如何在Matlab中计算信号的信噪比？

我想计算噪声信号和滤波信号的信噪比。我使用了以下代码，但我不确定结果是否正确。有人能帮我吗

%generate the noisy signal which will be filtered
x= cos(2*pi*12*[0:0.001:1.23]);
x(end) = [];
[b,a] = butter(2,[0.6 0.7],'bandpass');
filtered_noise = filter(b,a,randn(1, length(x)*2));
y = (x + 0.5*filtered_noise(500:500+length(x)-1))/length(x)*2;

%Use matlabs built-in buttord function to get the optimum order to meet a      
specification
[N,Wn] = buttord(0.1, 0.5, 5, 40)

%use the N and Wn values obtained above to design the filter in the usual 
way
[b,a] = butter(N, Wn, 'low');

%filter the signal and plot the ouput of the filter
Y_filtered = filter(b,a,y);

%calculation of snr before filtering
snr_before = mean(x.^2) / mean(filtered_noise.^2);
snr_before_db = 10 * log10(snr_before) % in dB

%calculation of snr after filtering
residual_noise = x - Y_filtered; 
snr_after = mean(x.^2) / mean(residual_noise.^2); 
snr_after_db = 10 * log10(snr_after)

我得到的结果是：

snr_before_db =
      6.8725
snr_after_db =
      0.0132

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我认为在滤波前后计算峰值信噪比是不对的。此外，计算峰值信噪比的方法也不正确。可以仅在滤波后计算峰值信噪比。试试这个

peaksnr = psnr(X,Y_filtered)

或

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可以那么，在滤波之前，我如何知道信噪比的值呢？这样我可以比较不同类型的过滤器的结果。

MSE = (1/length(X))*sum((X-Y_filtered).^2);
peaksnr = 10*log10(max(X(:))^2/MSE);