武漢工程大學(xué)數(shù)字信號(hào)處理實(shí)驗(yàn)四 離散傅里葉變換DFT及IDFT

1、.實(shí)驗(yàn)四 離散傅里葉變換DFT及IDFT一、實(shí)驗(yàn)?zāi)康脑诶碚搶W(xué)習(xí)的基礎(chǔ)上，通過(guò)本實(shí)驗(yàn)，加深對(duì)DFT的理解，熟悉DFT子程序。掌握計(jì)算離散信號(hào)DFT的方法。體會(huì)有限長(zhǎng)序列DFT與離散時(shí)間傅里葉變化DTFT之間的關(guān)系。掌握用MATLAB進(jìn)行離散傅里葉變換DFT及其逆變換IDFT的方法。三、實(shí)驗(yàn)內(nèi)容已知有限長(zhǎng)序列x(n)=7,6,5,4,3,2,求x(n)的IDFT。要求： 畫(huà)出序列DFT對(duì)應(yīng)的|X(k)|和argX(k)的圖形。程序：xn=7,6,5,4,3,2;N=length(xn)n=0:(N-1);k=0:(N-1);Xk=xn*exp(-j*2*pi/N).(n*k);x=(Xk*exp(

2、j*2*pi/N).(n*k)/N;subplot(2,2,1);stem(n,xn);title(x(n);subplot(2,2,2);stem(n,Xk);title(IDFTX(k);subplot(2,2,3);stem(k,abs(Xk);title(|X(k)|);subplot(2,2,4);stem(k,angle(Xk);title(arg|X(k)|);title(arg|X(k)|);波形如下： 畫(huà)出原信號(hào)與IDFTX(k)的圖形，并進(jìn)行比較。程序：N=length(xn) n=0:(N-1); k=0:(N-1); Xk=xn*exp(-j*2*pi/N).(n*k)

3、; x=(Xk*exp(j*2*pi/N).(n*k)/N;subplot(1,2,1); stem(k,abs(Xk); title(|X(k)|); subplot(1,2,2); stem(k,angle(Xk); title(arg|X(k)|);將第一題中的x(n)以補(bǔ)零方式加長(zhǎng)到0n100，重復(fù)第題。程序：n=78xn=7,6,5,4,3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,00,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

4、0,0,0,0,0,0,0,0,0,0,0; N=length(xn) n=0:(N-1); k=0:(N-1); Xk=xn*exp(-j*2*pi/N).(n*k); x=(Xk*exp(j*2*pi/N).(n*k)/N; subplot(2,2,1); stem(n,xn); title(x(n); subplot(2,2,2); stem(n,x); title(IDFTX(k);subplot(2,2,3); stem(k,abs(Xk); title(|X(k)|); subplot(2,2,4); stem(k,angle(Xk); title(arg|X(k)|);四、思考題如何驗(yàn)證試驗(yàn)預(yù)習(xí)中