Benchtop NMR spectroscopy parameter explanation; tau and number of points I have just carried out an exploration of the effect of different solvents and conditions on the 1H caffeine relaxation by benchtop NMR spectroscopy.
When collecting the 1D 1H NMR spectra of the caffeine in CDCl3 solution, the parameter for the number of points was set up, but when the relaxation run for T1 and T2 were done, the parameter was replaced by the value of time delay, tau.
I think I kind of get a clear view from your discussion, as the number of points is needed in determining the right peaks for 1D 1H spectra. But, as for the relaxation time, the intensities behaviour during the time delay is now being the subject of interest, hence the np parameter is neglected.
This is what I understand by far.
#updated
They are the number of points (np) and tau.
I think I kind of understand how np works;

it's the discrete points of analogue FID that are being converted to
digital points along with the FID signal envelope. Therefore it's
associated with the resolution of the spectra which the lesser np used
to define the FID, the lower the resolution.
*Let me know if I interpreted this wrongly.

This question raised when I'm analysing my data though, would really appreciate it if someone can enlighten me.
AS Karl said read the instrument's manual and add the meaning of the symbols. However there is one important point in discrete Fourier transform (DFT).

I think I kind of understand how np works; it's the discrete points of analogue FID that are being converted to digital points along with the FID signal envelope. Therefore it's associated with the resolution of the spectra. *Let me know if I interpreted this wrongly.

I have been recently discussing this exact point with signal processing engineers and spectroscopist friend with a lot of good constructive discussions. No, the number of points cannot enhance the intrinsic resolution of the signals whether it is NMR or FTIR or any other FT spectroscopic technique. What you increase, when you collect more points, is the frequency resolution on the x-axis, and consequently more points per peak. That is it.
For an N-point DFT, the frequency step is
$$\frac{1}{N\Delta t}$$
For example if your sampling frequency is fixed to 1 s (an arbitrary number), in one experiment you collect 1000 points, the frequency step on the axis is
$$\frac{1}{1000 . 1 s}=0.001 Hz $$
In another experiment, you only collect 250 points with a time step of 1 s
$$\frac{1}{250 . 1 s}= 0.004Hz$$
Note the time to sample the signal in each case is different, because it is given by $N\Delta t$. So by chance, if your original experimental spectrum was &quot;limited&quot; by the number of points per peak by increasing the number of points, you might see an improvement in the peak shape and apparent resolution when you increase the number of points in an FID.