第7章 線性代數(shù)在工程中的應(yīng)用實(shí)例

1、第7章在科技及工程中的應(yīng)用實(shí)例在科技及工程中的應(yīng)用實(shí)例.........................................................................17.1由拉壓桿組成的桁架結(jié)構(gòu).........................................................................................................

2、...17.2格型梯形濾波器系統(tǒng)函數(shù)的推導(dǎo)................................................................................................17.3計(jì)算頻譜用的DFT矩陣........................................................................................

3、......................27.4顯示器色彩制式轉(zhuǎn)換問題............................................................................................................47.5人員流動(dòng)問題.................................................................

4、...............................................................57.6二氧化碳分子結(jié)構(gòu)的振動(dòng)頻率....................................................................................................57.7二自由度機(jī)械振動(dòng)............................

5、............................................................................................67.8FIR數(shù)字濾波器最優(yōu)化設(shè)計(jì)[12]....................................................................................................87.9彈性梁

6、的柔度矩陣........................................................................................................................97.10用二次樣條函數(shù)插值5個(gè)點(diǎn)..............................................................................

7、......................117.11飛行器三維空間運(yùn)動(dòng)的矩陣描述............................................................................................127.12金融公司支付基金的流動(dòng).....................................................................

8、...................................147.13質(zhì)譜圖實(shí)驗(yàn)結(jié)果分析..............................................................................................................157.14用特征方程解Fibonacci數(shù)列問題...................................

9、.......................................................167.15簡單線性規(guī)劃問題....................................................................................................................18第2章時(shí)域中的離散信號(hào)和系統(tǒng)22性的好處。例如要求出圖72所示的濾

10、波器的系統(tǒng)函數(shù)：先列出方程，令q=z1，得到x1?u?k3x4x2?x1x3?k3x2?x4x4?qx7x5?x2?k2x8x6?x5x7?k2x6?x8x8?qx11x9?x6?k1x12x10?x9x11?k1x10?x12x12?qx10x13?y?C0x12?C1x11?C2x7?C3x3這是一組含有13個(gè)變量的13個(gè)聯(lián)立方程，用過去的手工方法一個(gè)一個(gè)消元，理論上是可行的，但它運(yùn)算極其繁瑣，可以預(yù)期，95%以上的師生恐怕一個(gè)小時(shí)

11、也解不出來，而且做對(duì)的概率極低。用矩陣的思路和方法來解就完全不同，它不是通過消元來減少變量，而是想辦法補(bǔ)上所有的零元素，把方程擴(kuò)充為完整的矩陣形式：13421332447522865721234656789881196112109111101212101310111213xukxxxxkxxxqxxxkxxxxkxxxqxxxkxxxxkxxxqxxxxxxxxxxxxxxx???????????????????????????????

12、???????????????????????????????????????????330000000000001000000000000001000kk?????????2000000000000q000000010000000000000k201000000000000001000000000000000q0k10000001000000000000001000000000000k132100010000000000q00000C

13、000C000CC0k???????????????????????????123456789101112131000000000000xxxxxxxuxxxxxx????????????????????????????????????????????????????????????????????????????????????????????????????X=QXPUXU=inv(IQ)P看似把模型搞復(fù)雜了，其實(shí)計(jì)算卻非常容易。程

14、序pla703先對(duì)P，Q矩陣賦值，鍵入，馬上就得出了系統(tǒng)函數(shù)。W=inv(IQ)P編程時(shí)要注意，本例雖然是數(shù)值計(jì)算，但計(jì)算的內(nèi)容中帶有z變換算子q=z1，所以P，Q矩陣仍然必須用符號(hào)屬性，對(duì)P，Q賦值時(shí)第一個(gè)元素必須取含q的算式。熟練后不必列出Q和P的矩陣形式，可以按其下標(biāo)規(guī)律直接進(jìn)行元素賦值。用以下參數(shù)：k0=1k1=14k2=12k3=13C0=0.2C1=0.8C2=1.5C3=1，編成了程序pla703。運(yùn)行此程序就得到：323

15、2132321(13)244942.930.8244942.930.8(13)81513248151324xqqqzzzWuqqqzzz?????????????????????用矩陣模型解信號(hào)流圖的最大優(yōu)點(diǎn)是一步到位，依靠計(jì)算機(jī)，既快速，又極易查錯(cuò)。7.3計(jì)算頻譜用的DFT矩陣有限長序列x(n)(0≤n≤N1)有N個(gè)樣本值。它的傅里葉變換在頻率區(qū)間()Xk（0≤ω＜2π）的N個(gè)等間隔分布的點(diǎn)ωk=2πkN(0≤k≤N1)上也有N個(gè)樣本