Sum, then filter, then re-separate data

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Hi all,
Trying to get some help with a problem I'm having:
I have two vectors that, when summed together, create a signal that has noise (spikes) that I'm wanting to filter out.
I need to filter the summed signal and then revert it back to the two vectors such that they can be re-summed without any noise.
Not sure if this is possible or if anyone has any ideas? I've attached some images and a .mat file with the data contained.

Accepted Answer

Star Strider
Star Strider on 1 Oct 2022
Edited: Star Strider on 2 Oct 2022
It would help to have the sampling frequency.
I am not certain what you want to filter, however for now I am assuming that is the noise in the valley between the summed signals —
LD = load(websave('data',''))
LD = struct with fields:
front: [20000×1 double] rear: [20000×1 double]
front = LD.front;
rear = LD.rear;
Fs = 2000; % Default Sampling Frequency
Fn = Fs/2; % Nyquist Frequency
L = numel(front);
t = linspace(0, L-1, L)/Fs; % Time Vector
NFFT = 2^nextpow2(L); % For Efficiency
FTfr = fft([front rear]-mean([front rear]),NFFT)/L; % Fourier Transform
Fv = linspace(0, 1, NFFT/2+1)*Fn; % Frequency Vector
Iv = 1:numel(Fv); % Index Vector (One-Sided Fourier Transform)
plot(Fv, abs(FTfr(Iv,:))*2)
xlabel('Frequency (Units)')
ylabel('Magnitude (Units)')
title('Fourier Transform')
xlim([0 Fs/100])
lim1 = [min([front rear]); max([front rear])]; % Signal Limits
Fco = 5; % Cutoff Frequency
fr_filt = lowpass([front rear], Fco, Fs, 'ImpulseResponse','iir'); % Filter Signals
lim2 = [min(fr_filt); max(fr_filt)]; % Signal Limits
fr_filt = max(fr_filt-9, 0); % Eliminate Baseline Transients
lim3 = [min(fr_filt); max(fr_filt)]; % Signal Limits
fr_filt = fr_filt .* lim1(2,:)./lim3(2,:); % Rescale Data
lim3 = [min(fr_filt); max(fr_filt)]; % Check Signal Limits
plot(t, fr_filt)
title('Filtered Signals')
plot(t, sum(fr_filt,2))
title('Summed Filtered Signals')
This lowpass filter eliminates the noise reasonably well, at the expense of eliminating some other high-frequency information. That can be fine-tuned (to an extent) by changing the cutoff frequency ‘Fco’ in the lowpass call. Since I am not certain what you want to filter out, I leave that fine-tuning to you. I will help as necessary to get the desired result.
NOTE — Since I do not have the actual sampling frequency, I have scaled everything here in terms of it so this code should work with a different sampling frequency without alteration.
EDIT — (2 Oct 2022 at 03:34)
Added known sampling frequency, adjusted ‘Fco’ and thresholded the result to attenuate the baseline transients after filtering.

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