Interpolate non-uniform signals
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I have a 12 hour signal X, that was recorded at 1Hz.
However, some samples were missed and I don't have all 43200 samples (the 12h period in seconds [1Hz]). Furthermore, the sampling rate does not seem to be constant, meaning that besides missed samples, the interval between the ones I do have might be slightly above or below 1s.
Together with my signal of interest (X) I also recorded the timestamps (t) at which each sample was recorded (lengths of X and t are equal).
I need to resample/interpolate my signal sucha that I have 43200 samples.
Any suggestion how I could accomplish this?
Thanks in advance!
5 Comments
Accepted Answer
Jan
on 31 May 2021
Edited: Jan
on 31 May 2021
John D'Erricos warning is important: The data do not look like an interpolation is fair. But if you have a good reason to do this, this is how it works:
data2 = interp1(data(:, 1), data(:, 2), 0:(12 * 3600 - 1));
A comparison:
figure;
plot(data(:, 1), data(:, 2), 'ro');
hold on;
plot(0:43199, data2, '-');
You see the typical effect of removed spikes for a linear interpolation.
2 Comments
John D'Errico
on 31 May 2021
You definitely never want to use a spline interpolant with data like this. But even a linear interpolant may be too much, as the linear interpolant tends to average neighboring points together, but somewhat randomly.
plot(t,X,'.')
[min(t),max(t)]
ans =
0 43198.1130371094
that = 0:1:max(t);
Xhat0 = interp1(t,X,that,'nearest');
Xhat1 = interp1(t,X,that,'linear');
plot(that,Xhat0,'.')
plot(that,Xhat1,'.')
So the nearest neighbor interpolant retains much more of the character of the original plot, showing the dual nature of the series, where it seems to oscillate between two distinct levels.
Once the data is onto a uniform spacing, now some variety of Savitsky-Golay filter (with a wide window), or perhaps a wide window median filter might be appropriate.
More Answers (1)
Star Strider
on 31 May 2021
LD = load('example_data.mat');
data = LD.data;
t = data(:,1);
s = data(:,2);
Fs = 1; % Sampling Frequency (Hz)
[sr,tr] = resample(s,t,1); % Resample At Uniform Sampling Frequency Of 1 Hz, Return Interpolated Signal (‘sr’) and Time (‘tr’) Vectors
figure
plot(t, s)
hold on
plot(tr,sr)
hold off
grid
legend('Original','Resampled', 'Location','best')
.
2 Comments
Star Strider
on 31 May 2021
My pleasure!
The resample function uses a common technique to interpolate unevenly-sampled signals to a uniform sampling frequency, since this is required by all digital signal processing procedures that I am aware of. The function uses an anti-aliasing filter to prevent aliased signals from appearing in the resampled vectors, a common problem using simple interpolation.
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