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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:

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

The result is as follows: enter image description here

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?


share|improve this question
filtfilt does a forward-backward filtering. Have you tried filtering, reversing the output, filtering again and finally reversing again in Mathematica? – R. M. Apr 21 '14 at 5:24
up vote 2 down vote accepted

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]

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.

share|improve this answer
Good. Great Thanks. – Algohi Apr 21 '14 at 22:07
it is nice I upvote this answer and you edited it. this was my second question in this forum and that time I didn't know there is upvote. sorry for waiting all this time to upvote your answer :) – Algohi Oct 15 '14 at 19:09

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