How to filter noise from a time series without losing important informations?
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as described in the topic I have a time series like this:
Zoomed in you can see there is a lot of noise.
I need to filter the noise in the green rectangle without losing informations like the spike in the green circle.
As can be seen in the frequency domain there is a lot going on.
I have tried smoothing and filtering endlessly with Data Analyser Toobox and the Signal Processing Toolbox. I have tried the Filter Designer just like the filter funktion with various settings like Savitzky-Golay Filter or Exponential Moving Average Filter or Bandpass. But everytime I get rid of the noise I also lose to much important informations.
Can anybody tell if and how I can achive this?
I have attached the data.mat with the time series in case there is someone who likes to try.
Mathieu NOE 2021 年 6 月 28 日
this is my suggestion and the result : as you can see , the large amplitude spikes are not changed by the filtering (perfect overlay with raw data)
x = data(:,1);
y = data(:,2);
t = data(:,3);
dt = mean(diff(t));
Fs = 1/dt;
ind = find(t>3.9 & t < 4);
t = t(ind);
x = x(ind);
y = y(ind);
samples = length(y);
%% "smart" data smoothing
N = 9;
xs = medfilt1(x, N,'truncate');
xs = medfilt1(xs, N,'truncate');
% replace noisy data by smoothed (only low amplitude signal is affected)
ind = find(abs(xs)<1);
xx = x;
xx(ind) = xs(ind);
title(['Data samples at Fs = ' num2str(round(Fs)) ' Hz / Smoothed with medfilt1' ]);