MATLAB 代码分析：两个信号的相关性和相位差计算

这段代码主要用于计算两个信号之间的相关性和相位差。下面是对每一行代码的详细分析：/n/n1. s = 4000; % the width of filter windows, ts numbers per windows/n定义了筛选器窗口的宽度，即每个窗口包含的数据点数。/n/n2. wx = hann(ts); % generates a hanning filter coefficients/n生成一个汉宁滤波器系数，用于窗口化数据。/n/n3. fs = 2000; % the sampling rate of probes, [kHz]/n探针的采样频率，以kHz为单位。/n/n4. fre_cal = fix((length(data1)-ts)/(ts/2)); % calculate the frequency of analysis/n计算信号频率的分析范围。/n/n5. range_butter = [1, 999999]/1000000; % the frequency range of butterworth filter/nButterworth滤波器的频率范围。/n/n6. [coef1, coef2] = butter(1, range_butter); % generates the coefficients of butterworth filter/n生成Butterworth滤波器的系数。/n/n7. data1_but = filter(coef1, coef2, filter(coef1, coef2, data1)); % data processed by butterworth filter/n用Butterworth滤波器处理信号1。/n/n8. data2_but = filter(coef1, coef2, filter(coef1, coef2, data2)); % data processed by butterworth filter/n用Butterworth滤波器处理信号2。/n/n9. data1_fft = zeros(fre_cal, ts); % generates a box for the data after FFT/n为FFT处理后的数据生成一个盒子。/n/n10. data2_fft = zeros(fre_cal, ts); % generates a box for the data after FFT/n为FFT处理后的数据生成一个盒子。/n/n11. disp('系综平均数：') disp(fre_cal)/n输出系综平均数。/n/n12. for i = 1 : fre_cal/n data1_fft(i, :) = data1_but((i-1)*ts/2 + 1 : (i-1)*ts/2 + ts); % read the data for every filter windows/n data2_fft(i, :) = data2_but((i-1)*ts/2 + 1 : (i-1)*ts/2 + ts);/n data1_detr(i, :) = detrend(data1_fft(i, :)); % reduce the ripple of data/n data2_detr(i, :) = detrend(data2_fft(i, :));/n data1_fft(i, :) = fft(data1_detr(i, :).*wx', ts);/n data2_fft(i, :) = fft(data2_detr(i, :).*wx', ts);/nend/n对每个筛选器窗口的数据进行FFT处理，并减去趋势成分。然后将窗口化后的数据进行FFT变换。/n/n13. frequency = (0 : (ts/2 - 1))*(fs/(ts - 2)); % calculate the frequency series./n计算频率序列。/n/n14. mx12 = sum(abs(data1_fft(:, 1:ts/2)).*abs(data2_fft(:, 1:ts/2)))/fre_cal; % calculate (Σ|x1|·|x2|)/fre_cal/n计算两个信号之间的相关性。/n/n15. phase = angle(sum(data1_fft(:, 1:ts/2).*conj(data2_fft(:, 1:ts/2))))/pi; % calculate the phase of all filter windows, [rad]/n计算所有筛选器窗口的相位差。/n/n16. power_cross = abs(sum(data1_fft(:, 1:ts/2).*conj(data2_fft(:, 1:ts/2))))/fre_cal; % calculate the average cross power of all filter windows/n计算所有筛选器窗口的平均交叉功率。/n/n17. power1 = sum(((abs(data1_fft(:, 1:ts/2))).^2))/fre_cal; % calculate the power of data1/n计算信号1的功率。/n/n18. power2 = sum(((abs(data2_fft(:, 1:ts/2))).^2))/fre_cal; % calculate the power of data2/n计算信号2的功率。/n/n19. corherency = power_cross./mx12; % calculate corherency/n计算相关性。/n/n20. freOutput = frequency(2:ts/2); phaseOutput = phase(2 : end); power1Output = power1(2:end); power2Output = power2(2:end); powerCsOutput = power_cross(2:end); CorrOutput = corherency(2:end);/n将计算的结果存入输出变量中。/n/n21. figure/nsubplot(511) plot(frequency(2 : ts/2), smooth(power1(2 : end), 3), 'LineWidth', 1), xlim([fBegin, fEnd]) ylabel('power1 (a.u)')/nsubplot(512) plot(frequency(2 : ts/2), smooth(power2(2 : end), 3), 'LineWidth', 1), xlim([fBegin, fEnd]) ylabel('power2 (a.u)')/nsubplot(513) plot(frequency(2 : ts/2), power_cross(2 : end), 'LineWidth', 1), xlim([fBegin, fEnd]) ylabel('cross power (a.u)')/nsubplot(514) plot(frequency(2 : ts/2), smooth(corherency(2 : end), 5), 'LineWidth', 1), xlim([fBegin, fEnd]) ylabel('corherency')/nsubplot(515) plot(frequency(2 : ts/2), smooth(phase(2 : end), 3), 'LineWidth', 1), xlim([fBegin, fEnd]) hold on plot([0, 500], [0, 0], 'b--', 'linewidth', 1), ylim([-1, 1]) ylabel('phase (rad//pi)') xlabel('f (kHz)')/n绘制相关性和相位差的图像。subplot函数将不同的图像绘制在一个图中。每个图像的横轴为频率，纵轴为功率、相关性或相位差。