sukkan_sukha asked . 2021-12-27

Help With Starting Point for a Low Pass Filter

I am brand new to signal processing and having a lot of trouble understanding the documentation ot implement a low pass filter, which is what I think I need. An exmaple of what I'm working with is shown in Fig1.

The signal is oxygen amperometry changes which are necessarily slow. I've been attempting to use matlab find peaks function which does a decent job at finding peaks, but I cannot get it to find an appropriate width as it is considering all the smaller peaks instead of the one large one. For example, see Fig2. I'm primarily interested in peaks 1,2, and 4. The findpeaks does a good job with the widths of peaks 1 and 3, but in 4 it's considering that a small peak. Changing factors within the findpeaks function also doesn't appear to help as even though the smaller peaks may not appear in the output, findpeaks still considers them in the anlysis. In Fig2 I've been able to have findpeaks suppress the output of peaks near peak 4, but that doesn't help its width estimation.

I'm pretty sure the answer to my issue is preprocessing, but a smoothing such as moving average doesn't quite capture what I need and so I think I need a more advanced filter like a low pass. Can anyone suggest starting parameters in some code for me to work with ? I'm having trouble getting any implementation to work. An example dataset is in ExData.xlsx where time point 0 is the event of interest.

signal processing , Matlab , Programming

Expert Answer

Prashant Kumar answered . 2024-12-21 00:20:14

I am not certain what result you want.

Here is a prototype lowpass filter design you can experiment with. It has a passband frequency of 0.08 Hz (it stops everything above that) and a reasonably short transition region. I will help you refine it to do what you want, and help with findpeaks as well.

The Filter —

[D,S] = xlsread('ExData.xlsx');
t = D(:,1);
s = D(:,2);

figure
plot(t,s)                                               % Plot Original Signal
grid

Ts = mean(diff(t));                                     % Sampling Interval
L = numel(t);
Fs = 1/Ts;                                              % Sampling Frequency
Fn = Fs/2;                                              % Nyquist Frequency
smc = s-mean(s);                                        % Subtract Mean (0 Hz)
FTs = fft(smc)/L;                                       % Fourier Transform
Fv = linspace(0,1,fix(L/2)+1)*Fn;                       % Frequency Vector
Iv = 1:numel(Fv);                                       % Index Vector

figure
plot(Fv, abs(FTs(Iv))*2)                                % Plot Fourier Transform
grid
xlim([0 1])

Ws = 0.09/Fn;                                           % Lowpass Stopband Frequency
Wp = 0.08/Fn;                                           % Lowpass Passband Frequency
Rp =  1;                                                % Passband Ripple
Rs = 50;                                                % Stopband Ripple & Attenuation
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                         % Elliptical Filter Parameters
[z,p,k] = ellip(n,Rp,Rs,Wp,'low');                      % Elliptical Filter Design (Specify Lowpass)
[sos,g] = zp2sos(z,p,k);                                % Second-Order-Section For Stability

figure
freqz(sos, 2^14, Fs)                                    % Plot Filter Characteristics
set(subplot(2,1,1),'XLim',[0 2.5])
set(subplot(2,1,2),'XLim',[0 2.5])

s_filt = filtfilt(sos,g,s);                             % Filter Signal

figure
plot(t, s_filt)                                         % Plot Filtered Signal
grid

Experiment with the filter. Remember that with a lowpass filter, the stopband frequency (Ws) has to be greater than the passband frequency (Wp). The Fourier transform plot will help you decide on the frequencies.

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