探究FM信号的调制与解调方波的调制：clear allts=0.001; %信号抽样时间间隔t=0:ts:10-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft的频率分辨率msg=square(4*t);msg2=reshape(msg.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(2,1,1)plot(t,fftshift(abs(Pm)))title('消息信号频谱')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=250; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号Pfm=fft(Sfm)/fs; % FM信号频谱subplot(2,1,2)plot(f,fftshift(abs(Pfm))) % 画出已调信号频谱title('FM信号频谱')Pc=sum(abs(Sfm).^2)/length(Sfm) %已调信号功率Ps=sum(abs(msg2).^2)/length(msg2) %消息信号功率fm=50;betaf=kf*max(msg)/fm % 调制指数W=2*(betaf+1)*fm % 调制信号带宽0123456789100246消息信号频谱-500-400-300-200-10001002003004005000123FM 信号频谱已调信号的功率：Pc =0.5000消息信号的功率：Ps =1调制指数：betaf =1调制信号的带宽：W =200正弦信号的FM 调制：clear allts=0.001; %信号抽样时间间隔t=0:ts:10-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft 的频率分辨率msg=sin(2*pi*t);msg2=reshape(msg.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(2,1,1)plot(t,fftshift(abs(Pm)))title('消息信号频谱')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=250; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号Pfm=fft(Sfm)/fs; % FM 信号频谱subplot(2,1,2)plot(f,fftshift(abs(Pfm))) % 画出已调信号频谱title('FM 信号频谱')Pc=sum(abs(Sfm).^2)/length(Sfm) %已调信号功率Ps=sum(abs(msg2).^2)/length(msg2) %消息信号功率fm=50;betaf=kf*max(msg)/fm % 调制指数W=2*(betaf+1)*fm % 调制信号带宽012345678910012345消息信号频谱-500-400-300-200-100010020030040050000.51FM 信号频谱Pc = 0.5000 Ps = 0.5000betaf =1 W = 200已调信号的功率：Pc =0.5007消息信号的功率：Ps =0.4975调制指数：betaf =1调制信号的带宽：W =200锯齿波FM 调制：clear allts=0.001; %信号抽样时间间隔t=0:ts:10-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft的频率分辨率msg=sawtooth(8*pi*t);msg2=reshape(msg.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(2,1,1)plot(t,fftshift(abs(Pm)))title('消息信号频谱')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=250; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号Pfm=fft(Sfm)/fs; % FM信号频谱subplot(2,1,2)plot(f,fftshift(abs(Pfm))) % 画出已调信号频谱title('FM信号频谱')Pc=sum(abs(Sfm).^2)/length(Sfm) %已调信号功率Ps=sum(abs(msg2).^2)/length(msg2) %消息信号功率fm=50;betaf=kf*max(msg)/fm % 调制指数W=2*(betaf+1)*fm01234567891001234消息信号频谱-500-400-300-200-100010020030040050000.511.5FM 信号频谱已调信号的功率：Pc =0.5000消息信号的功率：Ps =0.3333调制指数：betaf =0.9920调制信号的带宽： W =199.2000不同信号的调制与解调信号：输入信号：square 方波clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft 的频率分辨率msg=2*square(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,20,'measured'); %调制信号通过A WGN信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1,'g');title('信噪比为20dB时的解调信号')00.51 1.52 2.53 3.54 4.55-22消息信号00.51 1.52 2.53 3.54 4.55-55无噪声的解调信号00.51 1.52 2.53 3.54 4.55-505信噪比为20dB 时的解调信号信噪比为10dB 时clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft 的频率分辨率msg=2*square(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM 调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号 dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,20,'measured'); %调制信号通过A WGN 信道 y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1,'g');title('信噪比为10dB 时的解调信号')00.51 1.52 2.53 3.54 4.55-22消息信号00.51 1.52 2.53 3.54 4.55-55无噪声的解调信号00.51 1.52 2.53 3.54 4.55-10010信噪比为10dB 时的解调信号信噪比为2dB 时clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft的频率分辨率msg=2*square(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,20,'measured'); %调制信号通过A WGN信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1,'g');title('信噪比为2dB时的解调信号')00.51 1.52 2.53 3.54 4.55-22消息信号00.51 1.52 2.53 3.54 4.55-55无噪声的解调信号00.51 1.52 2.53 3.54 4.55-10010信噪比为2dB 时的解调信号余弦波：clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft 的频率分辨率msg=cos(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式 msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM 调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,20,'measured'); %调制信号通过A WGN 信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1,'g');title('信噪比为20dB 时的解调信号')00.51 1.52 2.53 3.54 4.55-11消息信号00.51 1.52 2.53 3.54 4.55-22无噪声的解调信号00.51 1.52 2.53 3.54 4.55-202信噪比为20dB 时的解调信号clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft的频率分辨率msg=cos(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,10,'measured'); %调制信号通过A WGN信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1);title('信噪比为10dB时的解调信号')00.51 1.52 2.53 3.54 4.55-11消息信号00.51 1.52 2.53 3.54 4.55-22无噪声的解调信号00.51 1.52 2.53 3.54 4.55-505信噪比为10dB 时的解调信号信噪比为2dB 时 clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft 的频率分辨率msg=cos(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM 调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,2,'measured'); %调制信号通过A WGN 信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1);title('信噪比为2dB 时的解调信号')00.51 1.52 2.53 3.54 4.55-11消息信号00.51 1.52 2.53 3.54 4.55-22无噪声的解调信号00.51 1.52 2.53 3.54 4.55-10010信噪比为2dB 时的解调信号方波信号的解调信噪比为20dB 时clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft的频率分辨率msg=2*square(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,20,'measured'); %调制信号通过A WGN信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1);title('信噪比为20dB时的解调信号')00.51 1.52 2.53 3.54 4.55-22消息信号00.51 1.52 2.53 3.54 4.55-55无噪声的解调信号00.51 1.52 2.53 3.54 4.55-505信噪比为20dB 时的解调信号信噪比为10dB 时clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft 的频率分辨率msg=2*square(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM 调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,10,'measured'); %调制信号通过A WGN 信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1);title('信噪比为10dB 时的解调信号')00.51 1.52 2.53 3.54 4.55-22消息信号00.51 1.52 2.53 3.54 4.55-55无噪声的解调信号00.51 1.52 2.53 3.54 4.55-10010信噪比为10dB 时的解调信号信噪比为2dB 时clear allts=0.001; %信号抽样时间间隔t=0:ts:5-ts; %时间向量fs=1/ts; %抽样频率df=fs/length(t); %fft的频率分辨率msg=2*square(8*pi*[0:0.001:0.999]);msg1=msg.'*ones(1,fs/200); %扩展成取样信号形式msg2=reshape(msg1.',1,length(t));Pm=fft(msg2)/fs; %求消息信号的频谱f=-fs/2:df:fs/2-df;subplot(3,1,1)plot(t,msg2) %画出消息信号title('消息信号')int_msg(1)=0; %消息信号积分for ii=1:length(t)-1int_msg(ii+1)=int_msg(ii)+msg2(ii)*ts;endkf=50;fc=300; %载波频率Sfm=cos(2*pi*fc*t+2*pi*kf*int_msg); %调频信号phase=angle(hilbert(Sfm).*exp(-j*2*pi*fc*t)); %FM调制信号相位phi=unwrap(phase);dem=(1/(2*pi*kf)*diff(phi)/ts); %求相位微分，得到消息信号dem(length(t))=0;subplot(3,1,2)plot(t,dem);title('无噪声的解调信号')y1=awgn(Sfm,2,'measured'); %调制信号通过A WGN信道y1(find(y1>1))=1; %调制信号限幅y1(find(y1<-1))=-1;phase1=angle(hilbert(y1).*exp(-j*2*pi*fc*t)); %信号解调phi1=unwrap(phase1);dem1=(1/(2*pi*kf)*diff(phi1)/ts);dem1(length(t))=0;subplot(3,1,3)plot(t,dem1);title('信噪比为2dB时的解调信号')00.51 1.52 2.53 3.54 4.55-22消息信号00.51 1.52 2.53 3.54 4.55-55无噪声的解调信号00.51 1.52 2.53 3.54 4.55-10010信噪比为2dB 时的解调信号 FM 信号的解调采用的解调器是具有频率—电压转换特性的鉴频器，因而解调出的消息信号幅度是随着输入频率变化的。