Is it normal that i have emotional delays?

I just noticed this and the fact that it's been going on for years. Basically what happens is that I seem to have a delay in the way my emotions are. For example, someone can tell me that they love me and though I will reply with a simply "I love you, too" (providing this is a reciprocated love), I won't feel the actual emotion until way later on in the day. Same scenario for other emotions. For example, when my grandma died: I kept my usual good mood for several hours even after receiving the news. It wasn't until about a week later that the emotions I was supposed to feel (I guess?) finally hit me. I'm like that with good news, too. So, is it normal?