如何在MATLAB中使用Welch的方法估计平均相干性

Question

我试图在MATLAB中估计信号的不连续片段的平均相干性。对于韦尔奇的频谱估计，以下工作：

w = blackmanharris(50);  % window
n = numel(w);            % fft length
o = 0;                   % overlap

x = rand(200,1); x1 = x(1:100); x2 = x(101:200);

s  = pwelch(x,  w, o, n);
s1 = pwelch(x1, w, o, n);
s2 = pwelch(x2, w, o, n);
sa = (s1+s2)/2;

max(abs(s-sa))  % almost zero

然而，当使用Welch的方法估计相干性时，算术平均值会产生错误的结果：

y = rand(200,1); y1 = y(1:100); y2 = y(101:200);

c  = mscohere(x,  y,  w, o, n);
c1 = mscohere(x1, y1, w, o, n);
c2 = mscohere(x2, y2, w, o, n);
ca = (c1+c2)/2;

max(abs(c-ca))  % very different from zero

如何正确平均两个相干估计？