There was a thread here this year where the sounds of highly amplified dither were posted, they can serve as a hint of how those "dither sounds" are applied.
Here I post an example of my batch file for conversion to 16/48. For 16/44.1 (which I use primarily for CDs) I would use the next command line (lower). Dither can be altered as desired. Also SoX filtering can be left at the default (95 passband, aliasing off) - if you omit the parameters -b -a (e.g. rate -v 48000/44100).------16/48------rem Example of how to do batch processing with SoX on MS-Windows.remrem Place this file in the same folder as sox.exe (& rename it as appropriate).rem You can then drag and drop a selection of files onto the batch file (orrem onto a `short-cut' to it).remrem In this example, the converted files end up in a folder called `converted',rem but this, of course, can be changed, as can the parameters to the soxrem command.c: cd %~dp0mkdir "c:\music\Sox converted%~p1"FOR %%A IN (%*) DO sox -V2 %%A -b 16 "c:\music\SoX converted%~p1%%~nxA" rate -v -b 88 48000 dither -f modified-e-weighted---------16/44.1----------FOR %%A IN (%*) DO sox -V2 %%A -b 16 "c:\music\SoX CD converted%~p1%%~nxA" rate -v -b 92 -a 44100 dither