The following documents describe how high end DSOs implement their algorithms.
Sin(x)/x Interpolation: An Important Aspect of Proper Oscilloscope Measurements
By Chris Rehorn, Agilent Technologies
m.eet.com/media/1051226/Sin%28x%29x_Agilent.pdf
Interpolation in Your DSO
Peter J. Pupalaikis, Product Marketing Manager
WaveMaster Oscilloscopes
LeCroy Corporation
cdn.teledynelecroy.com/files/whi … 102203.pdf
The essence of what they’re saying is
Linear interpolation performs well when the sample rate is ten times the highest
frequency signal content. SinX interpolation works well the sample rate is at least three
times the highest frequency content
I am too underskilled to implement this. However, these articles might give suitable tips to those better equipped at such work.