如何从输入向量计算滚动均值，偏度，峰度，均方根和其他一些统计特征？

Question

我有一个信号每秒收集3小时，速率为40赫兹，数据长度为432,000。我想计算每分钟的平均值，偏度，峰度和其他一些统计特征。从这个意义上说，我想计算前40个数据点和后40个数据点的平均值等。最后，我希望有一个长度为180的矢量。如果有人能够分享脚本来做到这一点，那将会很棒。提前致谢。

Answer 1

function [M, S, A, E] = slideStats(x, window, step) 
% sliding: M-mean, S-std, A-skewness, E-kurtosis 

n=fix((length(x)-window)/step+1); 
M=zeros(n,1); 
S=zeros(n,1); 
E=zeros(n,1); 
A=zeros(n,1); 

sum=0; 
mean=0; 
mean2=0; 
mean3=0; 
mean4=0; 

for i=1:window 
    sum = x(i); 
    mean = mean + sum; 
    sum = sum * x(i); 
    mean2 = mean2 + sum; 
    sum = sum * x(i); 
    mean3 = mean3 + sum; 
    sum = sum * x(i); 
    mean4 = mean4 + sum; 
end 
mean=mean/window; 
mean2=mean2/window; 
mean3=mean3/window; 
mean4=mean4/window; 

M(1)= mean; 
S(1)= (mean2-mean*mean)^0.5; 
A(1)= (mean3-3*mean2*mean+2*mean*mean*mean) /S(1)^3; 
E(1)= (mean4-4*mean3*mean+6*mean2*mean*mean-3*mean*mean*mean*mean) /S(1)^4 -3; 

for i=0:n-2 
    for k=1:step 
     stepInd = i*step;  
     first = stepInd+k; 
     last = stepInd+k+window; 

    % recalculating means without previous element 
     sum = x(first)/window; 
     mean = mean - sum; 
     sum = sum*x(first); 
     mean2 = mean2 - sum; 
     sum = sum*x(first); 
     mean3 = mean3 - sum; 
     sum = sum*x(first); 
     mean4 = mean4 - sum; 

    % recalculating means with next element 
     sum = x(last)/window; 
     mean = mean + sum; 
     sum = sum * x(last); 
     mean2 = mean2 + sum; 
     sum = sum * x(last); 
     mean3 = mean3 + sum; 
     sum = sum * x(last); 
     mean4 = mean4 + sum; 
    end 

    M(i+2)= mean; 
    S(i+2)= (mean2-mean*mean)^0.5; 
    A(i+2)= (mean3-3*mean2*mean+2*mean*mean*mean) /S(i+2)^3; 
    E(i+2)= (mean4-4*mean3*mean+6*mean2*mean*mean-3*mean*mean*mean*mean) /S(i+2)^4 -3; 
end 

end