MATLAB比較，觀察周期信號(hào)的分解與合成過(guò)程。%dm09101%觀察周期方波信號(hào)的分解與合成%m：傅里葉級(jí)數(shù)展開(kāi)的項(xiàng)數(shù)display('Pleaseinputthevalueofm(傅里葉級(jí)數(shù)展開(kāi)的項(xiàng)數(shù))');%在命令窗口顯示提示信息m=input('m); 鍵盤(pán)輸入傅里葉級(jí)數(shù)展開(kāi)的項(xiàng)數(shù)t-2*pi:0.01:2*pi; 時(shí)域波形的時(shí)間范圍-2π~2π，0.01nround(length(t)/4); 1/2周期的數(shù)據(jù)點(diǎn)數(shù)fcos(t).*(t<(-3*pi/2))+cos(t).*((t>(-pi/2))&(t<(pi/2)))+cos(t).*(t>3*pi/2); %周期方波信號(hào)y=zeros(m+1,max(size(t)));y(m+1,:)=f';figure(1);plot(t/pi,y(m+1,:),'LineWidth',2); %繪制方波信grid; %在圖形中加入柵格axis([-22-0.51.5]); %范圍title('周期信號(hào)'); %給顯示的圖形加上標(biāo)題xlabel('單位pi','Fontsize',8); %顯示橫坐標(biāo)單x=zeros(size(t));kk='直流分量';pause;k=1;x=x+1/pi;y(1,:x; %計(jì)算各次諧波疊加和plot(t/pi,y(m+1,:),'LineWidth',2);holdon;plot(t/pi,y(1,:),'r','LineWidth',3); %繪制諧波疊加信號(hào)holdoff;grid;axis([-22-0.51.5]);title(strcat(kk));xlabel('單位pi','Fontsize',8);kk=strcat(kk,'和第',num2str(k));pause;k=k+1;x=x+0.5.*cos(t);y(2,:x; %計(jì)算各次諧波疊加和plot(t/pi,y(m+1,:),'LineWidth',2);holdon;plot(t/pi,y(2,:),'r','LineWidth',3); %繪制諧波疊加信號(hào)holdoff;grid;axis([-22-0.51.5]);title(strcat(kk,'次諧波疊加'));xlabel('單位pi','Fontsize',8);kk=strcat(kk,'、',num2str(k));pause;x=x+2/(3.*pi).*cos(2.*t);y(3,:x; %計(jì)算各次諧波疊加和plot(t/pi,y(m+1,:),'LineWidth',2);holdon;plot(t/pi,y(3,:),'r','LineWidth',3);holdoff;grid;axis([-22-0.51.5]);title(strcat(kk,'次諧波疊加'));xlabel('單位pi','Fontsize',8);kk=strcat(kk,'、',num2str(k+2));pause;x=x-2/(15.*pi).*cos(4.*t);

%繪制諧波疊加信號(hào)y(4,:)=x;plot(t/pi,y(m+1,:),'LineWidth',2);holdon;plot(t/pi,y(4,:),'r','LineWidth',3);holdoff;grid;axis([-22-0.51.5]);title(strcat(kk,'次諧波疊加'));xlabel('單位pi','Fontsize',8);pause;plot(t/pi,y(1:m+1,:),'LineWidth',3);grid;axis([-22-0.51.5]);title('各次諧波疊加波形');xlabel('單位pi','Fontsize',8);%End

%計(jì)算各次諧波疊加和

%繪制諧波疊加信號(hào)-0.5-2-1.5-1-0.50單位pi0.5-0.5-2-1.5-1-0.50單位pi0.511.521.510.50-0.5-2 -1.5 -1

周期信號(hào)0 0.5 1 1.5 2單位pi1.510.50

直流分量1.510.50

直流分量和第次諧波疊加-0.5-2 -1.5 -1

0 0.5 1 1.5 2單位pi1.510.50

直流分量和第次諧波疊加1.510.50

直流分量和第次諧波疊加-0.5-2 -1.5 -1

0 0.5 1 1.5 2單位pi1.510.50

各次諧波疊加波形%dm09201%繪制周期信號(hào)的頻譜特性functionCTFS_RP%以周期矩形脈沖信號(hào)為例，計(jì)算其頻譜特性%%%%1,2,3,...次諧波余弦項(xiàng)展開(kāi)系數(shù)%1,2,3,...次諧波正弦項(xiàng)展開(kāi)系數(shù)%%display('PleaseinputthevalueofT,taoandNf'); T=input('Ttao=input('tao=');Nf=input('Nf=');symstnkx;%變量Nn=32;32位an=zeros(Nf+1,1);分配n系數(shù)數(shù)組bn=zeros(Nf+1,1);分配n系數(shù)數(shù)組x=(heaviside(t+tao/2)-heaviside(t-tao/2))*cos((pi/tao)*t);個(gè)周期的脈沖信號(hào)u(t+tao/2)-u(t-tao/2)

構(gòu)造%A0=2*int(x,t,-T/2,T/2)/T;As=2*int(x*cos(2*pi*n*t/T),t,-T/2,T/2)/T;Bs=2*int(x*sin(2*pi*n*t/T),t,-T/2,T/2)/T;an(1)=double(vpa(A0,Nn));fork=1:Nfan(k+1)=double(vpa(subs(As,n,k),Nn));bn(k+1)=double(vpa(subs(Bs,n,k),Nn));endcn=sqrt(an.*an+bn.*bn);t=-T*2:0.001:T*2;

求出a0anbnA0ASCII碼數(shù)值數(shù)組AsASCII碼數(shù)值數(shù)組BsASCII碼數(shù)值數(shù)組計(jì)算度譜xx=(heaviside(t+tao/2)-heaviside(t-tao/2)).*cos((pi/tao).*t);forkk=1:2xx=xx+(heaviside(t+tao/2+kk*T)-heaviside(t-tao/2+kk*T)).*cos((pi/tao).*(t+kk*T))+(heaviside(t+tao/2-kk*T)-heaviside(t-tao/2-kk*T)).*cos((pi/tao).*(t-kk*T)); pulstran函數(shù)生成矩形脈沖信號(hào)endsubplot(211);clearsubplot;plot(t,xx);axis([-T*2T*201.1]);%title('周期矩形脈沖信號(hào)','Fontsize',8);

將顯示31個(gè)子窗口%指定標(biāo)系范圍注標(biāo)題s1strcat('周期矩形脈沖信號(hào)T=',num2str(T),'Tao=',num2str(tao),'t');xlabel(s1,'Fontsize',8); 簽subplot(212);k=0:Nf;stem(k,cn);holdon;plot(k,cn);xlabel('幅度譜\omega','Fontsize',8);%EndPleaseinputthevalueofT,taoandNfT=2*pitao=piNf=3010.80.60.4

指向第2%譜%譜包絡(luò)線(xiàn)0.20

-10 -5 0 5 10周期矩形脈沖信號(hào)T=6.2832Tao=3.1416t0.80.60.40.200 5 10 15幅度譜

20 25 30PleaseinputthevalueofT,taoandNfT=2*pitao=2*piNf=3010.80.60.40.20

-10 -5 0 5 10周期矩形脈沖信號(hào)T=6.2832Tao=6.2832t1.510.500 5 10 15幅度譜

20 25 30PleaseinputthevalueofT,taoandNfT=20*pitao=piNf=3010.80.60.40.20

-100 -50 0 50 100周期矩形脈沖信號(hào)T=62.8319Tao=3.1416t0.080.060.040.0200 5 10 15幅度譜

20 25 30PleaseinputthevalueofT,taoandNfT=20*pitao=4*piNf=3010.80.60.40.20

-100 -50 0 50 100周期矩形脈沖信號(hào)T=62.8319Ta