如何计算含脉冲噪声曲线的SNR及滤波后的信噪比提升

一、SNR核心计算逻辑 #

信噪比（dB）的计算公式为：
SNR(dB) = 10×log₁₀(信号功率 / 噪声功率)
其中：

• 信号功率：干净信号的平方均值 Pₛ = mean(s.²)
• 噪声功率：噪声分量的平方均值 Pₙ = mean((x - s).²)（x为加噪/滤波后信号，s为对应干净信号）

二、修正加噪代码（避免索引越界） #

原加噪循环存在索引越界问题，调整为随机选取干净信号生成1000组加噪数据，同时存储对应干净信号用于后续SNR计算：

cd 'C:blah\blah\'
z_numfiles = 100;
for k = 1:z_numfiles
    myfilename = sprintf('scope_%d.csv', k);
    nometal{k} = xlsread(myfilename, 'C4:C500');
end

% 修正后的加噪流程
pd1 = makedist('Stable','alpha',0.5,'beta',0,'gam',0.001,'delta',0);
distr_puls_nometal = cell(1000, 1);
clean_corresponding = cell(1000, 1); % 存储加噪信号对应的干净信号
samplesize = 497;

for m = 1:1000
    k = randi(100); % 随机选一组干净信号
    s = cell2mat(nometal{k});
    temp = s;
    
    for i = 1:samplesize
        a = random(pd1);
        temp(i) = temp(i) + a;
        temp(i) = max(0, min(3, temp(i))); % 限幅简化写法
    end
    distr_puls_nometal{m} = temp;
    clean_corresponding{m} = s;
end

三、计算加噪后SNR下降幅度 #

批量计算所有加噪信号的SNR，并与干净信号的SNR对比得到下降幅度：

SNR_noisy = zeros(1000, 1);
SNR_clean = zeros(1000, 1);

for m = 1:1000
    s = clean_corresponding{m};
    x = distr_puls_nometal{m};
    noise = x - s;
    
    P_s = mean(s.^2);
    P_n = mean(noise.^2);
    P_n = max(P_n, 1e-10); % 避免除以0
    
    SNR_noisy(m) = 10*log10(P_s / P_n);
    
    % 计算干净信号的固有SNR（以自身波动为噪声）
    P_n_clean = var(s - mean(s));
    P_n_clean = max(P_n_clean, 1e-10);
    SNR_clean(m) = 10*log10(P_s / P_n_clean);
end

avg_SNR_drop = mean(SNR_clean - SNR_noisy);
fprintf('加噪后平均SNR下降幅度：%.2f dB\n', avg_SNR_drop);

四、评估滤波后的SNR提升效果 #

假设已用滚动均值和分块算术均值滤波，计算滤波后的SNR并对比加噪信号的SNR：

% 滤波处理（窗口/块大小设为5，可按需调整）
window_size = 5;
block_size = 5;
filtered_rolling = cell(1000, 1);
filtered_mean = cell(1000, 1);
clean_filtered_rolling = cell(1000, 1);
clean_filtered_mean = cell(1000, 1);

for m = 1:1000
    x = distr_puls_nometal{m};
    s = clean_corresponding{m};
    
    % 滚动均值滤波（丢弃端点）
    filtered_rolling{m} = movmean(x, window_size, 'Endpoints', 'discard');
    clean_filtered_rolling{m} = movmean(s, window_size, 'Endpoints', 'discard');
    
    % 分块算术均值滤波
    num_blocks = floor(samplesize / block_size);
    mean_block = zeros(num_blocks, 1);
    s_mean_block = zeros(num_blocks, 1);
    for b = 1:num_blocks
        idx = (b-1)*block_size+1 : b*block_size;
        mean_block(b) = mean(x(idx));
        s_mean_block(b) = mean(s(idx));
    end
    filtered_mean{m} = mean_block;
    clean_filtered_mean{m} = s_mean_block;
end

% 计算滤波后SNR及提升幅度
SNR_rolling = zeros(1000, 1);
SNR_mean = zeros(1000, 1);

for m = 1:1000
    % 滚动均值滤波SNR
    s_roll = clean_filtered_rolling{m};
    x_roll = filtered_rolling{m};
    noise_roll = x_roll - s_roll;
    
    P_s_roll = mean(s_roll.^2);
    P_n_roll = mean(noise_roll.^2);
    P_n_roll = max(P_n_roll, 1e-10);
    SNR_rolling(m) = 10*log10(P_s_roll / P_n_roll);
    
    % 算术均值滤波SNR
    s_mean = clean_filtered_mean{m};
    x_mean = filtered_mean{m};
    noise_mean = x_mean - s_mean;
    
    P_s_mean = mean(s_mean.^2);
    P_n_mean = mean(noise_mean.^2);
    P_n_mean = max(P_n_mean, 1e-10);
    SNR_mean(m) = 10*log10(P_s_mean / P_n_mean);
end

avg_SNR_boost_rolling = mean(SNR_rolling - SNR_noisy(1:length(SNR_rolling)));
avg_SNR_boost_mean = mean(SNR_mean - SNR_noisy(1:length(SNR_mean)));

fprintf('滚动均值滤波平均SNR提升：%.2f dB\n', avg_SNR_boost_rolling);
fprintf('算术均值滤波平均SNR提升：%.2f dB\n', avg_SNR_boost_mean);

五、对其他噪声分布的适用性分析 #

• 高斯/均匀白噪声：均值类滤波效果显著，因为这类噪声均值为0，多次平均后噪声功率会按比例降低（算术均值噪声功率为原噪声的1/N，N为平均次数），滚动均值窗口越大降噪越强，但会损失信号细节。
• 脉冲噪声（如椒盐噪声）：均值类滤波效果有限，脉冲的极端值会拉高窗口/块的均值，无法有效抑制脉冲；此时中值滤波是更优选择。
• 有色噪声（如粉红噪声）：均值类滤波本质是低通滤波，对低频占优的有色噪声抑制效果差，需改用自适应滤波或频域滤波方法。
• 其他重尾分布噪声：和alpha稳定分布类似，均值类滤波受极端值影响大，降噪效果弱于针对重尾噪声的专用滤波器（如分数低阶统计量滤波器）。

内容的提问来源于stack exchange，提问作者ChrisD91