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clear; clc; close all;
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% 1. 参数
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fs = 10000; % 采样频率 10kHz
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f0 = 1000; % 基频 1kHz
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t_total = 1;
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t = 0:1/fs:t_total-1/fs;
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N = length(t);
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% 2. 生成混合信号（强杂波+弱谐波+噪声）
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r = 10*cos(2*pi*f0*t) + 0.5*cos(2*pi*2*f0*t); % 杂波：10cos(2πf0t) 目标：0.5cos(2π*2f0t)
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r = r + 0.5*randn(size(r)); % 加上高斯噪声
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% 3. 设计高通滤波器（滤除1kHz，保留2kHz）
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fc = 1500;
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[n_butter, Wn] = buttord(fc/(fs/2), (fc+500)/(fs/2), 1, 40);
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[b,a] = butter(n_butter, fc/(fs/2), 'high'); % 四阶巴特沃斯高通，截止频率1500Hz
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% 进行滤波
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r_filtered = filtfilt(b,a,r);
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% 画滤波器的幅频响应曲线
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[h,f_req] = freqz(b,a,N,fs);
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figure('Color','w');
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plot(f_req, 20*log10(abs(h)));
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xlabel('频率/Hz');
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ylabel('幅度/dB');
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title('高通滤波器幅频响应曲线');
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xlim([0,5000]);
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ylim([-100,5]);
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% 4. 频谱计算
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f = (0:N-1)*fs/N;
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f = f(1:N/2+1);
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R = abs(fft(r))/N; R = R(1:N/2+1);
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R_filt = abs(fft(r_filtered))/N; R_filt = R_filt(1:N/2+1);
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% 5. 绘图
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figure('Color','w');
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% 时域前后对比
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subplot(2,1,1);
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plot(t*1000, r, 'b'); hold on;
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plot(t*1000, r_filtered, 'r','LineWidth',1.2);
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xlim([0,5]);
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xlabel('时间/ms');
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ylabel('幅度');
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legend('滤波前','滤波后');
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title('滤波前后时域波形');
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% 频域前后对比
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subplot(2,1,2);
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plot(f, 20*log10(R/max(R)), 'b'); hold on;
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plot(f, 20*log10(R_filt/max(R_filt)), 'r');
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xlim([0,5000]);
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ylim([-100,10]);
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xlabel('频率/Hz');
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ylabel('幅度/dB');
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legend('滤波前','滤波后');
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title('滤波前后频谱');
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% 6. 计算信干比 SIR
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f1_idx = find(f>=1000,1); % 基频杂波是1kHz
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f2_idx = find(f>=2000,1); % 二次谐波目标是2kHz
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% 滤波前
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P_signal_before = R(f2_idx)^2;
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P_clutter_before = R(f1_idx)^2;
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SIR_before = 10*log10(P_signal_before / P_clutter_before);
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% 滤波后
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P_signal_after = R_filt(f2_idx)^2;
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P_clutter_after = R_filt(f1_idx)^2;
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SIR_after = 10*log10(P_signal_after / P_clutter_after);
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fprintf('滤波前 SIR = %.2f dB\n', SIR_before);
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fprintf('滤波后 SIR = %.2f dB\n', SIR_after);
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fprintf('SIR 提升 %.2f dB\n', SIR_after - SIR_before); |
