Resampling of signal with non uniform sampling frequency
Without specific constraints on the data/noise properties or sampling assumptions, smoothing splines could be helpful. Indeed, constraining the curve to pass exactly through the given points could be too harsh.

One example of such a toolbox in Matlab is SPLINEFIT with several examples:




  Direct spline interpolation of noisy data may result in a curve with 
  unwanted oscillations. This is particularly bad if the slope of the 
  curve is important.  A better approach is to reduce the degrees of
  freedom for the spline  and use the method of least squares to fit the
  spline to the noisy data.  The deegres of freedom are connected to the
  number of breaks (knots),  so the smoothing effect is controlled by
  the selection of breaks.


Matlab also has Cubic smoothing spline (csaps).

One possible reading:


Flexible Smoothing with B-splines and Penalties, Paul H. C. Eilers; Brian D. Marx, 1996