周一。题目：证明DFT{a*gn+b*hn}=a*Gk+b*Hk；已知gn=2*cos(0.2*pi*n1);n1=0:12hn=3*cos(0.3*pi*n2);n2=0:10;N=15;a=2;b=3;程序代码：n1=0:12;gn=2*cos(0.2*pi*n1);n2=0:10;hn=3*cos(0.3*pi*n2);N=15;n=0:N-1;gn=[gnzeros(1,N-length(gn))];hn=[hnzeros(1,N-length(hn))];a=2;b=3;yn=a*gn+b*hn;Gk=fft(gn);Hk=fft(hn);Yk=fft(yn);Yk1=a*Gk+b*Hk;Yd=Yk-Yk1;subplot(3,1,1);stem(n,Yk);title('Yk');xlabel('indexn');ylabel('Amplitude');subplot(3,1,2);stem(n,Yk1);title('Yk1');xlabel('indexn');ylabel('Amplitude');subplot(3,1,3);stem(n,Yd);title('Diffrencesequence');xlabel('indexn');ylabel('Amplitude');axis([015-5050]);周二。题目证明圆周频移DFT{*gn}=G[(n-k0)]n=0:9;gn=[1,-2,3,4,-5,6,7,8,9,-3];N=10;k0=3;w=exp(-j*2*pi/N);wk=w.^(n*k0);gk=gn.*wk;Gk=fft(gn,N);Gk0=fft(gk,N);Gk1=cirshftt(Gk,k0,N);yd=Gk0-Gk1;subplot(3,1,1);stem(n,abs(Gk0));title('Gk0');xlabel('indexn');ylabel('Amplitude');subplot(3,1,2);stem(n,abs(Gk1));title('Gk1');xlabel('indexn');ylabel('Amplitude');subplot(3,1,3);stem(n,abs(yd));title('yd');xlabel('Diffrencesequence');ylabel('Amplitude');axis([01001]);周四。题目：证明圆周时移：IDFT{G[k]}=g[（n-k0）]n=0:9;gn=[1,-2,3,4,-5,6,7,8,9,-3];N=10;k0=3;W=exp(j*2*pi/N);Wn=W.^(n*k0);Gk=fft(gn,N);Gk0=Gk.*Wn;y=ifft(Gk0,N);gk=cirshftt(gn,k0,N);yd=y-gk;subplot(3,1,1);stem(n,y);title('y');xlabel('indexn');ylabel('Amplitude');subplot(3,1,2);stem(n,gk);title('gk');xlabel('indexn');ylabel('Amplitude');subplot(3,1,3);stem(n,yd);title('yd');xlabel('Diffrencesequence');ylabel('Amplitude');axis([010-8080]);周六。题目：验证帕森瓦尔定理，g[n]=g1+g2N=12n1=0:11;g1=-2*exp(-j*0.2*pi*n1);n2=0:9;g2=3*sin(0.15*pi*n2);g2=[g200];g=g1+g2;y1=abs(g.*g);G=fft(g);Y2=abs(G.*G);s1=sum(y1);s2=sum(Y2)/N;d=s1-s2%输出d，若等于0，便得到验证subplot(3,1,1);stem(s1);subplot(3,1,2);stem(s2);subplot(3,1,3);stem(d);星期三题目：验证调制定理DFT{g[n]h[n]}=N=12;k=2;n1=0:11;gn=-2*exp(-j*0.2*pi*n1);n2=0:9;hn=3*sin(0.15*pi*n2);hn=[hn,0,0];wn=gn.*hn;Wn1=fft(wn,N);Gn=fft(gn,N);Hn=fft(hn,N);Wn2=circonv(Gn,Hn,N);Delter=Wn1-Wn2;Subplot(3,1,1);st