用MATLAB實(shí)現(xiàn)序列圓周卷積

數(shù)字信號處理實(shí)驗(yàn)報(bào)告實(shí)項(xiàng)名：

用MATLAB現(xiàn)列圓卷實(shí)日：實(shí)評標(biāo)：1實(shí)結(jié)是正2實(shí)結(jié)分3實(shí)報(bào)是按規(guī)格

實(shí)成：A）（）（）A）（）（）A）（）（）一實(shí)目

通過本實(shí)驗(yàn)，掌握一些基本而且重要的離散時(shí)間信號，熟悉基本離散時(shí)間信號的MATLAB實(shí)現(xiàn)方法。二實(shí)器PC，MATLAB軟件。三實(shí)內(nèi)計(jì)兩序列（n={1,2,3,4,5}（={1,2,3,4,5,4,3,2,1}圓周卷積。四實(shí)結(jié)實(shí)代碼：clearallcloseallclcx1=[1,2,3,4,5,6,7,8];x2=[1,2,3,4,5,6,7,8,7,6,5,4,3,2,1];

N=length(x1)+length(x2);n=0:N-1n1=0:N-2;n2=0:N-3;y1=circonvt(x1,x2,N);y2=circonvt(x1,x2,N-1);1/3

y3=circonvt(x1,x2,N-2);x1=[x1zeros(1,N-length(x1))];x2=[x2zeros(1,N-length(x2))];Xf1=dft(x1,N);Xf2=dft(x2,N);Xf=Xf1.*Xf2;x=idft(Xf,N);x=real(x);subplot(2,3,1)stem(n,x1);title('x1(n)');subplot(2,3,2)stem(n,x2);functiony=circonvt(x1,x2,N)iflength(x1)>Nerror('N必須>=x1的長度')endiflength(x2)>Nerror('N必須>=x2的長度')endx1=[x1zeros(1,N-length(x1))];x2=[x2zeros(1,N-length(x2))];m=[0:1:N-1];x2=x2(mod(-m,N)+1);H=zeros(N,N);forn=1:1:NH(n,:)=cirshift(x2,n-1,N);endy=x1*H;functiony=cirshift(x,m,N)

title('x2(n)')subplot(2,3,3);stem(n,x);title('x(n)=IDFT(X(k))');subplot(2,3,4);stem(n,y1);title('N點(diǎn)圓周卷積');subplot(2,3,5);stem(n1,y2);title('N-1點(diǎn)圓周卷積');subplot(2,3,6);stem(n2,y3);title('N-2點(diǎn)圓周卷積');iflength(x)>Nerror('N必須>=x的長度')endx=[xzeros(1,N-length(x))];n=[0:1:N-1];n=mod(n-m,N);y=x(n+1);function[Xk]=dft(xn,N)n=[0:1:N-1];k=[0:1:N-1];WN=exp(-j*2*pi/N);nk=n'*k;WNnk=WN.^nk;Xk=xn*WNnk;function[xn]=idft(Xk,N)%計(jì)算逆離散傅里葉變換%[xn]=idft(Xk,N)n=[0:1:N-1];2/3

k=[0:1:N-1];WN=exp(-j*2*pi/N);nk=n'*k;實(shí)驗(yàn)結(jié)果：x1(n)

WNnk=WN.^(-nk);xn=(Xk*WNnk)/N;x2(n)

8642

8642

250200150100500

05102025

0

0510152025

0

05102025點(diǎn)圓周卷

點(diǎn)

點(diǎn)25020015010050

2502