# 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
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
[filtr,~]=highpass(nutr,f_lo,fs);
filtr=filtr(padn+1:end-padn); % removing prefixed and appended parts
tr1=filtr;

% lopass filter
[filtr2,~]=lowpass(nutr,f_hi,fs);
tr1=filtr2;

% bandpass filter
[filtr,~]=bandpass(nutr,[f_lo,f_hi],fs);
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?

• You're designing very narrow filters near DC; that's difficult in general. I would try several steps of downsampling to reduce the sampling rate first, followed by a filter to reject DC.
– MBaz
Feb 23 '21 at 22:19
• So, basically this devolves down to a Matlab question, because the devil is in the details, and the details are in the way Matlab implements highpass, lowpass, and bandpass. I suggest you build your own filters so that you know what's going on, and get back to us if there's problems. Feb 23 '21 at 22:21
• @MBaz Thanks Guys!! For now I am satisfied with the results of sequential filtering. Reading some related questions is giving me a better insight into the pitfalls in this specific area. Like this one: dsp.stackexchange.com/questions/19245/… Feb 23 '21 at 22:57