高斯滤波器特性

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1、单击此处编辑母版标题样式,,单击此处编辑母版文本样式,,第二级,,第三级,,第四级,,第五级,,,*,——,a,=0.25，,B,b,=2.4,,——,,a,=0.5，,B,b,=1.2,,——,,a,=1，,B,b,=0.6,,——,,a,=2，,B,b,=0.3,高斯滤波器的传输函数,H,(,f,),f=0:0.05:2.5;,,y1=exp(-(0.25*f).^2);,,y2=exp(-(0.5*f).^2);,,y3=exp(-(f.^2));,,y4=exp(-(2*f).^2);,,plot(f,y1,'r',f,y2,'g',f,y3,'b',f,y4,'m');,,axis(

2、[0 2.5 0.7 1]);,,xlabel('f');ylabel('H(f)');,,title('Transfer Function of Gaussian Filter');,,——,a,=0.25,,——,,a,=0.5,,——,,a,=1,,——,,a,=2,t=0:0.01:1.5;,,y1=sqrt(pi)/0.25*exp(-((pi*t).^2)/0.25.^2);,,y2=sqrt(pi)/0.5*exp(-((pi*t).^2)/0.5.^2);,,y3=sqrt(pi)*exp(-(pi*t).^2);,,y4=sqrt(pi)/2*exp(-((pi*t).^2)

3、/2.^2);,,plot(t,y1,'r',t,y2,'g',t,y3,'b',t,y4,'m');,,xlabel('t/T');ylabel('h(t)');,,title('Impulse Response of Gaussian Filter');,高斯滤波器的冲激响应,h,(,t,),,高斯脉冲成形滤波器对矩形脉冲,b,(,t,)的响应波形,g,(,t,),——,a,=0.25，,B,b,=2.4,,——,,a,=0.5，,B,b,=1.2,,——,,a,=1，,B,b,=0.6,,——,,a,=2，,B,b,=0.3,,t1=-1.5:0.01:1.5;,,t2=-0.5:0.0

4、1:0.5;b1=ones(1,length(t2));,,y1=sqrt(pi)/0.25*exp(-((pi*t1).^2)/0.25.^2);,,z1=0.5*(erfc(pi/0.25*(t1-0.5))-erfc(pi/0.25*(t1+0.5)));,,y2=sqrt(pi)/0.5*exp(-((pi*t1).^2)/0.5.^2);,,z2=0.5*(erfc(pi/0.5*(t1-0.5))-erfc(pi/0.5*(t1+0.5)));,,y3=sqrt(pi)*exp(-(pi*t1).^2);,,z3=0.5*(erfc(pi*(t1-0.5))-erfc(pi*(t1

5、+0.5)));,,y4=sqrt(pi)/2*exp(-((pi*t1).^2)/2.^2);,,z4=0.5*(erfc(pi/2*(t1-0.5))-erfc(pi/2*(t1+0.5)));,,subplot(3,1,1),plot(t2,b1);axis([-1.5 1.5 0 1.5]);xlabel('t/T');ylabel('b(t)');,,title('rect impulse input of Gaussian pulse shaping filter');,,subplot(3,1,2),plot(t1,y1,'r',t1,y2,'g',t1,y3,'b',t1,y4

6、,'m');,,xlabel('t/T');ylabel('h(t)');title('impulse response of Gaussian pulse shaping filter');,,subplot(3,1,3),plot(t1,z1,'r',t1,z2,'g',t1,z3,'b',t1,z4,'m');xlabel('t/T');ylabel('g(t)');,,title('output (rect impulse response) of Gaussian pulse shaping filter');,,ASK、MSK信号及其功率谱仿真,2、,T,b,=0.1，,f,c,=

7、20时，,,比较时域波形和功率谱的情况（差异）,,注意：,采样频率,f,s,=1000，数据率,R,b,=10,,数字角频率=模拟角频率*,T,s,，数字频率=模拟角频率/采样频率=100/1000=0.1,,N,为pwelch的谱计算长度，采样数字频率,k,/,N,1、,T,b,=0.1，,f,c,=100时，观察区间,T=,1,,功率谱计算方法：,① 利用MATLAB的FFT函数,,② 利用MATLAB的,pwelch,函数,d,(,k,)={1,0,0,01,0,1,1,0,0}，采样间隔,T,s,=,0.001,,利用MATLAB的FFT函数计算功率谱,,t=0.001:0.001:1

8、;Tb=0.1;w0=20*pi/Tb;,,c=cos(w0*t);,,subplot(7,1,1),plot(t,c);,,d=[1 -1 -1 -1 1 -1 1 1 -1 -1];,,w=d*pi/(2*Tb);,,s=2*[ones(1,100) zeros(1,100) zeros(1,100) zeros(1,100) ones(1,100) zeros(1,100) ones(1,100) ones(1,100) zeros(1,100) zeros(1,100)]-1;,,subplot(7,1,2),plot(t,s);,,y0=c.*s;,,subplot(7,1,3),p

9、lot(t,y0);,,t1=0.001:0.001:Tb,,y1=cos((w0+w(1)).*t1);,,for i=1:9,,z(1)=0,,z(i+1)=z(i)+(d(i)-d(i+1))*i*pi/2;,,end,,y2=cos((w0+w(2)).*(t1+Tb)+z(2));,,y3=cos((w0+w(3)).*(t1+2*Tb)+z(3));,,y4=cos((w0+w(4)).*(t1+3*Tb)+z(4));,,y5=cos((w0+w(5)).*(t1+4*Tb)+z(5));,,y6=cos((w0+w(6)).*(t1+5*Tb)+z(6));,,y7=cos((

10、w0+w(7)).*(t1+6*Tb)+z(7));,,y8=cos((w0+w(8)).*(t1+7*Tb)+z(8));,,y9=cos((w0+w(9)).*(t1+8*Tb)+z(9));,,y10=cos((w0+w(10)).*(t1+9*Tb)+z(10));,,y=[y1 y2 y3 y4 y5 y6 y7 y8 y9 y10];,,subplot(7,1,4),plot(y);,,S=fft(s);,,subplot(7,1,5),plot(10*log10(abs(S).^2/max(abs(S).^2)));axis([0 1000 -50 0]);,,Y0=fft(y0

11、);,,subplot(7,1,6),plot(10*log10((abs(Y0).^2)/max(abs(Y0).^2)));axis([0 1000 -50 0]);,,Y=fft(y);,,subplot(7,1,7),plot(10*log10(abs(Y).^2/max(abs(Y).^2)));axis([0 1000 -50 0]);,,利用MATLAB的pwelch函数计算功率谱,,,t=0.001:0.001:1;Tb=0.1;w0=10*2*pi/Tb;,,c=cos(w0*t);,,subplot(7,1,1),plot(t,c);,,d=[1 -1 -1 -1 1 -1

12、 1 1 -1 -1];,,w=d*pi/(2*Tb);,,s=2*[ones(1,100) zeros(1,100) zeros(1,100) zeros(1,100) ones(1,100) zeros(1,100) ones(1,100) ones(1,100) zeros(1,100) zeros(1,100)]-1;,,subplot(7,1,2),plot(t,s);,,y0=c.*s;,,subplot(7,1,3),plot(t,y0);,,t1=0.001:0.001:Tb,,y1=cos((w0+w(1)).*t1);,,for i=1:9,,z(1)=0,,z(i+1)=

13、z(i)+(d(i)-d(i+1))*i*pi/2;,,end,,y2=cos((w0+w(2)).*(t1+Tb)+z(2));,,y3=cos((w0+w(3)).*(t1+2*Tb)+z(3));,,y4=cos((w0+w(4)).*(t1+3*Tb)+z(4));,,y5=cos((w0+w(5)).*(t1+4*Tb)+z(5));,,y6=cos((w0+w(6)).*(t1+5*Tb)+z(6));,,y7=cos((w0+w(7)).*(t1+6*Tb)+z(7));,,y8=cos((w0+w(8)).*(t1+7*Tb)+z(8));,,y9=cos((w0+w(9)).

14、*(t1+8*Tb)+z(9));,,y10=cos((w0+w(10)).*(t1+9*Tb)+z(10));,,y=[y1 y2 y3 y4 y5 y6 y7 y8 y9 y10];,,subplot(7,1,4),plot(y);,,N=4096;Fn=(-0.5:1/N:0.5-1/N);,,Y=pwelch(y,hamming(33),16,N,'whole');,,Y=10*log10(Y/max(Y)+0.000001);,,S=pwelch(s,hamming(33),16,N,'whole');,,S=10*log10(S/max(S)+0.000001);,,Y0=pwel

15、ch(y0,hamming(33),16,N,'whole');,,Y0=10*log10(Y0/max(Y0)+0.000001);,,subplot(7,1,5),plot(Fn,fftshift(S));,,subplot(7,1,6),plot(Fn,fftshift(Y0));,,subplot(7,1,7),plot(Fn,fftshift(Y));,,利用MATLAB的pwelch函数计算功率谱,,,利用MATLAB的pwelch函数计算功率谱,,,,t=0.001:0.001:1;Tb=0.1;w0=10*2*pi/Tb;,,c=cos(w0*t);,,d=[1 -1 -1 -

16、1 1 -1 1 1 -1 -1];,,w=d*pi/(2*Tb);,,s=2*[ones(1,100) zeros(1,100) zeros(1,100) zeros(1,100) ones(1,100) zeros(1,100) ones(1,100) ones(1,100) zeros(1,100) zeros(1,100)]-1;,,y0=c.*s;,,t1=0.001:0.001:Tb,,y1=cos((w0+w(1)).*t1);,,for i=1:9,,z(1)=0,,z(i+1)=z(i)+(d(i)-d(i+1))*i*pi/2;,,end,,y2=cos((w0+w(2))

17、.*(t1+Tb)+z(2));,,y3=cos((w0+w(3)).*(t1+2*Tb)+z(3));,,y4=cos((w0+w(4)).*(t1+3*Tb)+z(4));,,y5=cos((w0+w(5)).*(t1+4*Tb)+z(5));,,y6=cos((w0+w(6)).*(t1+5*Tb)+z(6));,,y7=cos((w0+w(7)).*(t1+6*Tb)+z(7));,,y8=cos((w0+w(8)).*(t1+7*Tb)+z(8));,,y9=cos((w0+w(9)).*(t1+8*Tb)+z(9));,,y10=cos((w0+w(10)).*(t1+9*Tb)+

18、z(10));,,y=[y1 y2 y3 y4 y5 y6 y7 y8 y9 y10];,,N=4096;,,Fn=-0.5:1/N:0.5-1/N;,,Y=pwelch(y,hamming(33),16,N,'whole');,,Y=10*log10(Y/max(Y)+0.000001);,,S=pwelch(s,hamming(33),16,N,'whole');,,S=10*log10(S/max(S)+0.000001);,,Y0=pwelch(y0,hamming(33),16,N,'whole');,,Y0=10*log10(Y0/max(Y0)+0.000001);,,plot(Fn,fftshift(Y0),'g',Fn,fftshift(Y),'b',Fn,fftshift(S),'r');grid on;,,