（1）所用滤波器函数：巴特沃斯滤波器% 注: wp（或Wp）为通带截止频率 ws(或Ws)为阻带截止频率 Rp为通带衰减 As为阻带衰减%butterworth低通滤波器原型设计函数要求Ws>Wp>0 As>Rp>0function [b,a]=afd_butt(Wp,Ws,Rp,As)N=ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(Wp/Ws)));%上条语句为求滤波器阶数 N为整数%ceil 朝正无穷大方向取整fprintf('\n Butterworth Filter Order=%2.0f\n',N)OmegaC=Wp/((10^(Rp/10)-1)^(1/(2*N))) %求对应于N的3db截止频率[b,a]=u_buttap(N,OmegaC);（2）傅里叶变换函数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;设计部分：1.普通AM调制与解调%单音普通调幅波调制y=amod(x,t,fs,t0,fc,Vm0,ma)要求fs>2fc%x调制信号，t调制信号自变量,t0采样区间，fs采样频率，%fc载波频率，Vm0输出载波电压振幅，ma调幅度t0=0.1;fs=12000;fc=1000;Vm0=2.5;ma=0.25;n=-t0/2:1/fs:t0/2;x=4*cos(150*pi*n); %调制信号y2=Vm0*cos(2*pi*fc*n); %载波信号figure(1)subplot(2,1,1);plot(n,y2);axis([-0.01,0.01,-5,5]);title('载波信号');N=length(x);Y2=fft(y2); subplot(2,1,2);plot(n,Y2);title('载波信号频谱'); %画出频谱波形y=Vm0*(1+ma*x/Vm0).*cos(2*pi*fc*n); figure(2)subplot(2,1,1);plot(n,x)title('调制信号');subplot(2,1,2)plot(n,y)title('已调波信号');X=fft(x);Y=fft(y);w=0:2*pi/(N-1):2*pi; figure(3)subplot(2,1,1);plot(w,abs(X)) axis([0,pi/4,0,2000]); title('调制信号频谱'); subplot(2,1,2);plot(w,abs(Y)) axis([pi/6,pi/4,0,1200]);title('已调波信号频谱'); %画出频谱波形 y1=y-2*cos(800*pi*n);y2=Vm0*y1.*cos(2*pi*fc*n); %将已调幅波信号的频谱搬移到原调制信号频谱处 wp=40/N*pi;ws=60/N*pi;Rp=1;As=15;T=1; %滤波器参数设计OmegaP=wp/T;OmegaS=ws/T;[cs,ds]=afd_butt(OmegaP,OmegaS,Rp,As); [b,a]=imp_invr(cs,ds,T); y=filter(b,a,y2); figure(4)subplot(2,1,1);plot(n,y) title('解调波'); Y=fft(y);subplot(2,1,2);plot(w,abs(Y)) axis([0,pi/6,0,1000]);title('解调信号频谱'); %画出频谱波形 结果：Butterworth Filter Order= 6 OmegaC = 0.1171载波信号频谱-4-2024调制信号-4-2024已调波信号已调波信号频谱解调波解调信号频谱解调波解调信号频谱2.抑制双边带调制与解调%单音抑制载波双边带调制y=amod(x,t,fs,t0,fc,Vm0,ma)要求fs>2fc %x调制信号， t0采样区间，fs采样频率，%fc载波频率，Vm0输出载波电压振幅，ma调幅度t0=0.1;fs=12000;fc=1000;Vm0=2.5;ma=0.25;n=-t0/2:1/fs:t0/2;x=4*cos(150*pi*n); %调制信号y=Vm0*x.*cos(2*pi*fc*n); %载波信号figure(1)subplot(2,1,1)plot(n,x)title('调制信号');subplot(2,1,2)plot(n,y)title('已调波信号');N=length(x);X=fft(x);Y=fft(y);w=0:2*pi/(N-1):2*pi;figure(2)subplot(2,1,1)plot(w,abs(X))axis([0,pi/4,0,2000]);title('调制信号频谱'); %画出频谱波形subplot(2,1,2)plot(w,abs(Y)) axis([pi/6,pi/4,0,2200]);title('已调波信号频谱'); %画出频谱波形y1=y-2*cos(2000*pi*n);y2=Vm0*y1.*cos(2*pi*fc*n); %将已调幅波信号的频谱搬移到原调制信号频谱处wp=40/N*pi;ws=60/N*pi;Rp=1;As=15;T=1; %滤波器参数设计OmegaP=wp/T;OmegaS=ws/T;[cs,ds]=afd_butt(OmegaP,OmegaS,Rp,As); [b,a]=imp_invr(cs,ds,T);y=filter(b,a,y2);figure(3)subplot(2,1,1)plot(n,y)title('解调波');Y=fft(y);subplot(2,1,2)plot(w,abs(Y))axis([0,pi/6,0,5000]);title('解调信号频谱'); %画出频谱波形结果：Butterworth Filter Order= 6 OmegaC = 0.1171调制信号已调波信号500100015002000500100015002000解调波解调信号频谱3.单边带调制与解调%单音单边带调制y=amod(x,t,fs,t0,fc,Vm0,ma)要求fs>2fc %x 调制信号，t0采样区间，fs 采样频率， %fc 载波频率，Vm0输出载波电压振幅，ma 调幅度 t0=0.1;fs=12000;fc=1000;Vm0=2.5;ma=0.25; n=-t0/2:1/fs:t0/2; N=length(n);x1=4*cos(150*pi*n); %调制信号 x2=hilbert(x1,N);y=(Vm0*x1.*cos(2*pi*fc*n)-Vm0*x2.*sin(2*pi*fc*n))/2; figure(1) subplot(2,1,1)plot(n,x1) title('调制信号'); subplot(2,1,2) plot(n,y)title('已调波信号'); X=fft(x1); Y=fft(y);w=0:2*pi/(N-1):2*pi; figure(2) subplot(2,1,1)plot(w,abs(X))axis([0,pi/4,0,3000]);title('调制信号频谱'); %画出频谱波形subplot(2,1,2)plot(w,abs(Y))axis([pi/6,pi/4,0,2500]);title('已调波信号频谱'); %画出频谱波形y1=y-2*cos(1500*pi*n);y2=Vm0*y1.*cos(2*pi*fc*n); %将已调幅波信号的频谱搬移到原调制信号频谱处wp=40/N*pi;ws=60/N*pi;Rp=1;As=15;T=1; %滤波器参数设计OmegaP=wp/T;OmegaS=ws/T;[cs,ds]=afd_butt(OmegaP,OmegaS,Rp,As); [b,a]=imp_invr(cs,ds,T);y=filter(b,a,y2);figure(3)subplot(2,1,1)plot(n,y)title('解调波');Y=fft(y);subplot(2,1,2)plot(w,abs(Y))axis([0,pi/6,0,2500]);title('解调信号频谱'); %画出频谱波形结果：Butterworth Filter Order= 6 OmegaC = 0.1171调制信号已调波信号调制信号频谱已调波信号频谱解调波解调信号频谱7 参考文献[1] 信号与系统课程组. 信号与系统课程设计指导，2007.10[2] 吴大正. 信号与线性系统分析（第四版）. 高等教育出版社，2005.8[3] 谢嘉奎. 电子线路—非线性部分(第四版). 高等教育出版社，2003,2[4] 黄永安等.Matlab7.0/Simulink6.0建模仿真开发与高级工程应用. 清华大学出版社，2005.12[5] 江建军. LabVIEW程序设计教程. 电子工业出版社, 2008.03[6]张化光，孙秋野.MATLAB/Simulink实用教程. 北京人民邮电出版社，2009。