Can Ammonium Sulphate and Calcium Carbonate be used as a substitute for Calcium Sulphate in your garden?
They are not going to produce similar results. Calcium sulfate is gypsum - a soil amendment (for sodic soils), not a fertilizer. It does provide a small Ca contribution but has no effect on soil pH.
Ammonium sulfate is a high nitrogen fertilizer and calcium carbonate is essentially lime (raises pH) but also contributes Ca, although not an ideal source. They kind of work at cross purposes as the lime counteracts any acidifying effect of the sulfur contribution of the ammonium sulfate.
What is it you are trying to do?