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MATLAB代码来生成根升余弦滤波器，并绘制其时域和频域特性

news 2026/8/8 15:29:20

根升余弦滤波器完整实现

%% 根升余弦滤波器生成与分析clear all;close all;clc;%% 参数设置Fs=1000;% 采样频率 (Hz)T=1;% 符号周期 (s)sps=10;% 每符号采样点数beta=0.5;% 滚降因子 (0~1)filter_span=6;% 滤波器跨度 (符号数)%% 生成根升余弦滤波器% 方法1: 使用rcosdesign函数 (推荐)h_rc=rcosdesign(beta,filter_span,sps,'sqrt');% 方法2: 手动实现 (备用方法)% t = (-filter_span*T/2 : 1/Fs : filter_span*T/2) + 1e-8; % 避免除零% h_rc_manual = manual_root_raised_cosine(t, T, beta);%% 时域分析t_filter=(-filter_span*sps/2:filter_span*sps/2)/(sps/T);figure('Position',[100,100,1200,800]);% 时域波形subplot(2,3,1);stem(t_filter,h_rc,'b','filled','MarkerSize',4);hold on;plot(t_filter,h_rc,'r-','LineWidth',1.5);grid on;xlabel('时间 (符号周期)');ylabel('幅度');title('根升余弦滤波器时域响应');legend('采样点','包络','Location','best');% 滤波器冲激响应细节subplot(2,3,2);plot(t_filter,h_rc,'b-','LineWidth',2);grid on;xlabel('时间 (符号周期)');ylabel('幅度');title('滤波器冲激响应');xlim([-3,3]);% 眼图模拟subplot(2,3,3);% 生成随机数据并滤波data=randi([01],1,100)*2-1;% BPSK信号upsampled_data=upsample(data,sps);tx_signal=conv(upsampled_data,h_rc,'same');% 绘制眼图plot_eye_diagram(tx_signal,sps,2);title('发射信号眼图');%% 频域分析% 计算频率响应N_fft=1024;H_rc=fftshift(fft(h_rc,N_fft));f=(-N_fft/2:N_fft/2-1)*(Fs/N_fft)/(1/T);% 归一化频率% 幅度响应subplot(2,3,4);plot(f,20*log10(abs(H_rc)/max(abs(H_rc))),'b-','LineWidth',2);grid on;xlabel('归一化频率 (fT)');ylabel('幅度 (dB)');title('根升余弦滤波器幅度响应');xlim([-2,2]);ylim([-80,5]);% 相位响应subplot(2,3,5);phase_response=angle(H_rc);phase_response_unwrapped=unwrap(phase_response);plot(f,phase_response_unwrapped,'r-','LineWidth',2);grid on;xlabel('归一化频率 (fT)');ylabel('相位 (弧度)');title('相位响应');xlim([-2,2]);% 群延迟subplot(2,3,6);group_delay=-diff(phase_response_unwrapped)./diff(f*2*pi);plot(f(1:end-1),group_delay,'g-','LineWidth',2);grid on;xlabel('归一化频率 (fT)');ylabel('群延迟 (样本)');title('群延迟响应');xlim([-2,2]);%% 不同滚降因子的比较figure('Position',[100,100,1000,600]);beta_values=[0.2,0.5,0.8,1.0];colors=['b','r','g','m'];t_compare=(-filter_span*sps/2:filter_span*sps/2)/(sps/T);subplot(1,2,1);hold on;fori=1:length(beta_values)h_temp=rcosdesign(beta_values(i),filter_span,sps,'sqrt');plot(t_compare,h_temp,colors(i),'LineWidth',2,...'DisplayName',['\beta = ',num2str(beta_values(i))]);endgrid on;xlabel('时间 (符号周期)');ylabel('幅度');title('不同滚降因子的时域响应');legend('show');xlim([-3,3]);subplot(1,2,2);hold on;fori=1:length(beta_values)h_temp=rcosdesign(beta_values(i),filter_span,sps,'sqrt');H_temp=fftshift(fft(h_temp,N_fft));f_compare=(-N_fft/2:N_fft/2-1)*(Fs/N_fft)/(1/T);plot(f_compare,20*log10(abs(H_temp)/max(abs(H_temp))),...colors(i),'LineWidth',2,...'DisplayName',['\beta = ',num2str(beta_values(i))]);endgrid on;xlabel('归一化频率 (fT)');ylabel('幅度 (dB)');title('不同滚降因子的频域响应');legend('show');xlim([-2,2]);ylim([-80,5]);%% ISI性能分析figure('Position',[100,100,800,400]);% 测试符号间干扰test_symbols=[0,0,1,0,0];% 单个脉冲test_signal_upsampled=upsample(test_symbols,sps);filtered_signal=conv(test_signal_upsampled,h_rc,'same');% 找到峰值位置[~,peak_idx]=max(filtered_signal);sampling_points=peak_idx:sps:length(filtered_signal);subplot(1,2,1);plot(filtered_signal,'b-','LineWidth',2);hold on;stem(sampling_points,filtered_signal(sampling_points),'ro','filled');grid on;xlabel('采样点');ylabel('幅度');title('单个脉冲的滤波器响应');legend('滤波器输出','采样时刻');% ISI分析 - 采样时刻的值subplot(1,2,2);isi_samples=filtered_signal(sampling_points);stem(0:length(isi_samples)-1,isi_samples,'b','filled');hold on;% 标记主瓣和旁瓣plot([2,2],[0,max(isi_samples)],'r--','LineWidth',1.5);text(2.2,max(isi_samples)*0.8,'主瓣','Color','r');grid on;xlabel('符号索引');ylabel('幅度');title('采样时刻的ISI分析');%% 自定义函数定义functionplot_eye_diagram(signal,samples_per_symbol,num_eyes)% 绘制眼图eye_length=samples_per_symbol*num_eyes;num_segments=floor(length(signal)/eye_length)-1;hold on;fori=1:num_segments start_idx=(i-1)*eye_length+1;end_idx=start_idx+eye_length-1;segment=signal(start_idx:end_idx);time_axis=(0:length(segment)-1)/samples_per_symbol;plot(time_axis,segment,'b-','LineWidth',0.5);endxlabel('时间 (符号周期)');ylabel('幅度');grid on;hold off;endfunctionh=manual_root_raised_cosine(t,T,beta)% 手动计算根升余弦滤波器h=zeros(size(t));fori=1:length(t)t_val=t(i);ifabs(t_val)==T/(4*beta)h(i)=(beta/sqrt(2*T))*...((1+2/pi)*sin(pi/(4*beta))+(1-2/pi)*cos(pi/(4*beta)));elseift_val==0h(i)=(1/sqrt(T))*(1+beta*(4/pi-1));elseterm1=sin(pi*(1-beta)*t_val/T+4*beta*t_val/T*cos(pi*(1+beta)*t_val/T));term2=pi*t_val/T*(1-(4*beta*t_val/T).^2);h(i)=(1/sqrt(T))*term1./term2;endendend%% 滤波器特性总结fprintf('=== 根升余弦滤波器特性总结 ===\n');fprintf('滚降因子 β: %.2f\n',beta);fprintf('滤波器长度: %d 个采样点\n',length(h_rc));fprintf('每符号采样点数: %d\n',sps);fprintf('滤波器跨度: %d 个符号\n',filter_span);% 计算关键参数energy=sum(h_rc.^2);fprintf('滤波器能量: %.4f\n',energy);% 检查奈奎斯特准则sampling_offset=round(length(h_rc)/2)+sps;isi_values=h_rc(sampling_offset:sps:end);isi_power=sum(isi_values.^2)-h_rc(round(length(h_rc)/2))^2;fprintf('ISI功率: %.6f\n',isi_power);