e<span class="_ _4"></span>l<span class="_ _2"></span>a<span class="_ _4"></span>n</span></div><div class="t m0 x19 h5 y31 ff1 fs2 fc0 sc0 ls0 ws0">[<span class="_ _1"></span>3<span class="_ _2"></span>]</div><div class="t m0 x1a h4 y32 ff3 fs1 fc0 sc0 ls0 ws0">提<span class="_ _2"></span>出<span class="_ _4"></span>了</div><div class="t m0 x18 h4 y33 ff3 fs1 fc0 sc0 ls0 ws0">基<span class="_ _2"></span>于<span class="_ _4"></span>小<span class="_ _2"></span>波<span class="_ _2"></span>变<span class="_ _4"></span>换<span class="_ _2"></span>的<span class="_ _2"></span>方<span class="_ _4"></span>向<span class="_ _2"></span>谱<span class="_ _4"></span>估<span class="_ _2"></span>计<span class="_ _2"></span>方<span class="_ _4"></span>法<span class="_ _2"></span>（<span class="_ _2"></span><span class="ff1">W<span class="_ _4"></span>D<span class="_ _2"></span>M<span class="_ _4"></span></span>）<span class="_ _2"></span>，<span class="_ _2"></span>并</div><div class="t m0 x18 h4 y34 ff3 fs1 fc0 sc0 ls0 ws0">用<span class="_ _4"></span>其<span class="_ _2"></span>分<span class="_ _4"></span>析<span class="_ _4"></span>了<span class="_ _2"></span>实<span class="_ _4"></span>测<span class="_ _4"></span>波<span class="_ _2"></span>面<span class="_ _4"></span>，<span class="_ _4"></span>将<span class="_ _2"></span>分<span class="_ _4"></span>析<span class="_ _4"></span>结<span class="_ _2"></span>果<span class="_ _4"></span>与<span class="_ _4"></span><span class="ff1">M<span class="_ _2"></span>L<span class="_ _4"></span>M<span class="_ _4"></span></span>对<span class="_ _4"></span>比</div><div class="t m0 x18 h4 y35 ff3 fs1 fc0 sc0 ls0 ws0">发<span class="_ _2"></span>现<span class="_ _2"></span>：<span class="_ _2"></span><span class="ff1">W<span class="_ _2"></span>D<span class="_ _2"></span>M<span class="_ _4"></span></span>比<span class="_ _1"></span><span class="ff1">M<span class="_ _2"></span>L<span class="_ _4"></span>M<span class="_ _1"></span></span>得<span class="_ _4"></span>到<span class="_ _1"></span>的<span class="_ _2"></span>频<span class="_ _4"></span>率<span class="_ _1"></span>方<span class="_ _4"></span>向<span class="_ _1"></span>谱<span class="_ _2"></span>更<span class="_ _4"></span>光<span class="_ _1"></span>滑<span class="_ _4"></span>，</div><div class="t m0 x18 h4 y36 ff3 fs1 fc0 sc0 ls0 ws0">方<span class="_ _4"></span>向<span class="_ _4"></span>上<span class="_ _4"></span>的<span class="_ _4"></span>分<span class="_ _4"></span>布<span class="_ _4"></span>更<span class="_ _4"></span>窄<span class="_ _4"></span>，<span class="_ _4"></span>在<span class="_ _4"></span>谱<span class="_ _4"></span>峰<span class="_ _2"></span>值<span class="_ _4"></span>附<span class="_ _4"></span>近<span class="_ _4"></span>更<span class="_ _4"></span>接<span class="_ _4"></span>近<span class="_ _4"></span>真<span class="_ _4"></span>实</div><div class="t m0 x18 h4 y37 ff3 fs1 fc0 sc0 ls0 ws0">海<span class="_ _1"></span>浪</div><div class="t m0 x1b h5 y38 ff1 fs2 fc0 sc0 ls0 ws0">[4<span class="_ _1"></span>]</div><div class="t m0 x1c h4 y39 ff3 fs1 fc0 sc0 ls0 ws0">。</div><div class="t m0 x1d h4 y3a ff3 fs1 fc0 sc0 ls0 ws0">虽然<span class="_ _1"></span><span class="ff1">WDM<span class="_ _1"></span></span>方法<span class="_ _1"></span>近年来<span class="_ _1"></span>广泛<span class="_ _1"></span>应用于<span class="_ _1"></span>估计<span class="_ _1"></span>多向随</div><div class="t m0 x18 h4 y3b ff3 fs1 fc0 sc0 ls0 ws0">机波<span class="_ _1"></span>浪<span class="_ _1"></span>的<span class="_ _1"></span>方向<span class="_ _1"></span>谱</div><div class="t m0 x1e h5 y3c ff1 fs2 fc0 sc0 ls0 ws0">[5<span class="_ _1"></span>-6]</div><div class="t m0 x1f h4 y3d ff3 fs1 fc0 sc0 ls0 ws0">，但<span class="_ _1"></span>是<span class="_ _1"></span>仍<span class="_ _1"></span>然存<span class="_ _1"></span>在<span class="_ _1"></span>很<span class="_ _1"></span>多值<span class="_ _1"></span>得<span class="_ _1"></span>研究</div><div class="t m0 x18 h4 y3e ff3 fs1 fc0 sc0 ls0 ws0">的<span class="_ _1"></span>问<span class="_ _1"></span>题<span class="_ _1"></span>，<span class="_ _1"></span>如<span class="_ _2"></span>该<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _1"></span>的<span class="_ _1"></span>适<span class="_ _2"></span>用<span class="_ _1"></span>条<span class="_ _1"></span>件<span class="_ _1"></span>、<span class="_ _1"></span>计<span class="_ _2"></span>算<span class="_ _1"></span>稳<span class="_ _1"></span>定<span class="_ _1"></span>性<span class="_ _1"></span>以<span class="_ _2"></span>及</div><div class="t m0 x18 h4 y3f ff3 fs1 fc0 sc0 ls0 ws0">该<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _1"></span>对<span class="_ _1"></span>不<span class="_ _2"></span>同<span class="_ _1"></span>测<span class="_ _1"></span>波<span class="_ _1"></span>阵<span class="_ _1"></span>列<span class="_ _2"></span>类<span class="_ _1"></span>型<span class="_ _1"></span>和<span class="_ _1"></span>不<span class="_ _1"></span>同<span class="_ _2"></span>波<span class="_ _1"></span>浪<span class="_ _1"></span>要<span class="_ _1"></span>素<span class="_ _1"></span>等<span class="_ _2"></span>因</div><div class="t m0 x18 h4 y40 ff3 fs1 fc0 sc0 ls0 ws0">素的<span class="_ _1"></span>响<span class="_ _1"></span>应。<span class="_ _1"></span>因此<span class="_ _1"></span>本<span class="_ _1"></span>文采<span class="_ _1"></span>用数<span class="_ _1"></span>值方<span class="_ _1"></span>法<span class="_ _1"></span>对<span class="ff1">W<span class="_ _1"></span>DM<span class="_ _1"></span></span>进<span class="_ _1"></span>行深</div><div class="t m0 x18 h4 y41 ff3 fs1 fc0 sc0 ls0 ws0">入的研究，分析该方法的实用性。</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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<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/626311c84f8811599e09e67c/bg2.jpg"><div class="t m0 x20 h3 y42 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x21 he y43 ff9 fs6 fc0 sc0 ls0 ws0">•</div><div class="t m0 x22 h3 y42 ff1 fs0 fc0 sc0 ls0 ws0"> <span class="_"> </span>25 </div><div class="t m0 x23 he y43 ff9 fs6 fc0 sc0 ls0 ws0">•</div><div class="t m0 x24 h2 y44 ff2 fs0 fc0 sc0 ls0 ws0">第<span class="ff1"> 9 </span>期</div><div class="t m0 x1 hf y45 ffa fs1 fc0 sc0 ls0 ws0">1 <span class="_ _7"> </span><span class="ff6">多向不规则波的产生</span></div><div class="t m0 x6 h4 y46 ff3 fs1 fc0 sc0 ls0 ws0">研<span class="_ _1"></span>究<span class="_ _1"></span>中<span class="_ _1"></span>，<span class="_ _1"></span>通<span class="_ _1"></span>常<span class="_ _1"></span>采<span class="_ _1"></span>用<span class="_ _1"></span>数<span class="_ _1"></span>值<span class="_ _1"></span>模<span class="_ _1"></span>拟<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _1"></span>对<span class="_ _1"></span>方<span class="_ _1"></span>向<span class="_ _1"></span>谱<span class="_ _1"></span>估</div><div class="t m0 x1 h4 y47 ff3 fs1 fc0 sc0 ls0 ws0">计<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _1"></span>的<span class="_ _1"></span>方<span class="_ _2"></span>向<span class="_ _1"></span>分<span class="_ _1"></span>辨<span class="_ _1"></span>率<span class="_ _1"></span>以<span class="_ _2"></span>及<span class="_ _1"></span>计<span class="_ _1"></span>算<span class="_ _1"></span>稳<span class="_ _1"></span>定<span class="_ _2"></span>性<span class="_ _1"></span>、<span class="_ _1"></span>可<span class="_ _1"></span>靠<span class="_ _1"></span>性<span class="_ _2"></span>和</div><div class="t m0 x1 h4 y48 ff3 fs1 fc0 sc0 ls0 ws0">适<span class="_ _1"></span>用<span class="_ _1"></span>性<span class="_ _1"></span>等<span class="_ _1"></span>方<span class="_ _2"></span>面<span class="_ _1"></span>进<span class="_ _1"></span>行<span class="_ _1"></span>检<span class="_ _1"></span>验<span class="_ _2"></span>。<span class="_ _1"></span>因<span class="_ _1"></span>此<span class="_ _1"></span>准<span class="_ _1"></span>确<span class="_ _2"></span>地<span class="_ _1"></span>数<span class="_ _1"></span>值<span class="_ _1"></span>模<span class="_ _1"></span>拟<span class="_ _2"></span>多</div><div class="t m0 x1 h4 y49 ff3 fs1 fc0 sc0 ls0 ws0">向不规则波浪非常必要。</div><div class="t m0 x6 h4 y4a ff3 fs1 fc0 sc0 ls0 ws0">基<span class="_ _1"></span>于<span class="_ _1"></span>线<span class="_ _1"></span>性<span class="_ _1"></span>波<span class="_ _1"></span>浪<span class="_ _1"></span>理<span class="_ _1"></span>论<span class="_ _1"></span>，<span class="_ _1"></span>多<span class="_ _1"></span>向<span class="_ _1"></span>不<span class="_ _1"></span>规<span class="_ _1"></span>则<span class="_ _1"></span>波<span class="_ _1"></span>的<span class="_ _1"></span>模<span class="_ _1"></span>拟<span class="_ _1"></span>可</div><div class="t m0 x1 h4 y4b ff3 fs1 fc0 sc0 ls0 ws0">采用频率方<span class="_ _1"></span>向对应法</div><div class="t m0 x25 h5 y4c ff1 fs2 fc0 sc0 ls0 ws0">[7]</div><div class="t m0 x26 h4 y4d ff3 fs1 fc0 sc0 ls0 ws0">：将多向不<span class="_ _1"></span>规则波的波能同</div><div class="t m0 x1 h4 y4e ff3 fs1 fc0 sc0 ls0 ws0">时<span class="_ _1"></span>分<span class="_ _1"></span>布<span class="_ _1"></span>在<span class="_ _1"></span>一<span class="_ _2"></span>定<span class="_ _1"></span>的<span class="_ _1"></span>频<span class="_ _1"></span>域<span class="_ _1"></span>和<span class="_ _2"></span>方<span class="_ _1"></span>向<span class="_ _1"></span>范<span class="_ _1"></span>围<span class="_ _1"></span>内<span class="_ _2"></span>，<span class="_ _1"></span>可<span class="_ _1"></span>把<span class="_ _1"></span>频<span class="_ _1"></span>域<span class="_ _2"></span>区</div><div class="t m0 x1 h4 y4f ff3 fs1 fc0 sc0 ls0 ws0">间分割<span class="_ _1"></span>成</div><div class="t m0 x13 h10 y50 ffb fs1 fc0 sc0 ls0 ws0">M</div><div class="t m0 x27 h4 y4f ff3 fs1 fc0 sc0 ls0 ws0">份，方<span class="_ _1"></span>向区间分<span class="_ _1"></span>成</div><div class="t m0 x28 h10 y50 ffb fs1 fc0 sc0 ls0 ws0">J</div><div class="t m0 x29 h4 y4f ff3 fs1 fc0 sc0 ls0 ws0">份，共<span class="_ _1"></span>有</div><div class="t m0 x3 h10 y50 ffb fs1 fc0 sc0 ls0 ws0">M</div><div class="t m0 x2a h4 y4f ff3 fs1 fc0 sc0 ls0 ws0">×</div><div class="t m0 x2b h10 y50 ffb fs1 fc0 sc0 ls0 ws0">J</div><div class="t m0 x2c h4 y4f ff3 fs1 fc0 sc0 ls0 ws0">个组</div><div class="t m0 x1 h4 y51 ff3 fs1 fc0 sc0 ls0 ws0">成<span class="_ _1"></span>单<span class="_ _1"></span>元<span class="_ _1"></span>，<span class="_ _1"></span>把<span class="_ _2"></span>每<span class="_ _1"></span>个<span class="_ _1"></span>单<span class="_ _1"></span>元<span class="_ _1"></span>的<span class="_ _2"></span>组<span class="_ _1"></span>成<span class="_ _1"></span>波<span class="_ _1"></span>看<span class="_ _1"></span>成<span class="_ _2"></span>是<span class="_ _1"></span>简<span class="_ _1"></span>谐<span class="_ _1"></span>波<span class="_ _1"></span>，<span class="_ _2"></span>则</div><div class="t m0 x1 h4 y52 ff3 fs1 fc0 sc0 ls0 ws0">经过叠加其波列为：</div><div class="c x1 y53 w2 h11"><div class="t m0 x2d h10 y54 ff5 fs1 fc0 sc0 ls4 ws0">(c<span class="_ _8"></span><span class="ls0">os<span class="_ _9"> </span><span class="ls5">si<span class="ls6">n)<span class="_ _a"></span><span class="ffb ls7">kx<span class="_ _b"> </span>ky<span class="_ _c"> </span><span class="ls0">t</span></span></span></span></span></div><div class="t m0 x2e hc y55 ff1 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 x2f h10 y56 ff5 fs1 fc0 sc0 ls8 ws0">++</div><div class="t m0 x30 h12 y54 ffc fs1 fc0 sc0 ls9 ws0">ii<span class="_ _d"></span><span class="lsa">~f<span class="_ _e"></span><span class="ff5 lsb">(,<span class="_ _4"></span><span class="lsc">,)<span class="_ _f"> </span><span class="lsd">co<span class="ls0">s<span class="_ _10"></span><span class="ffb lse">xyt<span class="_ _11"> </span><span class="ls0">a</span></span></span></span></span></span></span></div><div class="t m0 x24 h13 y57 ff5 fs7 fc0 sc0 ls0 ws0">1<span class="_ _12"></span>1</div><div class="t m0 x31 h13 y58 ffb fs7 fc0 sc0 lsd ws0">mj</div><div class="t m0 x1 h13 y57 ffb fs7 fc0 sc0 ls0 ws0">j</div><div class="t m0 x32 h13 y59 ffb fs7 fc0 sc0 ls0 ws0">J</div><div class="t m0 x33 h13 y57 ffb fs7 fc0 sc0 ls0 ws0">m</div><div class="t m0 x34 h13 y59 ffb fs7 fc0 sc0 ls0 ws0">M</div><div class="t m0 x35 h13 y58 ffb fs7 fc0 sc0 lsd ws0">mj<span class="_ _13"> </span><span class="lsf">jm<span class="_ _14"></span><span class="ls10">jj<span class="_ _15"></span><span class="lsd">mj<span class="_ _16"> </span>mj</span></span></span></div><div class="t m0 x36 h10 y5a ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x0 h12 y5b ffc fs1 fc0 sc0 ls0 ws0">h</div><div class="t m0 x32 h13 y5c ff5 fs7 fc0 sc0 ls0 ws0">=<span class="_ _17"></span>=</div><div class="t m0 x37 h14 y5d ffd fs8 fc0 sc0 ls0 ws0">/<span class="_ _18"></span>/</div></div><div class="t m0 x2b h4 y5e ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">1</span>）</div><div class="t m0 x1 h4 y5f ff3 fs1 fc0 sc0 ls0 ws0">式<span class="_ _2"></span>中<span class="_ _4"></span>：</div><div class="t m0 x38 h10 y60 ffb fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x39 h15 y61 ffb fs2 fc0 sc0 ls11 ws0">mj</div><div class="t m0 x3a h4 y62 ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _2"></span>第</div><div class="t m0 x30 h10 y63 ffb fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x3b h4 y62 ff3 fs1 fc0 sc0 ls0 ws0">个<span class="_ _2"></span>频<span class="_ _4"></span>率<span class="_ _4"></span>，<span class="_ _2"></span>第</div><div class="t m0 x3c h10 y63 ffb fs1 fc0 sc0 ls0 ws0">j</div><div class="t m0 x8 h4 y62 ff3 fs1 fc0 sc0 ls0 ws0">个<span class="_ _2"></span>方<span class="_ _4"></span>向<span class="_ _4"></span>的<span class="_ _2"></span>入<span class="_ _4"></span>射<span class="_ _2"></span>波<span class="_ _4"></span>的</div><div class="t m0 x1 h4 y64 ff3 fs1 fc0 sc0 ls0 ws0">振<span class="_ _2"></span>幅<span class="_ _2"></span>；</div><div class="t m0 x38 h10 y65 ffe fs1 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x13 h15 y66 ffb fs2 fc0 sc0 ls12 ws0">mj</div><div class="t m0 x3d h4 y67 ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _2"></span><span class="ff1">[</span></div><div class="t m0 x3e h10 y68 ffb fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x3f hc y67 ff1 fs1 fc0 sc0 ls0 ws0">-<span class="_ _2"></span>1<span class="_ _2"></span>~</div><div class="t m0 x40 h10 y68 ffb fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x41 h4 y67 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 x42 h10 y68 ffb fs1 fc0 sc0 ls0 ws0">j</div><div class="t m0 x43 hc y67 ff1 fs1 fc0 sc0 ls0 ws0">-<span class="_ _2"></span>1<span class="_ _2"></span>~</div><div class="t m0 x44 h10 y68 ffb fs1 fc0 sc0 ls0 ws0">j</div><div class="t m0 x28 h4 y67 ff1 fs1 fc0 sc0 ls0 ws0">]<span class="_ _2"></span><span class="ff3">之<span class="_ _2"></span>间<span class="_ _2"></span>随<span class="_ _4"></span>机<span class="_ _2"></span>选<span class="_ _2"></span>取<span class="_ _2"></span>的<span class="_ _4"></span>圆</span></div><div class="t m0 x1 h4 y69 ff3 fs1 fc0 sc0 ls0 ws0">频<span class="_ _2"></span>率<span class="_ _1"></span>；</div><div class="t m0 x45 h10 y6a ffb fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x46 h15 y6b ffb fs2 fc0 sc0 ls13 ws0">mj</div><div class="t m0 x35 h4 y6c ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _2"></span>波<span class="_ _1"></span>数<span class="_ _2"></span>；</div><div class="t m0 x47 h10 y6d ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 x25 h15 y6b ffb fs2 fc0 sc0 ls0 ws0">j</div><div class="t m0 x48 h4 y6c ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _2"></span>波<span class="_ _1"></span>向<span class="_ _2"></span>；</div><div class="t m0 x49 h10 y6d ffb fs1 fc0 sc0 ls0 ws0">M</div><div class="t m0 x4a h4 y6c ff3 fs1 fc0 sc0 ls0 ws0">按<span class="_ _2"></span>等<span class="_ _1"></span>分<span class="_ _2"></span>频<span class="_ _2"></span>率<span class="_ _2"></span>法<span class="_ _2"></span>取</div><div class="t m0 x1 h4 y6e ff1 fs1 fc0 sc0 ls0 ws0">1<span class="_ _1"></span>00<span class="_ _1"></span><span class="ff3">，</span></div><div class="t m0 x4b h10 y6f ffb fs1 fc0 sc0 ls0 ws0">J</div><div class="t m0 x4c h4 y6e ff3 fs1 fc0 sc0 ls0 ws0">取<span class="_ _1"></span><span class="ff1">60<span class="_ _1"></span></span>；</div><div class="t m0 x4d h10 y6f ffb fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 x30 h4 y6e ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 x4e h10 y6f ffb fs1 fc0 sc0 ls0 ws0">y</div><div class="t m0 x4f h4 y6e ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _1"></span>测点<span class="_ _1"></span>的<span class="_ _1"></span>位<span class="_ _1"></span>置坐<span class="_ _1"></span>标<span class="_ _1"></span>；</div><div class="t m0 x3 h10 y6f ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 x50 h4 y6e ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _1"></span>时间<span class="_ _1"></span>；</div><div class="t m0 x1 h10 y70 ffe fs1 fc0 sc0 ls0 ws0">ε</div><div class="t m0 x51 h15 y71 ffb fs2 fc0 sc0 ls14 ws0">mj</div><div class="t m0 x52 h4 y72 ff3 fs1 fc0 sc0 ls0 ws0">是<span class="_ _1"></span>入<span class="_ _2"></span>射<span class="_ _2"></span>波<span class="_ _2"></span>的<span class="_ _2"></span>初<span class="_ _1"></span>始<span class="_ _2"></span>相<span class="_ _2"></span>位<span class="_ _2"></span>，<span class="_ _2"></span>在<span class="_ _1"></span><span class="ff1">[<span class="_ _2"></span>0<span class="_ _2"></span></span>，<span class="_ _2"></span><span class="ff1">2<span class="_ _2"></span></span>π<span class="_ _1"></span><span class="ff1">]<span class="_ _2"></span></span>之<span class="_ _2"></span>间<span class="_ _2"></span>随<span class="_ _2"></span>机<span class="_ _1"></span>选</div><div class="t m0 x1 h4 y73 ff3 fs1 fc0 sc0 ls0 ws0">取。入射波的振幅</div><div class="t m0 x17 h10 y74 ffe fs1 fc0 sc0 ls0 ws0">α</div><div class="t m0 x47 h15 y75 ffb fs2 fc0 sc0 ls0 ws0">mj</div><div class="t m0 x53 h4 y76 ff3 fs1 fc0 sc0 ls0 ws0">可由下式计算：</div><div class="c x54 y77 w3 h16"><div class="t m0 x55 h10 y78 ff5 fs1 fc0 sc0 ls15 ws0">2(<span class="_ _19"> </span><span class="ls16">,)<span class="_ _1a"></span><span class="ffb ls17">aS</span></span></div><div class="t m0 x56 h17 y79 fff fs7 fc0 sc0 ls18 ws0">mj<span class="_ _1b"> </span>mj<span class="_ _1c"> </span><span class="ls0">j</span></div><div class="t m0 x57 h10 y7a ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x34 h18 y7b ffc fs1 fc0 sc0 ls19 ws0">~i<span class="_ _1d"> </span><span class="ls1a">~i<span class="_ _1e"></span><span class="ff10 ls1b">DD</span></span></div></div><div class="t m0 x58 h4 y7c ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span><span class="ff3">（</span>2<span class="ff3">）</span></div><div class="t m0 x1 h4 y7d ff3 fs1 fc0 sc0 ls0 ws0">式中：</div><div class="t m0 x59 h10 y7e ffb fs1 fc0 sc0 ls0 ws0">S</div><div class="t m0 x2d hc y7d ff1 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 x39 h10 y7e ffe fs1 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x3a h15 y7f ffb fs2 fc0 sc0 ls0 ws0">mj</div><div class="t m0 x5a h4 y80 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 x3e h10 y81 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 x5b h15 y7f ffb fs2 fc0 sc0 ls0 ws0">j</div><div class="t m0 x5c h4 y80 ff1 fs1 fc0 sc0 ls0 ws0">)<span class="ff3">是方向谱，圆频率</span></div><div class="t m0 x5d h10 y81 ffe fs1 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x5e h15 y7f ffb fs2 fc0 sc0 ls0 ws0">mj</div><div class="t m0 x5f h4 y80 ff3 fs1 fc0 sc0 ls0 ws0">取为：</div><div class="c x60 y82 w4 h19"><div class="t m0 x61 h10 y83 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x61 h10 y84 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x4b h10 y85 ff5 fs1 fc0 sc0 ls1c ws0">(1<span class="_ _1d"> </span><span class="ls0">)</span></div><div class="t m0 x62 h10 y86 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x63 h10 y85 ffb fs1 fc0 sc0 ls0 ws0">j</div><div class="t m0 x64 h10 y83 ffb fs1 fc0 sc0 ls0 ws0">J</div><div class="t m0 x61 h10 y87 ffb fs1 fc0 sc0 ls0 ws0">M</div><div class="t m0 x33 h1a y88 ff11 fs7 fc0 sc0 ls0 ws0">1</div><div class="t m0 x65 h1a y89 ff11 fs7 fc0 sc0 ls0 ws0">ma<span class="ls1d">xm<span class="_ _1f"></span><span class="ls0">in</span></span></div><div class="t m0 x66 h17 y8a fff fs7 fc0 sc0 ls18 ws0">mj<span class="_ _20"> </span>mj</div><div class="t m0 x67 h17 y8b fff fs7 fc0 sc0 ls1e ws0">mm</div><div class="t m0 x68 h1b y8c ff11 fs1 fc0 sc0 ls1f ws0">--</div><div class="t m0 x61 h1b y8d ff11 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 x69 h10 y8e ff5 fs1 fc0 sc0 ls20 ws0">=+<span class="_ _1f"></span><span class="ls0">+</span></div><div class="t m0 x6a h10 y8f ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x6b h10 y90 ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x6c h10 y91 ff5 fs1 fc0 sc0 ls0 ws0">+</div><div class="t m0 x56 h12 y92 ffc fs1 fc0 sc0 ls21 ws0">~~<span class="_ _21"> </span><span class="ls22">~d</span></div><div class="t m0 x4f h12 y93 ffc fs1 fc0 sc0 ls0 ws0">~</div><div class="t m0 x66 h12 y94 ffc fs1 fc0 sc0 ls0 ws0">~</div><div class="t m0 x67 h12 y95 ffc fs1 fc0 sc0 ls23 ws0">~~</div><div class="t m0 x56 h12 y96 ffc fs1 fc0 sc0 ls0 ws0">~</div><div class="t m0 x6d h12 y97 ffc fs1 fc0 sc0 ls24 ws0">~~</div><div class="t m0 x32 h18 y98 ff10 fs1 fc0 sc0 ls0 ws0">D</div><div class="t m0 x3b h18 y99 ff10 fs1 fc0 sc0 ls0 ws0">D</div><div class="t m0 x56 h18 y9a ff10 fs1 fc0 sc0 ls0 ws0">D</div><div class="t m0 x6e h1a y9b ff11 fs7 fc0 sc0 ls0 ws0">-</div><div class="t m0 x0 h1c y9c ffd fs1 fc0 sc0 ls0 ws0">Z</div><div class="t m0 x0 h1c y9d ffd fs1 fc0 sc0 ls0 ws0">[</div><div class="t m0 x0 h1c y9e ffd fs1 fc0 sc0 ls0 ws0">\</div><div class="t m0 x0 h1c y9f ffd fs1 fc0 sc0 ls0 ws0">]</div><div class="t m0 x0 h1c ya0 ffd fs1 fc0 sc0 ls0 ws0">]</div><div class="t m0 x0 h1c ya1 ffd fs1 fc0 sc0 ls0 ws0">]</div><div class="t m0 x0 h1c ya2 ffd fs1 fc0 sc0 ls0 ws0">]</div><div class="t m0 x0 h1c ya3 ffd fs1 fc0 sc0 ls0 ws0">]</div><div class="t m0 x0 h1c ya4 ffd fs1 fc0 sc0 ls0 ws0">]</div></div><div class="t m0 x6f h4 ya5 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _7"> </span> <span class="_ _7"> </span><span class="ff3">（</span>3<span class="ff3">）</span></div><div class="t m0 x1 h4 ya6 ff3 fs1 fc0 sc0 ls0 ws0">波向</div><div class="t m0 x70 h10 ya7 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 x71 h15 ya8 ffb fs2 fc0 sc0 ls0 ws0">j</div><div class="t m0 x4b h4 ya9 ff3 fs1 fc0 sc0 ls0 ws0">取：</div><div class="c x72 yaa w5 h1d"><div class="t m0 x73 h10 yab ff5 fs1 fc0 sc0 ls0 ws0">(<span class="_ _22"> </span>0.5)<span class="_ _23"></span><span class="ffb">j</span></div><div class="t m0 x74 h10 yac ffb fs1 fc0 sc0 ls0 ws0">J</div><div class="t m0 x75 h1a yad ff11 fs7 fc0 sc0 ls0 ws0">min</div><div class="t m0 x36 h1a yae ff11 fs7 fc0 sc0 ls0 ws0">ma<span class="ls25">xm<span class="_ _24"></span><span class="ls0">in</span></span></div><div class="t m0 x76 h17 yad fff fs7 fc0 sc0 ls0 ws0">j</div><div class="t m0 x1 h1b yaf ff11 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 x77 h1b yb0 ff11 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 x6b h10 yb1 ff5 fs1 fc0 sc0 ls26 ws0">=+</div><div class="t m0 x69 h10 yb2 ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x78 h12 yb3 ffc fs1 fc0 sc0 ls27 ws0">ii<span class="_ _25"> </span><span class="ls0">i</span></div><div class="t m0 x66 h12 yb4 ffc fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x55 h12 yb5 ffc fs1 fc0 sc0 ls23 ws0">ii</div><div class="t m0 x79 h18 yb3 ff10 fs1 fc0 sc0 ls0 ws0">D</div><div class="t m0 x78 h18 yb4 ff10 fs1 fc0 sc0 ls0 ws0">D</div><div class="t m1 x7a h1e yb6 ff12 fs9 fc0 sc0 ls0 ws0">*</div></div><div class="t m0 x4a hc yb7 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> </div><div class="t m0 x7b h1f yb8 ff1 fsa fc0 sc0 ls0 ws0"> </div><div class="t m0 x2b h4 yb7 ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">4</span>）</div><div class="t m0 x1 h4 yb9 ff3 fs1 fc0 sc0 ls0 ws0">式<span class="_ _1"></span>中<span class="_ _1"></span>：</div><div class="t m0 x4c h10 yba ffe fs1 fc0 sc0 ls0 ws0">δ</div><div class="t m0 x46 h15 ybb ffb fs2 fc0 sc0 ls28 ws0">mj</div><div class="t m0 x35 h4 ybc ff3 fs1 fc0 sc0 ls0 ws0">为<span class="_ _1"></span>在<span class="_ _1"></span><span class="ff1">[<span class="_ _1"></span>0<span class="_ _1"></span>,<span class="_ _1"></span>1<span class="_ _2"></span>]<span class="_ _1"></span></span>内<span class="_ _1"></span>均<span class="_ _1"></span>匀<span class="_ _1"></span>选<span class="_ _1"></span>取<span class="_ _1"></span>的<span class="_ _2"></span>随<span class="_ _1"></span>机<span class="_ _1"></span>数<span class="_ _1"></span>，<span class="_ _1"></span>保<span class="_ _1"></span>证<span class="_ _2"></span>模</div><div class="t m0 x1 h4 ybd ff3 fs1 fc0 sc0 ls0 ws0">拟<span class="_ _2"></span>所<span class="_ _2"></span>得<span class="_ _2"></span>的<span class="_ _2"></span>波<span class="_ _2"></span>浪<span class="_ _2"></span>序<span class="_ _2"></span>列<span class="_ _2"></span>不<span class="_ _2"></span>会<span class="_ _2"></span>以</div><div class="t m0 x7c h20 ybe ffb fs1 fc0 sc0 ls0 ws0">2<span class="_ _2"></span><span class="ff9">π<span class="_ _2"></span></span>J</div><div class="t m0 x7d h4 ybd ff1 fs1 fc0 sc0 ls0 ws0">/<span class="_ _2"></span><span class="ff3">Δ</span></div><div class="t m0 x7e h10 ybe ffe fs1 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x7f h4 ybd ff3 fs1 fc0 sc0 ls0 ws0">的<span class="_ _2"></span>周<span class="_ _2"></span>期<span class="_ _2"></span>重<span class="_ _2"></span>复<span class="_ _2"></span>出</div><div class="t m0 x1 h4 ybf ff3 fs1 fc0 sc0 ls0 ws0">现<span class="_ _1"></span>，<span class="_ _1"></span>而<span class="_ _1"></span>是<span class="_ _1"></span>在<span class="_ _2"></span>同<span class="_ _1"></span>一<span class="_ _1"></span>频<span class="_ _1"></span>段<span class="_ _1"></span>内<span class="_ _2"></span>每<span class="_ _1"></span>一<span class="_ _1"></span>个<span class="_ _1"></span>方<span class="_ _1"></span>向<span class="_ _2"></span>的<span class="_ _1"></span>组<span class="_ _1"></span>成<span class="_ _1"></span>波<span class="_ _1"></span>的<span class="_ _2"></span>代</div><div class="t m0 x1 h4 yc0 ff3 fs1 fc0 sc0 ls0 ws0">表频率都不同。</div><div class="t m0 x6 h4 yc1 ff3 fs1 fc0 sc0 ls0 ws0">方<span class="_ _1"></span>向<span class="_ _1"></span>谱<span class="_ _1"></span>的<span class="_ _1"></span>靶<span class="_ _1"></span>谱<span class="_ _1"></span>可<span class="_ _1"></span>以<span class="_ _1"></span>采<span class="_ _1"></span>用<span class="_ _1"></span>频<span class="_ _1"></span>谱<span class="_ _1"></span>与<span class="_ _1"></span>方<span class="_ _1"></span>向<span class="_ _1"></span>分<span class="_ _1"></span>布<span class="_ _1"></span>函<span class="_ _1"></span>数</div><div class="t m0 x1 h4 yc2 ff3 fs1 fc0 sc0 ls0 ws0">相乘的形式：</div><div class="t m0 x80 h10 yc3 ffb fs1 fc0 sc0 ls0 ws0">S</div><div class="t m0 x81 h4 yc4 ff3 fs1 fc0 sc0 ls0 ws0">（</div><div class="t m0 x30 h10 yc3 ffb fs1 fc0 sc0 ls0 ws0">f</div><div class="t m0 x16 hc yc4 ff1 fs1 fc0 sc0 ls0 ws0">, </div><div class="t m0 x3b h10 yc3 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 x64 h4 yc4 ff3 fs1 fc0 sc0 ls0 ws0">）<span class="ff1">=</span></div><div class="t m0 x82 h10 yc3 ffb fs1 fc0 sc0 ls0 ws0">S</div><div class="t m0 x83 h4 yc4 ff3 fs1 fc0 sc0 ls0 ws0">（</div><div class="t m0 x84 h10 yc3 ffb fs1 fc0 sc0 ls0 ws0">f</div><div class="t m0 x85 h4 yc4 ff3 fs1 fc0 sc0 ls0 ws0">）</div><div class="t m0 x86 h10 yc3 ffb fs1 fc0 sc0 ls0 ws0">G</div><div class="t m0 x28 h4 yc4 ff3 fs1 fc0 sc0 ls0 ws0">（</div><div class="t m0 x87 h10 yc3 ffb fs1 fc0 sc0 ls0 ws0">f</div><div class="t m0 x88 hc yc4 ff1 fs1 fc0 sc0 ls0 ws0">, </div><div class="t m0 x89 h10 yc3 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 x58 h4 yc4 ff3 fs1 fc0 sc0 ls0 ws0">）<span class="ff1"> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span></span>（<span class="ff1">5</span>）</div><div class="c x5b yc5 w6 h21"><div class="t m0 x8a h10 yc6 ff5 fs1 fc0 sc0 ls29 ws0">(,<span class="_ _26"> </span><span class="ls2a">)d<span class="_ _27"> </span><span class="ls0">2<span class="_ _28"></span><span class="ffb ls2b">Gf</span></span></span></div><div class="t m0 x8b h10 yc7 ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x8c h12 yc6 ffc fs1 fc0 sc0 ls2c ws0">ii</div><div class="t m0 x8d h13 yc8 ff5 fs7 fc0 sc0 ls0 ws0">-</div><div class="t m0 x56 h22 yc9 ff10 fs7 fc0 sc0 ls0 ws0">r</div><div class="t m0 x8e h22 yca ff10 fs7 fc0 sc0 ls0 ws0">r</div><div class="t m0 x8f h14 ycb ffd fs8 fc0 sc0 ls0 ws0">y</div></div><div class="t m0 x8 h4 ycc ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span><span class="ff3">（</span>6<span class="ff3">）</span></div><div class="t m0 x6 h4 ycd ff3 fs1 fc0 sc0 ls0 ws0">在<span class="_ _1"></span>本<span class="_ _1"></span>文<span class="_ _2"></span>的<span class="_ _1"></span>数<span class="_ _2"></span>值<span class="_ _1"></span>试<span class="_ _1"></span>验<span class="_ _2"></span>中<span class="_ _1"></span>，<span class="_ _2"></span>频<span class="_ _1"></span>谱</div><div class="t m0 x7e h10 yce ffb fs1 fc0 sc0 ls0 ws0">S</div><div class="t m0 x58 h4 ycd ff3 fs1 fc0 sc0 ls0 ws0">（</div><div class="t m0 x5f h10 yce ffb fs1 fc0 sc0 ls0 ws0">f</div><div class="t m0 x90 h4 ycd ff3 fs1 fc0 sc0 ls0 ws0">）<span class="_ _1"></span>采<span class="_ _1"></span>用<span class="_ _2"></span>改<span class="_ _1"></span>进</div><div class="t m0 x18 h4 y45 ff3 fs1 fc0 sc0 ls0 ws0">的<span class="ff1">JONSW<span class="_ _1"></span>AP</span>谱</div><div class="t m0 x91 h5 ycf ff1 fs2 fc0 sc0 ls0 ws0">[8]</div><div class="t m0 x92 h4 y45 ff3 fs1 fc0 sc0 ls0 ws0">，而方向分布<span class="_ _1"></span>函数</div><div class="t m0 x93 h10 yd0 ffb fs1 fc0 sc0 ls0 ws0">G</div><div class="t m0 x94 h4 y45 ff3 fs1 fc0 sc0 ls0 ws0">（<span class="_ _29"></span><span class="ff1"> </span></div><div class="t m0 x95 h10 yd0 ffb fs1 fc0 sc0 ls0 ws0">f</div><div class="t m0 x96 hc y45 ff1 fs1 fc0 sc0 ls0 ws0">, </div><div class="t m0 x97 h10 yd0 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 x98 h4 y45 ff3 fs1 fc0 sc0 ls0 ws0">）<span class="_ _2a"></span>采用光</div><div class="t m0 x18 h4 y46 ff3 fs1 fc0 sc0 ls0 ws0">易型分布，采用柳淑学等给出的表达式</div><div class="t m0 x96 h5 yd1 ff1 fs2 fc0 sc0 ls0 ws0">[9]</div><div class="t m0 x97 h4 yd2 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="ff3">。</span></div><div class="t m0 x18 hf yd3 ffa fs1 fc0 sc0 ls0 ws0">2 <span class="_ _7"> </span><span class="ff6">基于小波变换方向谱的估计原理</span></div><div class="t m0 x1d h4 yd4 ff3 fs1 fc0 sc0 ls0 ws0">在信<span class="_ _1"></span>号<span class="_ _1"></span>的<span class="_ _1"></span>时<span class="ff1">-<span class="_ _1"></span></span>频<span class="_ _1"></span>分析<span class="_ _1"></span>中<span class="_ _1"></span>，<span class="ff1">H<span class="_ _1"></span>e<span class="_ _1"></span>is<span class="_ _1"></span>e<span class="_ _1"></span>nb<span class="_ _1"></span>e<span class="_ _1"></span>rg<span class="_ _1"></span></span>测<span class="_ _1"></span>不<span class="_ _1"></span>准原</div><div class="t m0 x18 h4 yd5 ff3 fs1 fc0 sc0 ls0 ws0">则<span class="_ _1"></span>是<span class="_ _1"></span>一<span class="_ _1"></span>个<span class="_ _1"></span>无<span class="_ _2"></span>法<span class="_ _1"></span>回<span class="_ _1"></span>避<span class="_ _1"></span>的<span class="_ _1"></span>问<span class="_ _2"></span>题<span class="_ _1"></span>，<span class="_ _1"></span>小<span class="_ _1"></span>波<span class="_ _1"></span>变<span class="_ _2"></span>换<span class="_ _1"></span>可<span class="_ _1"></span>以<span class="_ _1"></span>同<span class="_ _1"></span>时<span class="_ _2"></span>兼</div><div class="t m0 x18 h4 yd6 ff3 fs1 fc0 sc0 ls0 ws0">顾<span class="_ _1"></span>时<span class="_ _1"></span>间<span class="_ _1"></span>和<span class="_ _1"></span>频<span class="_ _2"></span>率<span class="_ _1"></span>上<span class="_ _1"></span>的<span class="_ _1"></span>分<span class="_ _1"></span>辨<span class="_ _2"></span>率<span class="_ _1"></span>，<span class="_ _1"></span>是<span class="_ _1"></span>有<span class="_ _1"></span>力<span class="_ _2"></span>的<span class="_ _1"></span>非<span class="_ _1"></span>平<span class="_ _1"></span>稳<span class="_ _1"></span>信<span class="_ _2"></span>号</div><div class="t m0 x18 h4 yd7 ff3 fs1 fc0 sc0 ls0 ws0">分析<span class="_ _1"></span>工<span class="_ _1"></span>具</div><div class="t m0 x99 h5 yd8 ff1 fs2 fc0 sc0 ls0 ws0">[10<span class="_ _1"></span>]</div><div class="t m0 x9a h4 yd9 ff3 fs1 fc0 sc0 ls0 ws0">。对<span class="_ _1"></span>一<span class="_ _1"></span>时间<span class="_ _1"></span>序<span class="_ _1"></span>列</div><div class="t m0 x9b h10 yda ffe fs1 fc0 sc0 ls0 ws0">η</div><div class="t m0 x9c hc yd9 ff1 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 x9d h10 yda ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 x9e h4 yd9 ff1 fs1 fc0 sc0 ls0 ws0">)<span class="ff3">，<span class="_ _1"></span>小<span class="_ _1"></span>波变<span class="_ _1"></span>换<span class="_ _1"></span>可以<span class="_ _1"></span>写</span></div><div class="t m0 x18 h4 ydb ff3 fs1 fc0 sc0 ls0 ws0">为：</div><div class="c x9f ydc w7 h23"><div class="t m0 x79 h1b ydd ff11 fs1 fc0 sc0 ls0 ws0">[<span class="_ _2b"></span><span class="ff5 ls2d">(,<span class="_ _4"></span><span class="ls2e">)(<span class="_ _2c"></span><span class="ls0">)]<span class="_ _7"> </span><span class="ls29">()<span class="_ _29"></span><span class="ls0">d<span class="_ _2d"></span><span class="ffb ls2f">Wa<span class="_ _2e"></span><span class="ls30">ba<span class="_ _12"></span><span class="ls2f">at<span class="_ _7"> </span><span class="ls31">bt<span class="_ _2f"></span><span class="ls0">t</span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x34 h13 yde ffb fs7 fc0 sc0 ls0 ws0">R</div><div class="t m0 xa0 h1a ydf ff11 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m0 xa1 h24 ydd ff13 fs1 fc0 sc0 ls32 ws0">;;</div><div class="t m0 xa2 h1b ye0 ff11 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 x67 h10 ye1 ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 xa3 h12 ye2 ffc fs1 fc0 sc0 ls33 ws0">}h</div><div class="t m0 x62 h14 ye3 ffd fs8 fc0 sc0 ls0 ws0">y</div></div><div class="t m0 xa4 h4 ye4 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _7"> </span> <span class="_ _7"> </span><span class="ff3">（</span>7<span class="ff3">）</span></div><div class="t m0 x18 h4 ye5 ff3 fs1 fc0 sc0 ls0 ws0">式<span class="_ _4"></span>中<span class="_ _4"></span>：</div><div class="t m0 xa5 h10 ye6 ffb fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 xa6 h4 ye5 ff3 fs1 fc0 sc0 ls0 ws0">为<span class="_ _4"></span>母<span class="_ _4"></span>小<span class="_ _2"></span>波<span class="_ _4"></span>伸<span class="_ _4"></span>缩<span class="_ _4"></span>因<span class="_ _4"></span>子<span class="_ _4"></span>；</div><div class="t m0 xa7 h10 ye6 ffb fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x5 h4 ye5 ff3 fs1 fc0 sc0 ls0 ws0">为<span class="_ _4"></span>母<span class="_ _4"></span>小<span class="_ _2"></span>波<span class="_ _4"></span>平<span class="_ _4"></span>移<span class="_ _4"></span>因</div><div class="t m0 x18 h4 ye7 ff3 fs1 fc0 sc0 ls0 ws0">子；</div><div class="t m0 xa8 h10 ye8 ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 xa9 h4 ye7 ff3 fs1 fc0 sc0 ls0 ws0">为积分空间。</div><div class="t m0 x1d h4 ye9 ff3 fs1 fc0 sc0 ls0 ws0">在<span class="_ _4"></span>实<span class="_ _4"></span>际<span class="_ _4"></span>应<span class="_ _4"></span>用<span class="_ _4"></span>中<span class="_ _4"></span>，<span class="_ _4"></span>小<span class="_ _4"></span>波<span class="_ _4"></span>母<span class="_ _4"></span>函<span class="_ _4"></span>数<span class="_ _4"></span>的<span class="_ _4"></span>选<span class="_ _4"></span>取<span class="_ _4"></span>至<span class="_ _4"></span>关<span class="_ _4"></span>重</div><div class="t m0 x18 h4 yea ff3 fs1 fc0 sc0 ls0 ws0">要<span class="_ _1"></span>。<span class="_ _2"></span>在<span class="_ _2"></span>海<span class="_ _2"></span>浪<span class="_ _1"></span>分<span class="_ _2"></span>析<span class="_ _2"></span>中<span class="_ _2"></span>，<span class="_ _1"></span><span class="ff1">M<span class="_ _2"></span>o<span class="_ _2"></span>r<span class="_ _2"></span>l<span class="_ _1"></span>e<span class="_ _2"></span>t<span class="_ _2"></span></span>小<span class="_ _2"></span>波<span class="_ _1"></span>是<span class="_ _2"></span>最<span class="_ _2"></span>被<span class="_ _2"></span>广<span class="_ _2"></span>泛<span class="_ _1"></span>应<span class="_ _2"></span>用</div><div class="t m0 x18 h4 yeb ff3 fs1 fc0 sc0 ls0 ws0">的</div><div class="t m0 xaa h5 yec ff1 fs2 fc0 sc0 ls0 ws0">[11<span class="_ _1"></span>]</div><div class="t m0 xa8 h4 yed ff3 fs1 fc0 sc0 ls0 ws0">，其表达式为：</div><div class="t m0 xab h10 yee ffe fs1 fc0 sc0 ls0 ws0">ψ</div><div class="t m0 xac h5 yef ff1 fs2 fc0 sc0 ls0 ws0">0</div><div class="t m0 xad hc yf0 ff1 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 xae h10 yf1 ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 xaf h4 yf0 ff1 fs1 fc0 sc0 ls0 ws0">)=<span class="ff3">π</span></div><div class="t m0 xb0 h5 yf2 ff1 fs2 fc0 sc0 ls0 ws0">-1/4</div><div class="t m0 xb1 hc yf0 ff1 fs1 fc0 sc0 ls0 ws0">exp(-</div><div class="t m0 xb2 h10 yf1 ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 xb3 h5 yf2 ff1 fs2 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb4 hc yf0 ff1 fs1 fc0 sc0 ls0 ws0">/2)exp(i</div><div class="t m0 xb5 h10 yf1 ffe fs1 fc0 sc0 ls0 ws0">ω</div><div class="t m0 xb6 h5 yef ff1 fs2 fc0 sc0 ls0 ws0">0</div><div class="t m0 x11 h10 yf3 ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 x12 h4 yf4 ff1 fs1 fc0 sc0 ls0 ws0">) <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span><span class="ff3">（</span>8<span class="ff3">）</span></div><div class="t m0 x18 h4 yf5 ff3 fs1 fc0 sc0 ls0 ws0">式中：</div><div class="t m0 xb7 h10 yf6 ffe fs1 fc0 sc0 ls0 ws0">ω</div><div class="t m0 xb8 h5 yf7 ff1 fs2 fc0 sc0 ls0 ws0">0</div><div class="t m0 xb9 h4 yf8 ff3 fs1 fc0 sc0 ls0 ws0">是中心圆频率。</div><div class="t m0 x1d h4 yf9 ff3 fs1 fc0 sc0 ls0 ws0">将<span class="_ _1"></span>一<span class="_ _2"></span>组<span class="_ _1"></span>时<span class="_ _2"></span>间<span class="_ _2"></span>序<span class="_ _1"></span>列</div><div class="t m0 xba h10 yfa ffe fs1 fc0 sc0 ls0 ws0">η</div><div class="t m0 xbb h15 yfb ffb fs2 fc0 sc0 ls0 ws0">i</div><div class="t m0 xbc hc yfc ff1 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 xbd h10 yfd ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 xbe hc yfc ff1 fs1 fc0 sc0 ls0 ws0">)<span class="_ _1"></span>(</div><div class="t m0 xbf h10 yfd ffb fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc0 h4 yfc ff1 fs1 fc0 sc0 ls0 ws0">=<span class="_ _1"></span>1<span class="_ _2"></span>,<span class="_ _1"></span><span class="ff3">…<span class="_ _2"></span></span>,</div><div class="t m0 xb5 h10 yfd ffb fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc1 h4 yfc ff1 fs1 fc0 sc0 ls0 ws0">)<span class="_ _1"></span><span class="ff3">作<span class="_ _2"></span>为<span class="_ _1"></span>分<span class="_ _2"></span>析<span class="_ _2"></span>的<span class="_ _1"></span>数</span></div><div class="t m0 x18 h4 yfe ff3 fs1 fc0 sc0 ls0 ws0">据<span class="_ _2"></span>，<span class="_ _4"></span>下<span class="_ _2"></span>标</div><div class="t m0 xc2 h10 yff ffb fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc3 h4 yfe ff3 fs1 fc0 sc0 ls0 ws0">代<span class="_ _2"></span>表<span class="_ _4"></span>测<span class="_ _2"></span>波<span class="_ _4"></span>点<span class="_ _2"></span>编<span class="_ _4"></span>号<span class="_ _2"></span>，<span class="_ _2"></span>对<span class="_ _4"></span>应<span class="_ _2"></span>的<span class="_ _4"></span>位<span class="_ _2"></span>置<span class="_ _4"></span>坐<span class="_ _2"></span>标<span class="_ _4"></span>为</div><div class="t m0 x18 hc y100 ff1 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 xc4 h10 y101 ffb fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 xc5 h15 y102 ffb fs2 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc6 h4 y103 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 xc7 h10 y104 ffb fs1 fc0 sc0 ls0 ws0">y</div><div class="t m0 xc8 h15 y102 ffb fs2 fc0 sc0 ls0 ws0">i</div><div class="t m0 x9f h4 y103 ff1 fs1 fc0 sc0 ls0 ws0">)<span class="ff3">。分析步骤如下：</span></div><div class="t m0 x1d h4 y105 ff1 fs1 fc0 sc0 ls0 ws0">1<span class="_ _2"></span><span class="ff3">）<span class="_ _2"></span>求<span class="_ _2"></span>第</span></div><div class="t m0 xc9 h10 y106 ffb fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xca h4 y105 ff3 fs1 fc0 sc0 ls0 ws0">个<span class="_ _2"></span>时<span class="_ _2"></span>间<span class="_ _2"></span>序<span class="_ _2"></span>列</div><div class="t m0 xbf h10 y106 ffe fs1 fc0 sc0 ls0 ws0">η</div><div class="t m0 xcb h15 y107 ffb fs2 fc0 sc0 ls0 ws0">i</div><div class="t m0 xcc hc y108 ff1 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 x9c h10 y109 ffb fs1 fc0 sc0 ls0 ws0">t</div><div class="t m0 x9d h4 y108 ff1 fs1 fc0 sc0 ls0 ws0">)<span class="_ _2"></span><span class="ff3">的<span class="_ _2"></span>小<span class="_ _2"></span>波<span class="_ _2"></span>变<span class="_ _2"></span>换<span class="_ _2"></span>，<span class="_ _2"></span>可<span class="_ _4"></span>以</span></div><div class="t m0 x18 h4 y10a ff3 fs1 fc0 sc0 ls0 ws0">得<span class="_ _1"></span>到在</div><div class="t m0 xcd h10 y10b ffb fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 xa6 h4 y10a ff3 fs1 fc0 sc0 ls0 ws0">个<span class="_ _1"></span>离散<span class="_ _1"></span>频<span class="_ _1"></span>率<span class="_ _1"></span>上<span class="_ _1"></span>的<span class="_ _1"></span>小<span class="_ _1"></span>波变<span class="_ _1"></span>换<span class="_ _1"></span>系<span class="_ _1"></span>数</div><div class="t m0 xa4 h10 y10b ffb fs1 fc0 sc0 ls0 ws0">W</div><div class="t m0 xce h15 y10c ffb fs2 fc0 sc0 ls34 ws0"> i</div><div class="t m0 xce h15 y10d ffb fs2 fc0 sc0 ls35 ws0">qp</div><div class="t m0 xcf h4 y10e ff3 fs1 fc0 sc0 ls0 ws0">，<span class="_ _1"></span>其中</div><div class="t m0 x18 h10 y10f ffb fs1 fc0 sc0 ls0 ws0">q</div><div class="t m0 xd0 h4 y110 ff1 fs1 fc0 sc0 ls0 ws0">=1,<span class="ff3">…</span>,</div><div class="t m0 xcd h10 y10f ffb fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 xa6 h4 y110 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 xd1 h10 y10f ffb fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xd2 h4 y110 ff1 fs1 fc0 sc0 ls0 ws0">=1,<span class="ff3">…</span>,</div><div class="t m0 xd3 h10 y10f ffb fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xd4 h4 y110 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 xd5 h10 y10f ffb fs1 fc0 sc0 ls0 ws0">p</div><div class="t m0 xd6 h4 y110 ff3 fs1 fc0 sc0 ls0 ws0">表示离散的<span class="_ _1"></span>时间点，根据采</div><div class="t m0 x18 h4 y111 ff3 fs1 fc0 sc0 ls0 ws0">样时间间<span class="_ _1"></span>隔决定。<span class="_ _1"></span>由于<span class="ff1">Mor<span class="_ _1"></span>let</span>小波<span class="_ _1"></span>是解析小<span class="_ _1"></span>波，进</div><div class="t m0 x18 h4 y112 ff3 fs1 fc0 sc0 ls0 ws0">而求得</div><div class="t m0 xb7 h10 y113 ffb fs1 fc0 sc0 ls0 ws0">W</div><div class="t m0 xa6 h15 y114 ffb fs2 fc0 sc0 ls0 ws0"> i</div><div class="t m0 xd7 h15 y115 ffb fs2 fc0 sc0 ls0 ws0">qp</div><div class="t m0 xd8 h4 y116 ff3 fs1 fc0 sc0 ls0 ws0">的幅值<span class="ff1">|</span></div><div class="t m0 xd9 h10 y117 ffb fs1 fc0 sc0 ls0 ws0">W</div><div class="t m0 x1f h15 y114 ffb fs2 fc0 sc0 ls0 ws0"> i</div><div class="t m0 xda h15 y115 ffb fs2 fc0 sc0 ls0 ws0">qp</div><div class="t m0 xb1 h4 y116 ff1 fs1 fc0 sc0 ls0 ws0">|<span class="ff3">和相位</span></div><div class="t m0 x9b h10 y117 ffe fs1 fc0 sc0 ls0 ws0">φ</div><div class="t m0 x9c h15 y118 ffb fs2 fc0 sc0 ls0 ws0">i</div><div class="t m0 xdb h4 y116 ff3 fs1 fc0 sc0 ls0 ws0">。</div><div class="t m0 x1d h4 y119 ff1 fs1 fc0 sc0 ls0 ws0">2<span class="ff3">）确定每两<span class="_ _1"></span>个时间序列之间的<span class="_ _1"></span>相位差与其测</span></div><div class="t m0 x18 h4 y11a ff3 fs1 fc0 sc0 ls0 ws0">点位置之间的关系：</div><div class="t m0 x1e h10 y11b ffe fs1 fc0 sc0 ls0 ws0">φ</div><div class="t m0 xd3 h15 y11c ffb fs2 fc0 sc0 ls0 ws0">ij</div><div class="t m0 xdc h5 y11d ff1 fs2 fc0 sc0 ls0 ws0">=</div><div class="t m0 xda h10 y11e ffb fs1 fc0 sc0 ls0 ws0">kr</div><div class="t m0 xd5 h15 y11c ffb fs2 fc0 sc0 ls0 ws0">ij</div><div class="t m0 xba hc y11f ff1 fs1 fc0 sc0 ls0 ws0">cos(</div><div class="t m0 xb2 h10 y120 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 xbf hc y11f ff1 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 xcb h10 y120 ffe fs1 fc0 sc0 ls0 ws0">α</div><div class="t m0 xdd h15 y11c ffb fs2 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x9d h4 y11f ff1 fs1 fc0 sc0 ls0 ws0">) <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span> <span class="_ _7"> </span><span class="ff3">（</span>9<span class="ff3">）</span></div><div class="t m0 x18 h4 y121 ff3 fs1 fc0 sc0 ls0 ws0">式中：</div><div class="t m0 xb7 h10 y122 ffb fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xde h15 y123 ffb fs2 fc0 sc0 ls36 ws0">ij</div><div class="t m0 xb8 h4 y124 ff3 fs1 fc0 sc0 ls0 ws0">和</div><div class="t m0 xd1 h10 y125 ffe fs1 fc0 sc0 ls0 ws0">α</div><div class="t m0 xdf h15 y123 ffb fs2 fc0 sc0 ls36 ws0">ij</div><div class="t m0 xe0 h4 y124 ff3 fs1 fc0 sc0 ls0 ws0">分别表示<span class="_ _1"></span>两个测点<span class="_ _1"></span>位置之间的<span class="_ _1"></span>位移矢</div><div class="t m0 x18 h4 y126 ff3 fs1 fc0 sc0 ls0 ws0">量</div><div class="t m0 xaa h25 y127 ff14 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xe1 h4 y126 ff3 fs1 fc0 sc0 ls0 ws0">的矢<span class="_ _1"></span>径和<span class="_ _1"></span>角度<span class="_ _1"></span>，即</div><div class="t m0 xba h25 y127 ff14 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xe2 hc y126 ff1 fs1 fc0 sc0 ls0 ws0">=(</div><div class="t m0 xe3 h10 y127 ffb fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xe4 h4 y126 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 x9b h10 y127 ffe fs1 fc0 sc0 ls0 ws0">α</div><div class="t m0 x9c h4 y126 ff1 fs1 fc0 sc0 ls0 ws0">)<span class="ff3">，</span></div><div class="t m0 x10 h25 y127 ff14 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 xe5 hc y126 ff1 fs1 fc0 sc0 ls0 ws0">=(</div><div class="t m0 xb6 h10 y127 ffb fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 xe6 h4 y126 ff3 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 xe7 h10 y127 ffe fs1 fc0 sc0 ls0 ws0">θ</div><div class="t m0 xe8 h4 y126 ff1 fs1 fc0 sc0 ls0 ws0">)<span class="ff3">是<span class="_ _1"></span>在给<span class="_ _1"></span>定</span></div><div class="t m0 x18 h4 y128 ff3 fs1 fc0 sc0 ls0 ws0">的<span class="_ _1"></span>频<span class="_ _1"></span>率<span class="_ _1"></span>和<span class="_ _1"></span>方<span class="_ _2"></span>向<span class="_ _1"></span>的<span class="_ _1"></span>波<span class="_ _1"></span>数<span class="_ _1"></span>矢<span class="_ _2"></span>量<span class="_ _1"></span>。<span class="_ _1"></span>可<span class="_ _1"></span>以<span class="_ _1"></span>推<span class="_ _2"></span>导<span class="_ _1"></span>出<span class="_ _1"></span>求<span class="_ _1"></span>解<span class="_ _1"></span>波<span class="_ _2"></span>数</div><div class="t m0 x18 h4 y129 ff3 fs1 fc0 sc0 ls0 ws0">矢量的公式如下：</div><div class="c x18 y12a w8 h26"><div class="t m0 xe9 h10 y12b ff5 fs1 fc0 sc0 ls5 ws0">si<span class="ls37">ns<span class="_ _30"></span><span class="lsd">in<span class="_ _31"> </span><span class="ls5">si<span class="ls38">n(<span class="_ _9"> </span><span class="ls2a">)c<span class="_ _29"></span><span class="ls0">os<span class="_ _32"></span><span class="ffb">k</span></span></span></span></span></span></span></div><div class="t m0 x6a h10 y12c ffb fs1 fc0 sc0 ls39 ws0">rr</div><div class="t m0 x6d h13 y12d ff5 fs7 fc0 sc0 ls0 ws0">12</div><div class="t m0 xea h13 y12e ff5 fs7 fc0 sc0 ls0 ws0">12</div><div class="t m0 x37 h13 y12f ff5 fs7 fc0 sc0 ls0 ws0">34</div><div class="t m0 x70 h13 y12d ff5 fs7 fc0 sc0 ls0 ws0">34</div><div class="t m0 x6 h13 y12e ff5 fs7 fc0 sc0 ls0 ws0">34</div><div class="t m0 x3d h13 y12f ff5 fs7 fc0 sc0 ls0 ws0">12<span class="_ _33"> </span>34<span class="_ _34"> </span>12</div><div class="t m0 x48 h1b y130 ff11 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m0 xeb h10 y131 ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 xec h12 y132 ffc fs1 fc0 sc0 ls0 ws0">{</div><div class="t m0 x73 h12 y133 ffc fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 xed h12 y132 ffc fs1 fc0 sc0 ls0 ws0">{</div><div class="t m0 x13 h12 y133 ffc fs1 fc0 sc0 ls3a ws0">aa<span class="_ _24"></span><span class="ls3b">ai</span></div><div class="t m0 x51 h1b y134 ff11 fs1 fc0 sc0 ls0 ws0">-</div><div class="t m2 x6b h27 y135 ff12 fsb fc0 sc0 ls3c ws0">`j</div><div class="t m3 x3e h28 y136 ff15 fsc fc0 sc0 ls0 ws0">6</div><div class="t m4 xee h29 y137 ff15 fsd fc0 sc0 ls0 ws0">@</div></div><div class="t m0 xa h4 y138 ff3 fs1 fc0 sc0 ls0 ws0">（<span class="_ _29"></span><span class="ff1">10<span class="_ _29"></span><span class="ff3">）</span></span></div><div class="c xef y139 w9 h26"><div class="t m0 xf0 h10 y12b ff5 fs1 fc0 sc0 lsd ws0">arctan<span class="_ _35"> </span>co<span class="ls3d">sc<span class="_ _18"></span><span class="ls0">os<span class="_ _13"> </span><span class="ls5"><span class="fc1 sc0">si</span><span class="ls3e"><span class="fc1 sc0">ns</span><span class="_ _36"></span><span class="lsd"><span class="fc1 sc0">in</span></span></span></span></span></span></div><div class="t m0 x52 h10 y12c ffb fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x52 h10 y13a ffb fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xf1 h10 y12c ffb fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">r</span></div><div class="t m0 xf1 h10 y13a ffb fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">r</span></div><div class="t m0 x32 h1a y12d ff11 fs7 fc0 sc0 ls5 ws0">34</div><div class="t m0 x32 h1a y12e ff11 fs7 fc0 sc0 ls5 ws0">12</div><div class="t m0 xf2 h1a y12d ff11 fs7 fc0 sc0 ls5 ws0">34</div><div class="t m0 xf2 h1a y13b ff11 fs7 fc0 sc0 ls5 ws0">12</div><div class="t m0 x13 h1a y12f ff11 fs7 fc0 sc0 ls5 ws0">34<span class="_ _37"> </span>12<span class="_ _38"> </span><span class="fc1 sc0">12</span></div><div class="t m0 xee h1a y12d ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">12</span></div><div class="t m0 xee h1a y12e ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">12</span></div><div class="t m0 xf3 h1a y12d ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">34</span></div><div class="t m0 x89 h1a y13b ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">12</span></div><div class="t m0 xf4 h1a y12f ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">34</span></div><div class="t m0 xf5 h1b y130 ff11 fs1 fc0 sc0 ls3f ws0">-<span class="fc1 sc0">-</span></div><div class="t m0 xeb h10 y131 ff5 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m0 x0 h12 y133 ffc fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xf6 h12 y13c ffc fs1 fc0 sc0 ls0 ws0">{</div><div class="t m0 xf6 h12 y132 ffc fs1 fc0 sc0 ls0 ws0">{</div><div class="t m0 x2d h12 y133 ffc fs1 fc0 sc0 ls40 ws0">aa<span class="_ _4"></span><span class="ls0"><span class="fc1 sc0">a</span></span></div><div class="t m0 xc h12 y13c ffc fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">{</span></div><div class="t m0 xc h12 y132 ffc fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">{</span></div><div class="t m0 xf7 h12 y133 ffc fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">a</span></div><div class="t m5 x6c h2a y13d ff12 fse fc0 sc0 ls41 ws0">c<span class="fc1 sc0">c</span><span class="_ _39"></span><span class="ls42">m<span class="fc1 sc0">m</span></span></div><div class="t m6 x62 h2b y13e ff15 fsf fc0 sc0 ls0 ws0">;</div><div class="t m7 x2a h2c y13f ff15 fs10 fc0 sc0 ls0 ws0"><span class="fc1 sc0">E</span></div></div><div class="c xd4 y140 wa h26"><div class="t m0 xf8 h10 y12b ff5 fs1 fc0 sc0 lsd ws0"><span class="fc1 sc0">arctan</span><span class="_ _3a"> </span><span class="fc1 sc0">co</span><span class="ls3d"><span class="fc1 sc0">sc</span><span class="_ _18"></span><span class="ls0"><span class="fc1 sc0">os</span><span class="_ _13"> </span><span class="ls5">si<span class="ls43">ns<span class="_ _3b"></span><span class="lsd">in</span></span></span></span></span></div><div class="t m0 xf9 h10 y12c ffb fs1 fc0 sc0 ls44 ws0"><span class="fc1 sc0">rr</span></div><div class="t m0 xfa h10 y13a ffb fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">r</span></div><div class="t m0 x1 h10 y12c ffb fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x1 h10 y13a ffb fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xfb h1a y12d ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">12</span></div><div class="t m0 xfc h1a y12e ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">12</span></div><div class="t m0 xfd h1a y12d ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">34</span></div><div class="t m0 xfd h1a y13b ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">12</span></div><div class="t m0 xfe h1a y12f ff11 fs7 fc0 sc0 ls5 ws0"><span class="fc1 sc0">34</span><span class="_ _37"> </span><span class="fc1 sc0">12</span><span class="_ _3c"> </span>12</div><div class="t m0 x6c h1a y12d ff11 fs7 fc0 sc0 ls5 ws0">34</div><div class="t m0 x6c h1a y12e ff11 fs7 fc0 sc0 ls5 ws0">12</div><div class="t m0 xff h1a y12d ff11 fs7 fc0 sc0 ls5 ws0">34</div><div class="t m0 x32 h1a y13b ff11 fs7 fc0 sc0 ls5 ws0">12</div><div class="t m0 x60 h1a y12f ff11 fs7 fc0 sc0 ls5 ws0">34</div><div class="t m0 x100 h1b y130 ff11 fs1 fc0 sc0 ls45 ws0"><span class="fc1 sc0">-</span>-</div><div class="t m0 x101 h10 y131 ff5 fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span></div><div class="t m0 x102 h12 y133 ffc fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div><div class="t m0 x103 h12 y132 ffc fs1 fc0 sc0 ls0 ws0"><span class="fc1 sc0">{</span></div><div class="t m0 x104 h12 y133 ffc fs1 fc0 sc0 ls40 ws0"><span class="fc1 sc0">aa</span><span class="_ _2"></span><span class="ls0">a</span></div><div class="t m0 x65 h12 y13c ffc fs1 fc0 sc0 ls0 ws0">{</div><div class="t m0 x65 h12 y132 ffc fs1 fc0 sc0 ls0 ws0">{</div><div class="t m0 x6 h12 y133 ffc fs1 fc0 sc0 ls0 ws0">a</div><div class="t m2 x105 h27 y135 ff12 fsb fc0 sc0 ls0 ws0"><span class="fc1 sc0">`</span></div><div class="t m5 x0 h2a y13d ff12 fse fc0 sc0 ls0 ws0">c</div><div class="t m2 x106 h27 y135 ff12 fsb fc0 sc0 ls0 ws0"><span class="fc1 sc0">j</span></div><div class="t m5 x15 h2a y13d ff12 fse fc0 sc0 ls0 ws0">m</div><div class="t m6 x107 h2b y13e ff15 fsf fc0 sc0 ls0 ws0"><span class="fc1 sc0">;</span></div><div class="t m7 x108 h2c y13f ff15 fs10 fc0 sc0 ls0 ws0">E</div></div><div class="t m0 x109 h4 y141 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _7"> </span><span class="ff3">（</span>11<span class="ff3">）</span></div><div class="t m0 x1d h4 y142 ff3 fs1 fc0 sc0 ls0 ws0">从<span class="_ _1"></span>而<span class="_ _1"></span>求<span class="_ _1"></span>得<span class="_ _1"></span>整<span class="_ _1"></span>个<span class="_ _1"></span>波<span class="_ _1"></span>浪<span class="_ _1"></span>场<span class="_ _1"></span>在<span class="_ _1"></span>时<span class="_ _1"></span>域<span class="_ _1"></span>和<span class="_ _1"></span>频<span class="_ _1"></span>域<span class="_ _1"></span>内<span class="_ _1"></span>的<span class="_ _1"></span>波<span class="_ _1"></span>数</div><div class="t m0 x18 h4 y143 ff3 fs1 fc0 sc0 ls0 ws0">矢量</div><div class="t m0 xa8 h25 y144 ff14 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x10a h4 y143 ff3 fs1 fc0 sc0 ls0 ws0">，最<span class="_ _3d"></span>少需<span class="_ _3d"></span>要两<span class="_ _3d"></span>对不<span class="_ _3d"></span>同的<span class="_ _3d"></span>下角<span class="_ _3d"></span>标，<span class="_ _3d"></span>即<span class="ff1">3<span class="_ _3d"></span><span class="ff3">个测<span class="_ _3d"></span>波。</span></span></div><div class="t m0 x10b h2 y145 ff2 fs0 fc0 sc0 ls0 ws0">张<span class="ff1"> <span class="_ _0"> </span></span>乐，等：基于小波变换的海浪方向谱估计方法研究</div><div class="t m0 xb1 h2d y146 ff1 fs11 fc0 sc0 ls0 ws0">*</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
