Bandpass filter vs sequential high and lowpass filter in Matlab: weird difference

I am trying to bandpass a neural signal acquired at 20kHz between 0.5 and 100 Hz. I have tried to do it in two ways. The first way is to sequentially highpass and lowpass the signal and the second one is to use the bandpass function in Matlab. To my surprise, the results were dramatically different. See image below:

Here is the code:

clear
close all
load('bandpass_vs_seq_lo_and_hi_pass','tr','fs') % loads variable called tr and fs
% tr is the signal vector and fs is the sampling rate, 20kHz
padlen=0.01; % padding length in secs to remove transients at signal start and end
padn=padlen*fs; % padding length in samples
f_lo=0.5; % lo cutoff
f_hi=100; % hi cutoff
tvec=(1/fs:1/fs:1/fs*length(tr));

figure
ax1=subplot(3,1,1);
ax2=subplot(3,1,2);
ax3=subplot(3,1,3);

% sequential highpass and lowpass filter
    % hipass filter     
      nutr=[flipud(tr(1:padn));tr;flipud(tr(end-(padn-1):end))];  % prefixing and appending signal  
      [filtr,~]=highpass(nutr,f_lo,fs);
      filtr=filtr(padn+1:end-padn); % removing prefixed and appended parts
      tr1=filtr;

       % lopass filter
      nutr=[flipud(tr1(1:padn));tr1;flipud(tr1(end-(padn-1):end))];    
      [filtr2,~]=lowpass(nutr,f_hi,fs);
       filtr2=filtr2(padn+1:end-padn);
       tr1=filtr2;

 % bandpass filter
      nutr=[flipud(tr(1:padn));tr;flipud(tr(end-(padn-1):end))];    
     [filtr,~]=bandpass(nutr,[f_lo,f_hi],fs);
     filtr=filtr(padn+1:end-padn);
     tr2=filtr;
 
 plot(ax1,tvec,tr)
 plot(ax2,tvec,tr1)
 plot(ax3,tvec,tr2)
 
 xlabel(ax3,'Time (s)')
 title(ax1,'Original signal, fs=20kHz')
 title(ax2,'Sequential high pass and lowpass (0.5 to 100 Hz)')
 title(ax3,'Bandpass (0.5 to 100 Hz)')

Can anyone shed light on what is going on here?

Also asked here:

https://dsp.stackexchange.com/questions/73407/bandpass-filter-vs-sequential-high-and-lowpass-filter-in-matlab-weird-differenc

[Mathieu NOE]

hello

this is weird... I tested your code on a simple white noise and it gives strange results...

I first believed there is too large a factor between the (high) sampling rate (20 kHz) and the frequency range of interest (0.5 -100 Hz) so I introduced a decimation first before filtering , but that did not really help.

I found that even the sequential approach gives some oscillations at the beginning of the signal - see below

to get rid of these oscillations, I had to increase the hipass cut off freq to 5 Hz ... quite siginficant !

also strange to me is the difference of resulting amplitude between plot 2 and 3 (?)

Also the code is very slow on my machine. I guess I would prefer to stick to the "old" way using butter and filtfilt

at least i know what filter orders I use and I can plot the filter transfer function...

[Anand Kulkarni]

Thanks @Mathieu NOE It was very useful to confirm that this is weird. The computational cost is also very strange. I agree that the good old butter followed by filtfilt looks good and gets done in a reasonable time.

[Mathieu NOE]

hello

just minor improvement, if you detrend (remove mean value of your signal), you can probably reduce the amount of padding needed

tr = tr -mean(tr );

Answer 1

[Mathieu NOE]

I prefer this code ... faster and I know what filters I use

i changed the input signal random + negative constant (to mimic your data)

I increased padding length to 2 secs to be coherent with the time constant of a 0.5 Hz high pass filter

and also both sequential and single bandpass filter outputs have same amplitude

       fs = 20e3;
       tr = randn(fs*10,1)-60;
       
% tr is the signal vector and fs is the sampling rate, 20kHz
padlen=2; % padding length in secs to remove transients at signal start and end
padn=padlen*fs; % padding length in samples
f_lo=0.5; % lo cutoff
f_hi=100; % hi cutoff
tvec=(1/fs:1/fs:1/fs*length(tr));
figure
ax1=subplot(3,1,1);
ax2=subplot(3,1,2);
ax3=subplot(3,1,3);
% sequential highpass and lowpass filter
    % hipass filter     
      nutr=[tr(padn:-1:1);tr;tr(end:-1:end-(padn-1))];  % prefixing and appending signal  
          N = 2; % MN
          [B,A] = butter(N,f_lo*2/fs,'high'); % MN
          filtr= filtfilt(B,A,nutr); % MN
      % lopass filter
          N = 2; % MN
          [B,A] = butter(N,f_hi*2/fs,'low'); % MN
          filtr2= filtfilt(B,A,filtr); % MN
       filtr2=filtr2(padn+1:end-padn);
       tr1=filtr2;
 % bandpass filter
      nutr=[tr(padn:-1:1);tr;tr(end:-1:end-(padn-1))];  % prefixing and appending signal  
           N = 2; % MN
          [B,A] = butter(N,[f_lo f_hi]*2/fs); % MN
          filtr= filtfilt(B,A,nutr); % MN
     filtr=filtr(padn+1:end-padn);
     tr2=filtr;
 
 plot(ax1,tvec,tr)
 plot(ax2,tvec,tr1)
 plot(ax3,tvec,tr2)
 
 xlabel(ax3,'Time (s)')
 title(ax1,'Original signal, fs=20kHz')
 title(ax2,'Sequential high pass and lowpass (0.5 to 100 Hz)')
 title(ax3,'Bandpass (0.5 to 100 Hz)')