數(shù)字信號(hào)處理第三次實(shí)驗(yàn)代碼及波形圖

1、數(shù)字信號(hào)處理第三次實(shí)驗(yàn)一、實(shí)驗(yàn)?zāi)康?1、掌握離散時(shí)間系統(tǒng)的DFT的MATLAB實(shí)現(xiàn);2、熟悉DTFT和DFT之間的關(guān)系。3、了解信號(hào)不同變形的DFT與原信號(hào)DFT之間的關(guān)系二、實(shí)驗(yàn)內(nèi)容:1.開(kāi)發(fā)一個(gè)時(shí)域圓周移位的matlab函數(shù)cirshift.m并測(cè)試:設(shè)x(n=9 8 7 6 5 4 3,求x(n-48R8(n以及x(n+58R8(n。function y=cirshift(x,m,N%長(zhǎng)度為N的x序列(時(shí)域作m點(diǎn)圓周位移%-%y=cirshift(x,m,N%y=包含圓周位移的輸出序列%x=長(zhǎng)度<=N的輸入序列%m=移位樣點(diǎn)數(shù)%N=圓周緩沖器長(zhǎng)度%方法:y(n=x(n-mmod N

2、%check for length of xif length(x>Nerror('N必須>=x的長(zhǎng)度'endx=x zeros(1,N-length(x;%將x補(bǔ)零到長(zhǎng)度為Nn=0:1:N-1;n=mod(n-m,N;y=x(n+1;%主函數(shù).mclc;clear all;x=9 8 7 6 5 4 3;y1=cirshift(x,4,8;y2=cirshift(x,-5,8; 2. 開(kāi)發(fā)一個(gè)圓周翻轉(zhuǎn)的matlab函數(shù)cirflip.m并測(cè)試:設(shè)x(n=9 8 7 6 5 4 3 2 1,求x(n的16點(diǎn)圓周翻轉(zhuǎn)x(-n16R16(n。function y=cir

3、filp(x,Nnx=0:1:N-1;y=x(mod(-nx,N+1;%主函數(shù).mclc;clear all;x=9 8 7 6 5 4 3 2 1;N=16;x=x zeros(1,N-length(x;nx=0:N-1;y=cirfilp(x,16;subplot(121,stem(0:N-1,x;title('原序列'xlabel('n'ylabel('x(n'grid;subplot(122,stem(0:N-1,y;title('圓周翻褶序列'xlabel('n'ylabel('x(n16r16(

4、n'grid; 3. 開(kāi)發(fā)一個(gè)分解圓周奇偶對(duì)稱(chēng)序列的matlab函數(shù)cirevod.m并測(cè)試:設(shè)x(n=9 8 7 6 5 4 3 2 1,將x(n分解圓周奇偶對(duì)稱(chēng)序列x ep(n 、x op(n。function xep,xop=circevod(x%將實(shí)序列分解為圓周偶和圓周奇兩部分%-%xep,xop=circevod(xif any(imag(x=0error('x非實(shí)序列'endN=length(x;n=0:N-1;xep=0.5*(x+x(mod(-n,N+1;xop=0.5*(x-x(mod(-n,N+1;%主函數(shù).mx=9 8 7 6 5 4 3 2 1

5、;xep,xop=circevod(x; 4. 開(kāi)發(fā)一個(gè)實(shí)現(xiàn)DFT矩陣的函數(shù)wN=dftmtx(N并測(cè)試N=4,8, 16的DFT矩陣,在此基礎(chǔ)上尋求IDFT矩陣wNI的編程方法并測(cè)試N=4,8,16的IDFT矩陣%這是matlab自帶的函數(shù)命令行輸入type+dftmtx可查看源代碼。function D = dftmtx(nn = ernal.sigcasttofloat(n,'double','dftmtx','N',.'allownumeric'D = fft(eye(n;命令行輸入:wN=dftmtx

6、(N;wNI=conj(dftmtx(N/NDFTN=4 N=8 N=16 IDFT: N=4 N=8 N=16 5.自編工具函數(shù)XK=dft(xn,N實(shí)現(xiàn)DFT以及IDFT,并測(cè)試x(n=9 8 7 6 5 4 3 2 1的DFT。functionXk=dft(xn,Nn=0:1:N-1;k=n;WN=exp(-j*2*pi/N;nk=n'*k;WNnk=WN.(nk;Xk=xn*WNnk;%主函數(shù)xn=9 8 7 6 5 4 3 2 1y=dft(x,9; functionXk=idft(xn,Nn=0:1:N-1;k=n;WN=exp(-j*2*pi/N;nk=n'*k;

7、WNnk=WN.(-nk;Xk=(xn*WNnk/N;6. 開(kāi)發(fā)一個(gè)圓周卷積計(jì)算的matlab函數(shù)y=circonvt(x1,x2,N,并測(cè)試x1(n=1 2 3 4 9, x2=7 6 5 4 3 2 1,求8點(diǎn)圓周卷積。function y=circonvt(x1,x2,Nif length(x1>Nerror('N必須>=x1的長(zhǎng)度'endif length(x2>Nerror('N必須>=x2的長(zhǎng)度'endx1=x1 zeros(1,N-length(x1; x2=x2 zeros(1,N-length(x2; m=0:1:N-1

8、; x2=x2(mod(-m,N+1; H=zeros(N,N;for n=1:1:NH(n,:=cirshift(x2,n-1,N; endy=x1*H'%test.6x1=1 2 3 4 9;x2=7 6 5 4 3 2 1;y=circonvt(x1,x2,8; 7.教材 P212 習(xí)題 3.36. 余弦頻率是正弦頻率的兩倍，故正弦周期是預(yù)先周期的兩倍。T=0.5s 抽樣間隔 T=0.01s，故 N=50； clear all;clc; N=50; n=0:1:N-1; k=n; xn=2*sin(0.04*pi*n+5*cos(0.08*pi*n; WN=exp(-j*2*pi

9、/N; nk=n'*k; WNnk=WN.(nk; Xk=xn*WNnk; magX=abs(Xk; angX=angle(Xk; subplot(121;stem(k,magX,'.'grid; xlabel('k'title('幅度譜曲線'ylabel('X(k' subplot(122;stem(k,angX,'.'grid; xlabel('k'title('相位譜曲線'ylabel('弧度' 第 11 頁(yè) 共 12 頁(yè) 因?yàn)槌闃宇l率不變，要增大 N 才能減少譜泄露，故 N=99； clear all;clc; N=99; n=0:1:N-1; k=n; xn=2*sin(0.04*pi*n+5*cos(0.08*pi*n; WN=exp(-j*2*pi/N; nk=n'*k; WNnk=WN.(nk; Xk=xn*WNnk; magX=abs(Xk; angX=angle(Xk; subplot(121;stem(k,magX,'.'grid; xlabel('k't