Data filtering using Butterworth filter

Question

I want to filter data using Butterworth filter. I am currently using Matlab and I want to know how to do it in Mathematica.

I have the following data:

data1 = Table[
   PDF[NormalDistribution[3.5, .8], i] + 
    PDF[NormalDistribution[6, 1], i], {i, -5, 15, .01}];
noise = RandomReal /@ RandomReal[{-0.2, .2}, Length[data1]];
data2 = data1 + noise;

I filtered this data using Matlab as follows:

[b,a] = butter(8,0.04);

filtfilt(b,a,data2 );

In the previous question's answer, bill s suggested to do it as follows in Mathematica:

RecurrenceFilter[
 ToDiscreteTimeModel[ButterworthFilterModel[{2, 0.04}], 1], data2
 ]

The result is as follows:

The problem I am facing is whatever I change the filter order and frequency, I am not able to produce the same filtered data as I am getting from Matlab.

Can someone suggest for me what to do and what values to use to get the same filtered data as I am getting from Matlab?

Thanks

Answer 1

filtfilt does a forwards and then a backwards filtering, as rm -rf suggests. To filter data in this way, you might try

forwards = RecurrenceFilter[ToDiscreteTimeModel[ButterworthFilterModel[5], 1], data];
backwards = RecurrenceFilter[ToDiscreteTimeModel[ButterworthFilterModel[5], 1], Reverse[data]];
(forwards + Reverse[backwards])/2

The nice thing about filtfilt (or the forwards/backwards filter above) is that the filtering has no phase shift/delay when compared with the original data.