Would you think it is correct if instead of subtracting the mean value from the data set, so that the svd or eig is applied on the fluctuating data, "detrend" is used?
** Considering that "detrend" MATLAB routing removes both the linear trends and mean value from the matrix while POD tries to provide the best approximation of the input fluctuating data by linearizing the system.
Dear Foad,
I guess if you use detrend, you might loose some very low frequency behavior in your signal. Therefore my first suggestion would be not to use it.
Regards,
Maarten Vanierschot
Subtracting the mean value is in itself not recommended unless you data is truly statistically stationary. If this is the case, the vector of constants (the temporal mean) is, in theory, eigenvector of the temporal correlation matrix. Therefore, you first mode will automatically reproduce the mean.
However, since random error and incomplete convergence may introduce some 'disturbance' to it, one often decides to take out the mean so that all the other modes are forced to have zero mean (recall that for a mode to be orthogonal to the vector of constants the must have also zero mean).
As answered by Maarten, using a de-trend will simply remove some low frequency behavior from the signal and then from all the modes. I do not really see the added value of the operation, unless you want to focus you analysis on higher frequencies than those removed by the detrend. In other words, it would be like high pass filter your data before doing POD.
Thank you Maarten and Miguel, I really appreciate your answers.
I was ruminating the topic for week now and deeply after Maarten`s answer. And now with Miguel`s insight on the role of mean subtraction I can see how keeping the low frequency components can be important.
It is interesting for me cause I also thought about the operation as a high-pass filter but since no initial information about low frequency component is available, I guess it would not be correct to apply detrend to the matrix.
Now I`m thinking that is it correct to argue that detrend on an arbitrary signal for FFT purposes - as it is suggested by MATLAB tutorials- would also be incorrect? since it removes the low frequency components?
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