Filtration is the easiest method. The water will pass through the filter paper, but the particles of silt are too large to pass through its pores.
“Gas chromatography” is incorrect. You can’t convert the silt particles into a gas.
“Electrolysis” is incorrect. Electrolysis destroys the water by converting it into hydrogen and oxygen.
“Distillation” is a possibility. The water would boil off and be condensed back to a liquid. The silt would stay behind as a solid residue.