数字信号处理实验一系统响应及系统稳定性附上机实验报告和原程序 206.32KB

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数字信号处理实验一系统响应及系统稳定性附上机实验报告和原程序

<link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89569411/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89569411/bg1.jpg"/><div class="c x1 y1 w2 h2"><div class="t m0 x2 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">**<span class="ff2">大学物联网工程学院上机报告</span></div><div class="t m0 x3 h4 y3 ff3 fs1 fc0 sc0 ls0 ws0">课程名称<span class="ff1"> <span class="_"> </span> <span class="_ _0"> </span></span>数字信号处理<span class="ff1"> <span class="_ _0"> </span> <span class="_ _1"> </span></span>上机名称<span class="ff1"> <span class="_"> </span> <span class="_"> </span></span>实验一<span class="ff1"> <span class="_"> </span></span>系统响应及系统稳定性<span class="ff1"> <span class="_ _0"> </span> <span class="_ _0"> </span></span>上机日期<span class="ff1"> <span class="_"> </span> <span class="_"> </span>*********** </span></div><div class="t m0 x3 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">班<span class="ff1"> <span class="_ _2"> </span></span>级<span class="ff1"> <span class="_"> </span> <span class="_ _3"> </span>******** <span class="_ _2"> </span> <span class="_ _4"> </span></span>姓<span class="ff1"> <span class="_ _2"> </span></span>名<span class="ff1"> <span class="_"> </span> <span class="_ _1"> </span>*********** <span class="_ _5"> </span> <span class="_ _1"> </span></span>学号<span class="ff1"> <span class="_ _0"> </span> <span class="_ _0"> </span>*********** <span class="fc1 sc0"> </span></span></div><div class="t m0 x3 h4 y5 ff3 fs1 fc0 sc0 ls0 ws0">上机报告要求<span class="ff1"> <span class="_ _0"> </span></span>一、实验目的<span class="ff1"> <span class="_ _0"> </span></span>二、实验内容及步骤<span class="ff1"> <span class="_ _0"> </span></span>三、程序代码及运行结果<span class="ff1"> <span class="_ _0"> </span></span>四、思考题<span class="ff1"> <span class="_ _0"> </span></span>五、上机体会<span class="ff1"> </span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x3 h6 y7 ff4 fs2 fc0 sc1 ls0 ws0">一、实验目<span class="_ _6"></span>的</div><div class="t m0 x3 h4 y8 ff1 fs1 fc0 sc0 ls0 ws0">1. <span class="_"> </span> <span class="_"> </span><span class="ff3">掌握求系统响应的方法。</span></div><div class="t m0 x3 h4 y9 ff1 fs1 fc0 sc0 ls0 ws0">2. <span class="_"> </span> <span class="_"> </span><span class="ff3">掌握时域离散系统的时域特性。</span></div><div class="t m0 x3 h4 ya ff1 fs1 fc0 sc0 ls0 ws0">3. <span class="_"> </span> <span class="_"> </span><span class="ff3">分析、观察及检验系统的稳定性。</span></div><div class="t m0 x3 h6 yb ff4 fs2 fc0 sc1 ls0 ws0">二、实验内<span class="_ _6"></span>容及步骤</div><div class="t m0 x4 h4 yc ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">1</span>）编<span class="_ _6"></span>制程序<span class="_ _6"></span>，包括<span class="_ _6"></span>产生输入<span class="_ _6"></span>信号、<span class="_ _6"></span>单位脉冲<span class="_ _6"></span>响应序<span class="_ _6"></span>列的子<span class="_ _6"></span>程序，以<span class="_ _6"></span>及用<span class="_ _7"> </span><span class="ff1">filter<span class="_"> </span></span>函数或<span class="_ _7"> </span><span class="ff1">conv<span class="_"> </span></span>函<span class="_ _6"></span>数求解<span class="_ _6"></span>系统</div><div class="t m0 x3 h4 yd ff3 fs1 fc0 sc0 ls0 ws0">输出响应的主程序。程序中要有绘制信号波形的功能。</div><div class="t m0 x4 h4 ye ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">2</span>）给定一个低通滤波器的差分方程为</div></div><div class="c x5 yf w3 h7"><div class="t m1 x6 h8 y10 ff1 fs3 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _2"> </span>0.05<span class="_ _0"> </span>(<span class="_ _8"> </span>)<span class="_ _9"> </span>0.05<span class="_ _0"> </span>(<span class="_ _a"> </span>1<span class="_ _b"></span>)<span class="_ _9"> </span>0.9<span class="_ _c"> </span>(<span class="_ _a"> </span>1<span class="_ _b"></span>)<span class="_ _d"></span><span class="ff5">y<span class="_ _e"> </span>n<span class="_ _f"> </span>x<span class="_ _e"> </span>n<span class="_ _10"> </span>x<span class="_ _e"> </span>n<span class="_ _11"> </span>y<span class="_ _e"> </span>n<span class="_ _12"></span><span class="ff6">=<span class="_ _11"> </span>+<span class="_ _13"> </span>-<span class="_ _2"> </span>+<span class="_ _10"> </span>-</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x4 h4 y11 ff3 fs1 fc0 sc0 ls0 ws0">输入信号</div></div><div class="c x7 y12 w4 h9"><div class="t m2 x8 ha y13 ff1 fs4 fc0 sc0 ls0 ws0">1<span class="_ _14"> </span>8<span class="_ _15"> </span>2</div><div class="t m2 x9 hb y14 ff1 fs5 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _1"> </span>(<span class="_ _8"> </span>)<span class="_ _16"> </span>(<span class="_ _8"> </span>)<span class="_ _17"> </span>(<span class="_ _8"> </span>)<span class="_ _18"></span><span class="ff5">x<span class="_ _19"> </span>n<span class="_ _a"> </span>R<span class="_ _1a"> </span>n<span class="_ _1b"> </span>x<span class="_ _3"> </span>n<span class="_ _1c"> </span>u<span class="_ _e"> </span>n<span class="_ _1d"></span><span class="ff6">=<span class="_ _1e"> </span>=<span class="_ _1f"></span><span class="ff3">，</span></span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x4 hc y15 ff7 fs1 fc0 sc0 ls0 ws0">①<span class="ff1"> <span class="_"> </span><span class="ff3">分别求出</span></span></div></div><div class="c xa y16 w5 hd"><div class="t m3 x8 he y17 ff1 fs6 fc0 sc0 ls0 ws0">1<span class="_ _20"> </span>8</div><div class="t m3 x9 hf y18 ff1 fs7 fc0 sc0 ls0 ws0">(<span class="_ _0"> </span>)<span class="_ _21"> </span>(<span class="_ _0"> </span>)<span class="_ _22"></span><span class="ff5">x<span class="_ _23"> </span>n<span class="_ _1c"> </span>R<span class="_ _19"> </span>n<span class="_ _24"></span><span class="ff6">=</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 xb h4 y15 ff3 fs1 fc0 sc0 ls0 ws0">和</div></div><div class="c xc y16 w6 h9"><div class="t m4 xd ha y13 ff1 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m4 xe h10 y14 ff1 fs5 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _17"> </span>(<span class="_ _8"> </span>)<span class="_ _25"></span><span class="ff5">x<span class="_ _3"> </span>n<span class="_ _1c"> </span>u<span class="_ _e"> </span>n<span class="_ _26"></span><span class="ff6">=</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 xf h4 y15 ff3 fs1 fc0 sc0 ls0 ws0">的系统响应，并画出其波形<span class="ff1">.</span></div><div class="t m0 x4 hc y19 ff7 fs1 fc0 sc0 ls0 ws0">②<span class="ff1"> <span class="_"> </span><span class="ff3">求出系统的单位脉冲响应，画出其波形。</span></span></div><div class="t m0 x4 h4 y1a ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">3</span>）给定系统的单位脉冲响应为</div></div><div class="c x10 y1b w7 h11"><div class="t m5 x8 h12 y1c ff1 fs8 fc0 sc0 ls0 ws0">1<span class="_ _27"> </span>10</div><div class="t m5 x8 h12 y1d ff1 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m5 x9 h13 y1e ff1 fs9 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _4"> </span>(<span class="_ _8"> </span>)</div><div class="t m5 xe h13 y1f ff1 fs9 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _28"> </span>(<span class="_ _8"> </span>)<span class="_ _9"> </span>2.5<span class="_ _c"> </span>(<span class="_ _a"> </span>1<span class="_ _b"></span>)<span class="_ _9"> </span>2.5<span class="_ _c"> </span>(<span class="_ _5"> </span>2)<span class="_ _17"> </span>(<span class="_ _29"> </span>3<span class="_ _2a"></span>)</div><div class="t m5 x11 h13 y1e ff5 fs9 fc0 sc0 ls0 ws0">h<span class="_ _23"> </span>n<span class="_ _a"> </span>R<span class="_ _9"> </span>n</div><div class="t m5 x11 h13 y1f ff5 fs9 fc0 sc0 ls0 ws0">h<span class="_ _1a"> </span>n<span class="_ _2b"> </span>n<span class="_ _13"> </span>n<span class="_ _2c"> </span>n<span class="_ _2d"> </span>n</div><div class="t m6 x12 h14 y1f ff8 fsa fc0 sc0 ls0 ws0">d<span class="_ _2e"> </span>d<span class="_ _2f"> </span>d<span class="_ _30"> </span>d</div><div class="t m5 x13 h15 y1e ff6 fs9 fc0 sc0 ls0 ws0">=</div><div class="t m5 x14 h15 y1f ff6 fs9 fc0 sc0 ls0 ws0">=<span class="_ _4"> </span>+<span class="_ _10"> </span>-<span class="_ _2"> </span>+<span class="_ _f"> </span>-<span class="_ _31"> </span>+<span class="_ _32"> </span>-</div></div><div class="c x1 y6 w2 h5"><div class="t m0 x4 h4 y20 ff3 fs1 fc0 sc0 ls0 ws0">用线性卷积发求</div></div><div class="c xb y21 w8 h9"><div class="t m7 x8 ha y13 ff1 fs4 fc0 sc0 ls0 ws0">1<span class="_ _14"> </span>8</div><div class="t m7 x9 h10 y14 ff1 fs5 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _1"> </span>(<span class="_ _8"> </span>)<span class="_ _33"></span><span class="ff5">x<span class="_ _19"> </span>n<span class="_ _a"> </span>R<span class="_ _1a"> </span>n<span class="_ _34"></span><span class="ff6">=</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x15 h4 y20 ff3 fs1 fc0 sc0 ls0 ws0">分别对系统</div></div><div class="c x16 y21 w9 h9"><div class="t m8 x8 ha y13 ff1 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m8 x9 h16 y14 ff1 fs5 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _35"></span><span class="ff5">h<span class="_ _23"> </span>n</span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x17 h4 y20 ff3 fs1 fc0 sc0 ls0 ws0">和</div></div><div class="c x18 y21 wa h9"><div class="t m9 x8 ha y13 ff1 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m9 xe h16 y14 ff1 fs5 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _36"></span><span class="ff5">h<span class="_ _1a"> </span>n</span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x19 h4 y20 ff3 fs1 fc0 sc0 ls0 ws0">的输出响应，并画出波形。</div><div class="t m0 x4 h4 y22 ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">4</span>）给定一谐振器的差分方程为</div></div><div class="c x1a y23 wb h9"><div class="t ma x1b ha y13 ff1 fs4 fc0 sc0 ls0 ws0">0<span class="_ _f"> </span>0</div><div class="t ma x6 h10 y14 ff1 fs5 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _37"> </span>1.8237<span class="_ _23"> </span>(<span class="_ _1c"> </span>1<span class="_ _b"></span>)<span class="_ _38"> </span>0.9801<span class="_ _0"> </span>(<span class="_ _5"> </span>2)<span class="_ _4"> </span>(<span class="_ _0"> </span>)<span class="_ _4"> </span>(<span class="_ _29"> </span>2<span class="_ _6"></span>)<span class="_ _39"></span><span class="ff5">y<span class="_ _e"> </span>n<span class="_ _3a"> </span>y<span class="_ _e"> </span>n<span class="_ _3b"> </span>y<span class="_ _e"> </span>n<span class="_ _3c"> </span>b<span class="_ _3d"> </span>x<span class="_ _e"> </span>n<span class="_ _1b"> </span>b<span class="_ _3d"> </span>x<span class="_ _3e"> </span>n<span class="_ _3f"></span><span class="ff6">=<span class="_ _40"> </span>-<span class="_ _2"> </span>-<span class="_ _41"> </span>-<span class="_ _31"> </span>+<span class="_ _42"> </span>-<span class="_ _43"> </span>-</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x4 h4 y24 ff3 fs1 fc0 sc0 ls0 ws0">令</div></div><div class="c x1c y25 wc h9"><div class="t mb x8 ha y13 ff1 fs4 fc0 sc0 ls0 ws0">0</div><div class="t mb x1d h10 y14 ff1 fs5 fc0 sc0 ls0 ws0">1<span class="_ _44"> </span>/<span class="_ _44"> </span>100.49<span class="_ _45"></span><span class="ff5">b<span class="_ _c"> </span><span class="ff6">=</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x2 h4 y24 ff3 fs1 fc0 sc0 ls0 ws0">，谐振器的谐振频率为<span class="_ _7"> </span><span class="ff1">0.4rad</span>。</div><div class="t m0 x4 hc y26 ff7 fs1 fc0 sc0 ls0 ws0">①<span class="ff1"> <span class="_"> </span><span class="ff3">用实验方法检查系统是否稳定。输入信号为</span></span></div></div><div class="c x1e y27 wd h7"><div class="t mc xd h17 y10 ff1 fs3 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _46"></span><span class="ff5">u<span class="_ _e"> </span>n</span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x1f h4 y26 ff3 fs1 fc0 sc0 ls0 ws0">时，画出系统输出波形。</div><div class="t m0 x4 hc y28 ff7 fs1 fc0 sc0 ls0 ws0">②<span class="ff1"> <span class="_"> </span><span class="ff3">给定输入信号</span></span></div></div><div class="c x20 y29 we h7"><div class="t md xd h8 y10 ff1 fs3 fc0 sc0 ls0 ws0">(<span class="_ _8"> </span>)<span class="_ _2"> </span>sin(0.014<span class="_ _8"> </span>)<span class="_ _37"> </span>sin(0.4<span class="_ _8"> </span>)<span class="_ _47"></span><span class="ff5">x<span class="_ _3e"> </span>n<span class="_ _48"> </span>n<span class="_ _49"> </span>n<span class="_ _4a"></span><span class="ff6">=<span class="_ _4b"> </span>-</span></span></div></div><div class="c x1 y6 w2 h5"><div class="t m0 x4 h4 y2a ff3 fs1 fc0 sc0 ls0 ws0">求出系统的输出响应，并画出波形。</div></div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><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="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89569411/bg2.jpg"><div class="c x1 y2b w2 h18"><div class="t m0 x3 h6 y2c ff4 fs2 fc0 sc1 ls0 ws0">三、程序代<span class="_ _6"></span>码及运行结<span class="_ _6"></span>果</div><div class="t m0 x4 h4 y2d ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">1</span>）程序如下：</div><div class="t m0 x21 h4 y2e ff3 fs1 fc0 sc0 ls0 ws0">图<span class="_ _7"> </span><span class="ff1">1</span></div><div class="t m0 x3 h19 y2f ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x22 h4 y30 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_"> </span><span class="ff3">结果如下：</span></div></div><div class="c x23 y31 wf h1a"><div class="t me x24 h1b y32 ff9 fsb fc2 sc0 ls0 ws0">0</div><div class="t me x24 h1b y33 ff9 fsb fc2 sc0 ls0 ws0">1</div><div class="t me x24 h1b y34 ff9 fsb fc2 sc0 ls0 ws0">2</div><div class="t me x24 h1b y35 ff9 fsb fc2 sc0 ls0 ws0">3</div><div class="t me x24 h1b y36 ff9 fsb fc2 sc0 ls0 ws0">4</div><div class="t me x24 h1b y37 ff9 fsb fc2 sc0 ls0 ws0">5</div><div class="t me x24 h1b y38 ff9 fsb fc2 sc0 ls0 ws0">6</div><div class="t mf x25 h1c y39 ff9 fsc fc2 sc0 ls0 ws0">y(n)</div><div class="t me x26 h1d y3a ff3 fsd fc0 sc0 ls0 ws0">利用<span class="ff9">conv</span>函数求解系统输出响应</div><div class="t me x22 h1b y3b ff9 fsb fc2 sc0 ls0 ws0">0<span class="_ _4c"> </span>2<span class="_ _4c"> </span>4<span class="_ _4c"> </span>6<span class="_ _4c"> </span>8<span class="_ _4d"> </span>10<span class="_ _1"> </span>12<span class="_ _1"> </span>14<span class="_ _1"> </span>16</div><div class="t me x27 h1e y3c ff9 fsd fc2 sc0 ls0 ws0">n</div></div><div class="c x1 y2b w2 h18"><div class="t m0 x21 h4 y3d ff3 fs1 fc0 sc0 ls0 ws0">图<span class="_ _7"> </span><span class="ff1">2</span></div><div class="t m0 x3 h19 y3e ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x22 h4 y3f ff3 fs1 fc0 sc0 ls0 ws0">结果分析：</div><div class="t m0 x3 h4 y40 ff1 fs1 fc0 sc0 ls0 ws0"> <span class="_ _16"> </span><span class="ff3">由于题目没有要求给出明确的输入信号，我这里设置输入信号为</span>[1 2 3 4 <span class="_ _6"></span>5 4 3 2 1]<span class="ff3">，然后让其与单位脉</span></div><div class="t m0 x3 h4 y41 ff3 fs1 fc0 sc0 ls0 ws0">冲响应相卷，得到如图所示的波形，可以看到有<span class="_ _7"> </span><span class="ff1">8<span class="_"> </span></span>条序列，符合理论长度，且波形很好看。</div></div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></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="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89569411/bg3.jpg"><div class="c x1 y42 w2 h1f"><div class="t m0 x4 h4 y43 ff3 fs1 fc0 sc0 ls0 ws0">（<span class="ff1">2</span>）</div><div class="t m0 x14 hc y44 ff7 fs1 fc0 sc0 ls0 ws0">①<span class="ff1"> <span class="_"> </span><span class="ff3">程序如下：</span></span></div><div class="t m0 x21 h4 y45 ff3 fs1 fc0 sc0 ls0 ws0">图<span class="_ _7"> </span><span class="ff1">3</span></div><div class="t m0 x22 h19 y46 ff1 fs1 fc0 sc0 ls0 ws0"> </div></div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div>

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