有關(guān)傅里葉變換的MATLAB仿真

1、有關(guān)傅里葉變換的MATLAB仿真Homework 1：1) Determine the DFT of sequence x(n)=R4(n) with N=4, N=8 and N=16 by MATLAB, and plot the figures;程序如下：functionXk = DFT(xn,N) k = 0:1:N-1; n = 0:1:N-1; Wn = exp(-j*2*pi/N); kn = k'*n; Wn_kn = Wn.kn; Xk = xn*Wn_kn; clearxn1=1 1 1 1;xn2=1 1 1 1 0 0 0 0;xn3=1 1 1 1 0 0 0

2、 0 0 0 0 0 0 0 0 0;N1=length(xn1);N2=length(xn2);N3=length(xn3);XK1=DFT(xn1,N1);magX1=abs(XK1);XK2=DFT(xn2,N2);magX2=abs(XK2);XK3=DFT(xn3,N3);magX3=abs(XK3)subplot(3,1,1);L1=0:1:N1-1;stem(L1,magX1);axis(0 N1 0 5);subplot(3,1,2);L2=0:1:N2-1;stem(L2,magX2);axis(0 N2 0 5);subplot(3,1,3);L3=0:1:N3-1;ste

3、m(L3,magX3);axis(0 N3 0 5);最終方針波形如下：2) Determine the FT of sequence x(n)=R4(n) by MATLAB, and plot the figure;程序如下：function Ke=FT(xn,N) n=0:1:N-1;w=0: 0.01*pi:2*pi; Wn=exp(-j*n'*w); Ke=xn*Wn; endclear;xn=1 1 1 1;w=0: 0.01*pi:2*pi;N=length(xn);Ke=FT(xn,N);Ke1=abs(Ke);plot(w,Ke1);axis(0 2*pi 0 5);

4、最終仿真波形如下：3) Compare figures and give the relationship between DFT and FT;程序如下：（調(diào)用函數(shù)上邊已經(jīng)求得，這里不再重復(fù)）clearxn1=1 1 1 1;xn2=1 1 1 1 0 0 0 0;xn3=1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0;N1=length(xn1);N2=length(xn2);N3=length(xn3);XK1=DFT(xn1,N1);magX1=abs(XK1);XK2=DFT(xn2,N2);magX2=abs(XK2);XK3=DFT(xn3,N3);magX3=a

5、bs(XK3);subplot(4,1,1);L1=0:1:N1-1;stem(L1,magX1);axis(0 N1 0 5);xlabel('N=4');subplot(4,1,2);L2=0:1:N2-1;stem(L2,magX2);axis(0 N2 0 5);xlabel('N=8');subplot(4,1,3);L3=0:1:N3-1;stem(L3,magX3);axis(0 N3 0 5);xlabel('N=16');subplot(4,1,4);xn=1 1 1 1;w=0: 0.01*pi:2*pi;N=length(x

6、n);Ke=FT(xn,N);Ke1=abs(Ke);plot(w,Ke1);axis(0 2*pi 0 5);xlabel('FT');Homework 2：1) Computing the 24-points DFTs of the two sequences that x1(n)= cos(n/6) and x2(n)= cos(n/4) using a single 24-point DFT by Matlab;2) Plot the figure of x1(n), x2(n), |X1(k)| and |X2(k)|;3) Analysis the value of

7、 |X1(k)| and |X2(k)|;4) Applying IDFT to X1(k) and X2(k) to obtain x1N(n) and x2N(n);程序如下：functionXk = DFT(xn,N) k = 0:1:N-1; n = 0:1:N-1; Wn = exp(-j*2*pi/N); kn = k'*n; Wn_kn = Wn.kn; Xk = xn*Wn_kn; functionxn =IDFT(Xk,N) k = 0:1:N-1; n = 0:1:N-1; Wn = exp(-j*2*pi/N); kn = k'*n; Wn_kn = Wn

8、.(-kn); xn = (Xk*Wn_kn)/N; clearN=24;n=0:23;xn1=cos(n*pi/6);xn2=cos(n*pi/4);xn=xn1+j*xn2;XK=DFT(xn,N);XKN=conj(XK);for k=2:NXKN(k)=conj(XK(N-k+2);endXK1=(XK+XKN)/2XK2=(XK-XKN)/(2*j)x1n=IDFT(XK1,N);x2n=IDFT(XK2,N);subplot(2,2,1)stem(n,xn1);subplot(2,2,2)stem(n,xn2);subplot(2,2,3)stem(n,x1n);axis(0 30 -1 1);subplot(2,2,4)stem(n,x2n);axis(0 30 -1 1);最終仿真波形