Dear all,

Here is a conversation long time ago on the necessity of removing linear trend before filtering, if we think linear trend is a kind of noise. Hope this information is helpful for some of us!

P.S., whether linear trend is meaningful or not, @WANG Xin-Di is going to have a nice work on that issue. Hopefully we can have it published in the near future.

Here is a very simple example:

Signal:

y=sin(4*2*pi*t)+sin(2*2*pi*t)+

temporal domain:

frequency domain:

If the signal with a linear trend:

y2=sin(4*2*pi*t)+sin(2*2*pi*t)+sin(0.8*2*pi*t)+sin(0.5*2*pi*t)+sin(0.2*2*pi*t)+t;

y2=sin(4*2*pi*t)+sin(2*2*pi*t)

temporal domain:

frequency domain:

If detrend first and then bandpass filter (0.01-1Hz):

temporal domain:

frequency domain:

However, If bandpass filter (0.01-1Hz) first and then detrend:

temporal domain:

frequency domain:

In conclusion, temporal filtering can not remove the linear trend very well (linear trend is not a single slow frequency component stuff and will leak and influence other band). So my opinion is detrend first and then do temporal filtering.

Best,

Chao-Gan

conge

Thu, 09/12/2013 - 18:31

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## Hi Chao-gan,

Hi Chao-gan,

It seems that the figures in the post can not be displayed.

Best,

Qingyang

YAN Chao-Gan

Fri, 09/13/2013 - 02:07

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## Thanks, Yang!

Now it should work.

Best,

Chao-Gan