That seems a lot like spaghetti alla puttanesca.
The way my dad likes it is basically making a fresh tomato sauce with homemade, jarred peeled tomatoes packed with basil. Saute garlic in olive oil, crush the tomatoes, cook them and add salt. Undercook the spaghetti and then finish cooking it in the sauce and then serve with parmesan cheese.
The variations from region to region include adding kalamata olives, anchovies or capers.