Without zero-filling (i.e. np = fn) the digital resolution is related to the acquisition time (as shown in equation below). Note, however, that while np can be any number, the Fourier Transform (FT) algorithm works only with fn values that are a multiples of 2 (..., 1024, 2056, 4096, 8192, 16384, 32768 etc. also called 1K, 2K, 4K, 8K 16K, 32K, 64K etc.).

Poor digital resolution, especially a problem in 2D experiments, can lead to severe peak distortion as shown in the examples below. All spectra show the same proton signal: on top at a very poor digital resolution with the two vertical lines showing two digitization points separated by 2.9 Hz, on the bottom at high digital resolution (0.2 Hz/pt). It is obvious that poor digitization can lead to misinterpretations.
A particular risk is the use of peak picking on poorly resolved peaks. The picking routine will always take the highest point which may be offset from the center of the peak. For precise measurements of chemical shifts and coupling constants, the center of a line, not its highest point, counts.

number of data points (np): 4K
Fourier number (fn): 4K
acquisition time (at): 0.35 sec

zero-filling: none

number of data points (np): 8K
Fourier number (fn): 8K
acquisition time (at): 0.70 sec

zero-filling: none

number of data points (np): 16K
Fourier number (fn): 16K
acquisition time (at): 1.40 sec

zero-filling: none

number of data points (np): 24K
Fourier number (fn): 32K
acquisition time (at): 2.00 sec

zero-filling: 1.33 x

number of data points (np): 24K
Fourier number (fn): 64K
acquisition time (at): 2.00 sec

zero-filling: 2.66 x