傅里叶系数,周期方波信号的傅里叶系数,周期方波信号的频谱,周期矩形波频谱,周期矩形波频谱对比（一）, subplot(2,1,1) x=-8:1:8; stem(x,0.5.*sinc(0.5.*x) subplot(2,1,2) x=-16:1:16; stem(x,0.25.*sinc(0.25.*x) axis(-16 16 -0.3 +0.3); grid on;,周期矩形波的频谱对比（二）, x=-8:0.001:8; subplot(3,1,1) plot(x,square(2*pi*x+0.5*pi,50) axis(-8 8 -1.5 +1.5); subplot(3,1,2) plot(x,square(pi*x+0.25*pi,25) axis(-8 8 -1.5 +1.5); subplot(3,1,3) plot(x,square(0.5*pi*x+0.125*pi,12.5) axis(-8 8 -1.5 +1.5);, subplot(3,1,1) x=-8:1:8; stem(x,0.5.*sinc(0.5.*x) subplot(3,1,2) x=-16:1:16; stem(x,0.25.*sinc(0.25.*x) axis(-16 16 -0.3 +0.3); subplot(3,1,3) x=-32:1:32; stem(x,0.125.*sinc(0.125.*x) axis(-32 32 -0.2 +0.2);,非周期矩形信号的频谱, subplot(1,2,1) x=-8:0.001:8; plot(x,square(0.5/4*pi*x+0.125/4*pi,12.5/4) axis(-8 8 -1.5 +1.5); subplot(1,2,2) x=-128:1:128; stem(x,0.125/4.*sinc(0.125/4.*x) axis(-128 128 -0.02 +0.05); box on,连续型频谱,周期矩形波的连续谱,周期矩形波的连续谱和离散谱对比, subplot(3,2,1) x=-8:1:8; stem(x,0.5.*sinc(0.5.*x) axis(-8 8 -0.2 +0.6); title(T=T_0);, subplot(3,2,3) x=-16:1:16; stem(x,0.25.*sinc(0.25.*x) axis(-16 16 -0.2 +0.6); title(T=2T_0); subplot(3,2,5) x=-32:1:32; stem(x,0.125.*sinc(0.125.*x) axis(-32 32 -0.2 +0.6); title(T=4T_0);, subplot(3,2,2) d=zeros(16,2); x=-8:1:8; for i=1:16 d(i)=x(i); d(16+i)= 0.5.*sinc(0.5.*x(i); end x=-8:0.001:8; plot(x,0.5.*sinc(0.5*x), r:); hold on; s=pulstran(x-0.5,d,rectpuls,1);plot(x,s) ; axis(-8 8 -0.2 +0.6);, subplot(3,2,4) d=zeros(32,2); x=-16:1:16; for i=1:32 d(i)=x(i); d(32+i)= 0.5.*sinc(0.25*x(i); end x=-16:0.001:16; plot(x,0.5.*sinc(0.25*x), r:); hold on; s=pulstran(x-0.5,d,rectpuls,1);plot(x,s) ; axis(-16 16 -0.2 +0.6); subplot(3,2,6) d=zeros(64,2); x=-32:1:32; for i=1:64 d(i)=x(i); d(64+i)= 0.5.*sinc(0.125*x(i); end x=-32:0.001:32; plot(x,0.5.*sinc(0.125*x), r:); hold on; s=pulstran(x-0.5,d,rectpuls,1);plot(x,s) ; axis(-32 32 -0.2 +0.6);,傅里叶变换,单位冲激函数,周期信号的傅立叶变换,复指数信号的傅立叶变换,Matlab实现, f=1; subplot(1,2,1); t=-5:0.001:5; x=cos(2*pi*f*t); y=sin(2*pi*f*t); plot3(x,t,y); xlabel(x); ylabel(t); zlabel(y); set(gca,YDir,reverse); grid on; title(ejomega_0t的波形); subplot(1,2,2); xlabel(x); ylabel(omega); zlabel(y);, axis(-10 10 -10 10 -10 10); set(gca,YDir,reverse); grid on; arrow3d(0,2*pi*f,0,2*pi,2*pi*f,0,10, cylinder,0.15,0.5); title(ejomega_0t的傅立叶变换); line(0 0,-10 10,0 0);,余弦信号的傅立叶变换, f=1; subplot(1,2,1); t=-5:0.001:5; x=cos(2*pi*f*t); plot3(x,t,0*t); xlabel(x); ylabel(t); zlabel(y); set(gca,YDir,reverse); grid on; title(cosomega_0t的波形);, subplot(1,2,2); xlabel(x); ylabel(omega); zlabel(y); axis(-10 10 -10 10 -10 10); set(gca,YDir,reverse); grid on; arrow3d(0,2*pi*f,0,1*pi,2*pi*f,0,10, cylinder,0.3,0.5); arrow3d(0,-2*pi*f,0,1*pi,-2*pi*f,0,10, cylinder,0.3,0.5); title(cosomega_0t的傅立叶变换); line(0 0,-10 10,0 0);,正弦信号的傅立叶变换, f=1; subplot(1,2,1); t=-5:0.001:5; y=sin(2*pi*f*t); plot3(0*t,t,y); xlabel(x); ylabel(t); zlabel(y); set(gca,YDir,reverse); grid on; title(sinomega_0t的波形);, subplot(1,2,2); xlabel(x); ylabel(omega); zlabel(y); axis(-10 10 -10 10 -10 10); set(gca,YDir,reverse); grid on; arrow3d(0,2*pi*f,0,0,2*pi*f, -1*pi,10, cylinder,0.3,0.5); arrow3d(0,-2*pi*f,0,0, -2*pi*f, 1*pi,10, cylinder,0.3,0.5); title(sinomega_0t的傅立叶变换); line(0 0,-10 10,0 0);,直流信号的傅里叶变换, subplot(1,2,1); t=-1.5:0.001:1.5; y=rectpuls(t,4); plot(t,y) axis(-1.5 1.5 -0.5 1.5); xlabel(time);ylabel(magnitude); grid on, subplot(1,2,2); f=-4*2*pi:0.001:4*2*pi; xlabel(omega);ylabel(magnitude); axis(-4*2*pi 4*2*pi -0.5 1.5); grid on arrow(0,0,0,1); gtext(2pidelta(omega);, subplot(2,2,1); t=-1.5:0.001:1.5; y=rectpuls(t,1); plot(t,y) axis(-1.5 1.5 -0.5 2.5); grid on subplot(2,2,2); f=-4:0.001:4; X=sinc(f); plot(f,X) axis(-4 4 -0.5 2.5); grid on, subplot(2,2,3); t=-1.5:0.001:1.5; y=rectpuls(t,2); plot(t,y) axis(-1.5 1.5 -0.5 2.5); grid on subplot(2,2,4); f=-4:0.001:4; X=2*sinc(2*f); plot(f,X) axis(-4 4 -0.5 2.5); grid on, subplot(2,2,3); t=-1.5:0.001:1.5; y=rectpuls(t,2); plot(t,y) axis(-1.5 1.5 -0.5 2.5); grid on subplot(2,2,4); f=-4:0.001:4; X=2*sinc(2*f); plot(f,X) axis(-4 4 -0.5 2.5); grid on, subplot(2,2,3); t=-1.5:0.001:1.5; y=rectpuls(t,2); plot(t,y) axis(-1.5 1.5 -0.5 2.5); grid on subplot(2,2,4); f=-4:0.001:4; X=2*sinc(2*f); plot(f,X) axis(-4