Cake cole fog

What does cockroach feces look like? - cockroach feces pics

We are new in a subtropical climate and are not familiar with cockroaches. We have found the little black smearing on our carpet and I suspect it could be that droppings of cockroaches trampled and clean. I have a small black object, slightly greasy and does not know where they come from. Do these sound like droppings of cockroaches? Everyone had this problem before and if so, how can I solve this problem?

Thank you.