What are the advantages and disadvantages of smoothing+ sin x/x interpolation+ and linear interpolation?

What are the advantages and disadvantages of smoothing+ sin x/x interpolation+ and linear interpolation?

Smoothing trades horizontal resolution and bandwidth for vertical resolution. It has the benefit of reducing noise above the bandwidth traded off. The disadvantages include requiring a greater record length and/or a higher sample rate to allow for the trade off. Amplitude measurement error can also be a problem.

Sine x/x and linear interpolation are two ways to join the sample points acquired on a waveform. If the signal is a band limited waveform (that is, if there is little frequency content in the waveform above the Nyquist frequency, half the sample rate) then sine x/x interpolation applied with a high quality algorithm can properly and accurately reconstruct the waveform shape and amplitude up to a frequency of 0.4 to 0.25 times the sample rate.

If the waveform is a fast rise pulse, with fast edge features with non-band limited frequency content, then linear interpolation may provide a more faithful representation.