高斯滤波器特性.ppt

a=0.25，Bb=2.4 a=0.5，Bb=1.2 a=1，Bb=0.6 a=2，Bb=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(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)/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，Bb=2.4 a=0.5，Bb=1.2 a=1，Bb=0.6 a=2，Bb=0.3,t1=-1.5:0.01:1.5; t2=-0.5:0.01:0.5;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+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,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、Tb=0.1，fc=20时， 比较时域波形和功率谱的情况（差异） 注意：采样频率fs=1000，数据率Rb=10 数字角频率=模拟角频率*Ts，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、Tb=0.1，fc=100时，观察区间T=1 功率谱计算方法： 利用MATLAB的FFT函数 利用MATLAB的pwelch函数,d(k)=1,0,0,01,0,1,1,0,0，采样间隔Ts=0.001,利用MATLAB的FFT函数计算功率谱,t=0.001:0.001:1;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),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)=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).*(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); 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 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)=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).*(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=pwelch(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 -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).*(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)+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,wh