Inter-point interpolation using FIR filter
From Hilmar's answer to the linked question, the Whittaker–Shannon interpolation formula is:


  $$x(t)=\sum_{n=-\infty }^{\infty }x[n]\cdot \operatorname{sinc}\left(\frac{t-nT}{T}\right).$$


If the signal is low-pass and the noise is high-pass, to filter high-pass noise, we can make a low-pass version of the interpolation formula:

$$x(t)=\sum_{n=-\infty }^{\infty }x[n]\cdot 2f_c/f_s\cdot \operatorname{sinc}\left(\frac{t-2f_c/f_s\cdot nT}{T}\right),$$

where $f_c$ is the cutoff frequency and $f_s$ is the sampling frequency. The highest signal-to-noise ratio is obtained by setting the cutoff frequency to a frequency for which the signal and the noise have equal power. Actually the Whittaker–Shannon interpolation formula is low-pass as well, with $f_c=f_s/2$.