Why does my filtered time series approach zero as time approaches zero?

I have some time series data:

I have built the following filter:

% Build filter
f_samp = 1;
f_nyq = f_samp/2;
f_cutoff = 0.1;
cutoff_norm = f_cutoff/f_nyq;
filt_order = 1;
[B,A] = butter(filt_order,cutoff_norm);
x_smooth = filter(B,A,x);

I apply the filter to the data:

From 10 seconds onwards the data is okay but before this it tends towards zero as t tends towards zero. Does anyone know why this is? Is it a charactersitic of the buuterworth filter or all filters?

I would like to know how to remove this characterstic so that the filtered data is accurate during the first few samples.

Thanks.

Answer 1

[Wayne King]

It's because your time series have a large mean value, which makes the start-up effects of the filter much more apparent.

Because it's an IIR filter, it's not trivial to calculate exactly what the length of the start-up transient will be. In the case of an FIR filter, the group delay is often constant and easy to correct for.

You can either:

1.) First remove the mean from your data. Assume X is your signal, you can do

   X = X-mean(X);
or
   X = detrend(X,0);

2.) Use filtfilt() to perform zero-phase filtering, this should alleviate the start-up transient

   y = filtfilt(B,A,X);