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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?


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filtfilt does a forward-backward filtering. Have you tried filtering, reversing the output, filtering again and finally reversing again in Mathematica? –  rm -rf Apr 21 at 5:24
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1 Answer 1

up vote 0 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]
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Good. Great Thanks. –  Algohi Apr 21 at 22:07
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