信号分选与数字滤波报告.doc

信号分选与数字滤波报告【摘要】：本实验主要是采用matlab实现两路带限信号分选数字接收机系统，其中涉及到数字信号处理的内容有：一、连续时间信号的采样，包括奈奎斯特抽样定理等；二、IIR数字滤波器的理论、结构设计与实现；三、信号处理的相关运算，包括信号卷积运算等；四、离散傅里叶变换，包括DFT、FFT等。本报告采用一个低通一个高通的方法将两个频段的波进行分离，并采用DTFT（离散时间傅里叶变换）的方法得到其频谱并进行分析。关键词：频谱分离，滤波器，DTFT，频谱分析1 实验设计：1.1 实验要求： 第一个载波信号幅度A1 =5V ，载波频率f1=2.45GHz，高斯包络脉冲宽度1=20ns；第二个载波信号幅度A2 =2V ，载波频率f2 =5.8GHz，高斯包络脉冲宽度2 =10ns。数字接收机结构如下图所示：2.2 设计方案：filter1可选择低通滤波器，最高截止频率5.5GHz；filter2采用高通滤波器，最低截止频率2.8GHz。具体设计流程：第一步：对信号进行A/D（模拟/数字）转换，由奈斯奎采样定律可知，采样信号，因为所以取=11.6GHz。第二步：采用fft算法得到r(t)的频谱。第三步：设计低通巴特沃思滤波器。 设计低通巴特沃思滤波器的原理既是用阶数，用巴特沃思滤波器的幅度平方响应|2=来求解3dB截止频率得到传输函数(z)的结果。由于，可取低通巴特沃思滤波器的，=5GHz，则第四步：用低通巴特沃思滤波器得到高通滤波器。第五步：通过滤波器相当于实现以下运算在时域上为卷积yn=xn*hn，在频域上频谱相乘Y()=X()H()第六步：经过ifft算法后可得时域信号， ifft算法相当于给信号做了离散时间傅里叶反变换，从而得到有频谱的时域上的信号；2 Matlab仿真结果：（程序见后源程序文件）第一步：第二步：第三、四步：第五步：第六步：3 实验结论：与以上分析和实验结果，我们可以得出：一个信号中如果带有不同频率的信息，可以通过相应的滤波器滤出所需要的信息，并且所得结果是比较准确的，而且精确度主要与滤波器是否理想有很大关系。附件（代码）实现模数转换A/D：Fs =20*109 ; % Sampling frequencyT = 1/Fs; % Sample timeL = 1000; % Length of signalt = (0:L-1)*T; % Time vectort1=20*10(-9);t2=10*10(-9);a1=5;a2=2;f1=2.45*109;f2=5.8*109;r=a1*exp(-(t/t1).2).*cos(2*pi*f1*t)+a2*exp(-(t/t2).2).*cos(2*pi*f2*t);plot(t,r)title(Signal )ylabel(|r(t)|)xlabel(time )采用fft算法得到r(t)的频谱：Fs =20*109 ; % Sampling frequencyT = 1/Fs; % Sample timeL = 1000; % Length of signalt = (0:L-1)*T; % Time vectort1=20*10(-9);t2=10*10(-9);a1=5;a2=2;f1=2.45*109;f2=5.8*109;r=a1*exp(-(t/t1).2).*cos(2*pi*f1*t)+a2*exp(-(t/t2).2).*cos(2*pi*f2*t);NFFT = 2nextpow2(L); % Next power of 2 from length of rR = fft(r,NFFT)/L;f = Fs/2*linspace(0,1,NFFT/2);% Plot single spectrum.plot(f,2*abs(R(1:NFFT/2) title(Single Spectrum of R(t)xlabel(Frequency (Hz)ylabel(|R(f)|)巴特沃兹低通滤波器：F =Fs/2;W =3*109; %3-dB cutoff angular frequency % Determine the transfer functionWn=W/F;num1,den1 = butter(N1,Wn,low);%高通滤波num2,den2 = butter(N2,Wn,low);num3,den3 = butter(N3,Wn,low);wd=0:1023*2*pi/1023;H1= freqz(num1,den1,wd);H2= freqz(num2,den2,wd);H3= freqz(num3,den3,wd);subplot(1,3,1);plot(f,abs(H1(1:NFFT/2)title(低通滤波1阶)xlabel(Frequency (Hz)ylabel(|H(f)|)subplot(1,3,2);plot(f,abs(H2(1:NFFT/2)title(低通滤波4阶)xlabel(Frequency (Hz)ylabel(|H(f)|)subplot(1,3,3);plot(f,abs(H3(1:NFFT/2)title(低通滤波8阶)xlabel(Frequency (Hz)ylabel(|H(f)|)低、高滤波器：Fs =20*109 ; % Sampling frequencyT = 1/Fs; % Sample timeL = 1000; % Length of signalNFFT = 2nextpow2(L); % Next power of 2 from length of rf = Fs/2*linspace(0,1,NFFT/2);N=8;%Type in filter orderF =Fs/2;W1=3*109; %3-dB cutoff angular frequency W2=5*109;% Determine the transfer functionWn1=W1/F;Wn2=W2/F;num1,den1 = butter(N,Wn1,low);%高通滤波num2,den2 = butter(N,Wn2,high);wd=0:1023*2*pi/1023;H1= freqz(num1,den1,wd);H2= freqz(num2,den2,wd);subplot(1,2,1);plot(f,abs(H1(1:NFFT/2)title(低通滤波)xlabel(Frequency (Hz)ylabel(|H(f)|)subplot(1,2,2);plot(f,abs(H2(1:NFFT/2)title(高通滤波)xlabel(Frequency (Hz)ylabel(|H(f)|)通过滤波器：Fs =20*109 ; % Sampling frequencyT = 1/Fs; % Sample timeL = 1000; % Length of signalt = (0:L-1)*T; % Time vectort1=20*10(-9);t2=10*10(-9);a1=5;a2=2;f1=2.45*109;f2=5.8*109;r=a1*exp(-(t/t1).2).*cos(2*pi*f1*t)+a2*exp(-(t/t2).2).*cos(2*pi*f2*t);NFFT = 2nextpow2(L); % Next power of 2 from length of rR = fft(r,NFFT)/L;f = Fs/2*linspace(0,1,NFFT/2);N =6;%Type in filter orderF =Fs/2;W =5*109; %3-dB cutoff angular frequency Wn=W/F;num,den = butter(N,Wn,high);%高通滤波wd=0:1023*2*pi/1023;H= freqz(num,den,wd);R1=R.*abs(H);subplot(1,2,1);plot(f,abs(R1(1:NFFT/2) title(通过高通滤波器后 )ylabel(|R(f)|)xlabel(Frequency (Hz) )W2=3*109;Wn2=W2/F;num2,den2 = butter(N,Wn2,low);%低通滤波H2= freqz(num2,den2,wd);R2=R.*abs(H2);subplot(1,2,2);plot(f,abs(R2(1:NFFT/2)title(通过低通滤波器后 )ylabel(|R(f)|)xlabel(Frequency (Hz) )时域信号：Fs =20*109 ; % Sampling frequencyT = 1/Fs; % Sample timeL = 1000; % Length of signalt = (0:L-1)*T; % Time vectort1=20*10(-9);t2=10*10(-9);a1=5;a2=2;f1=2.45*109;f2=5.8*109;r=a1*exp(-(t/t1).2).*cos(2*pi*f1*t)+a2*exp(-(t/t2).2).*cos(2*pi*f2*t);NFFT = 2nextpow2(L); % Next power of 2 from length of rR = fft(r,NFFT)/L;f = Fs/2*linspace(0,1,NFFT/2);N =6;%Type in filter orderF =Fs/2;W =5*109; %3-dB cutoff angular frequency Wn=W/F;num,den = butter(N,Wn,high);%高通滤波wd=0:1023*2*pi/1023;H= freqz(num,den,wd);R1=R.*abs(H);W2=3*109;Wn2=W2/F;num2,den2 = butter(N,Wn2,low);%低通滤波H2= freqz(num2,den2,wd);R2=R.*abs(H2);r3=ifft(R1,NFFT)*L;t3=(0:999)*T;r2=a2*exp(-(t3/t2).2).*cos(2*pi*f2*t3);subplot(2,2,1);%r2前后信号比较plot(t3,r3(1:1000)title(通过高通滤波器还原信号 )ylabel(|r2(t)|)xlabel(t/s)subplot(2,2,3);plot(t3,r2)r4=ifft(R2,NFFT)*L;title(原始低频载波 )ylabel(|r2(t)|)xlabel(t/s)subplot(2,2,2);%r1前后信号比较plot(t3,r4(1:1000)title(通过低通滤波器还原信号 )ylabel(|r1(t)|)xlabel(t/s)r1=a1*exp(-(t3/t1).2).*cos(2*pi*f1*t3);subplot(2,2,4);plot(t3,r1)title(原始高频载波 )ylabel(|r1(t)|)xlabel(t/s)