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.
