Rebekah asked . 2021-02-26

Distorted time domain signal for high pass butterworth filter designed

Distorted time domain signal for high pass butterworth filter designed using 'butter' command and filtered using 'filter' command

Why does the filtered samples of my high pass filter (12th order) look distorted in the time domain when I use the 'filter' command? The filter is designed with the butter command with a very low cut-off frequency of 0.65Hz. The frequency of the signal is 25Hz.

matlab , signal , signal processing

Expert Answer

Kshitij Singh answered . 2024-12-21 01:09:53

The butter worth filter has non-zero phase distortion characteristics which is observed in the time domain. A workaround to obtain signals with zero-distortions would be to use the 'filtfilt' command instead. Please find the attached script which shows an example comparision between the two.

OriginalSamples = [ ...
		790.000000	; ...
		774.000000	; ...
		769.000000	; ...
		761.000000	; ...
		752.000000	; ...
		743.000000	; ...
		733.000000	; ...
		732.000000	; ...
		733.000000	; ...
		732.000000	; ...
		725.000000	; ...
		732.000000	; ...
		770.000000	; ...
		806.000000	; ...
		815.000000	; ...
		818.000000	; ...
		822.000000	; ...
		817.000000	; ...
		803.000000	; ...
		793.000000	; ...
		776.000000	; ...
		773.000000	; ...
		763.000000	; ...
		756.000000	; ...
		743.000000	; ...
		737.000000	; ...
		731.000000	; ...
		728.000000	; ...
		726.000000	; ...
		724.000000	; ...
		739.000000	; ...
		738.000000	; ...
		804.000000	; ...
		812.000000	; ...
		816.000000	; ...
		820.000000	; ...
		817.000000	; ...
		807.000000	; ...
		796.000000	; ...
		788.000000	; ...
		774.000000	; ...
		768.000000	; ...
		762.000000	; ...
		755.000000	; ...
		745.000000	; ...
		736.000000	; ...
		732.000000	; ...
		729.000000	; ...
		729.000000	; ...
		746.000000	; ...
		754.000000	; ...
		797.000000	; ...
		809.000000	; ...
		814.000000	; ...
		819.000000	; ...
		820.000000	; ...
		814.000000	; ...
		801.000000	; ...
		790.000000	; ...
		773.000000	; ...
		768.000000	; ...
		762.000000	; ...
		757.000000	; ...
		747.000000	; ...
		743.000000	; ...
		738.000000	; ...
		736.000000	; ...
		735.000000	; ...
		743.000000	; ...
		753.000000	; ...
		791.000000	; ...
		808.000000	; ...
		814.000000	; ...
		817.000000	; ...
		818.000000	; ...
		815.000000	; ...
		799.000000	; ...
		790.000000	; ...
		772.000000	; ...
		769.000000	; ...
		763.000000	; ...
		754.000000	; ...
		744.000000	; ...
		737.000000	; ...
		734.000000	; ...
		732.000000	; ...
		735.000000	; ...
		743.000000	; ...
		750.000000	; ...
		798.000000	; ...
		811.000000	; ...
		816.000000	; ...
		819.000000	; ...
		820.000000	; ...
		813.000000	; ...
		802.000000	; ...
		791.000000	; ...
		774.000000	; ...
		770.000000	; ...
		765.000000	; ...
		760.000000	; ...
		750.000000	; ...
		747.000000	; ...
		743.000000	; ...
		741.000000	; ...
		740.000000	; ...
		739.000000	; ...
		746.000000	; ...
		785.000000	; ...
		808.000000	; ...
		814.000000	; ...
		819.000000	; ...
		819.000000	; ...
		816.000000	; ...
		801.000000	; ...
		792.000000	; ...
		776.000000	; ...
		768.000000	; ...
		763.000000	; ...
		755.000000	; ...
		746.000000	; ...
		738.000000	; ...
		730.000000	; ...
		725.000000	; ...
		725.000000	];
  
%OriginalSamples = OriginalSamples - mean(OriginalSamples); 
[z,p,k] = butter(12,.65/12.5,'high');
[sos,g] = zp2sos(z,p,k);

HPLR2 = dfilt.df2tsos(sos,g);

Y = filtfilt(sos,g,OriginalSamples);
MYT = filter(HPLR2,OriginalSamples');

figure;
plot([OriginalSamples, Y MYT'],'*')
legend('Orig', 'using filtfilt', 'using filter')

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