What resample method can I use for time series that increases nonlinearly?

I have a time series of data (that I have in a structure) that goes from 0 to 360 (degrees), which only increases from one sample in the time series to the next (i.e., always something like: 0, 1, 2, 3, 4 ... 360, never 0, 1, 2, 1, 2, 3, ... 360). The time series does not increase in a linear fashion, one data point to the next may increase by any amount between 0 and 360. I want to resample this time series to increase/decrease the number of samples within it. I've tried the standard resample() function as well as some other methods involving linspace() that did not work. I need the retain the fact that the time series only increases from one sample to the next, and never decreases. Is there a resample method that would work here?

Answer 1

[John D'Errico]

This is really an interpolation problem. You can call it a resampling, but interpolation is all it is. And you can do everything using just interp1. Simplest is to just use a linear interpolation. Here is a simple series that is monotonic, but is also difficult to interpolate if you want a monotonic interpolant.

y = cumsum(randi(10,1,10).^3);
ny = numel(y);
x = 1:ny;
plot(x,y,'o')

Now, if I were to use a spline, for example, it would produce results that are not monotonic.

xint = linspace(1,ny,5*ny - 4); % 4 new points between each original point.
yspl = interp1(x,y,xint,'spline'); % this won't be monotone
ylin = interp1(x,y,xint,'linear'); % linear MUST be monotonic
ypchip = interp1(x,y,xint,'pchip'); % pchip is also always monotonic

plot(x,y,'ro',xint,yspl,'r-',xint,ylin,'g-',xint,ypchip,'k-')
grid on
legend("Original series","Spline","Linear","Pchip")

So the red curve (the spline) is not monotonic on this crappy series. The green one is, but it is just connect the dots linear interpolation. It is not bad, but nothing spectacular. The black curve is as smooth as possible, and also monotonic.

[Spencer Ferris]

Thank you! This is super helpful, so if I wanted to decrease the number of data points by a specific amount, I have a number of time series that all vary in length with some larger and some smaller than the desired length, would I just change this line from this...

xint = linspace(1,ny,5*ny - 4);

to this? If I wanted to decrease the length of the time series by 4?

xint = linspace(1,ny,5*ny + 4);

EDIT: I ran this and can see now that this is not how it works, is there another method I would have to use to decrease the length of the time series?

[John D'Errico]

NO. Think about how linspace works. It generates a vector of length that third argument. If you want to decrease the number of points, then you would use a SMALLER value than ny.

y = cumsum(randi(10,1,30).^3);
ny = numel(y)

ny = 30

How long is y? y has 30 elements here. If you wanted to have only 10 elements, then specify a SMALLER number than 30.

xint = linspace(1,ny,10);

[Spencer Ferris]

Okay, I think I understand now, thanks for the clarification. So if I had a time series y with a length of 100 and wanted to decrease the length to 90, I would run this and then pass it to one the interporlation methods, correct?

y = cumsum(randi(10,1,100).^3);
ny = numel(y);
x = 1:ny;

xint = linspace(1,ny,90);

This goes a bit beyond the Matlab aspect of it so no worries if you have no advice for this, but if this is the method I use, would it generally be better (in terms of maintaining the fidelity of the curves and trajectories of my data) to increase each time series in length rather than decrease them?