The sermons in the book of Acts are short, certainly summaries of the actual sermons he summarizes. But it’s also clear that Luke was not simply generically summarizing what was said at these speeches or simply spitting out what he thought they probably said. How do we know this? Luke himself tells us (Lk. 1:1-4) that he put together a careful, orderly account from eyewitnesses, and we know that he was an eyewitness to much of what took place in the book of Acts. And the book bears out his record. The language, style and content of the speeches match the other works written by the speakers. Peter’s speeches are like his letters. William Ramsay, a New Testament researcher in the nineteenth century, reversed his belief that Luke was not a reliable reporter by studying this very subject. Roger Wagner asks

How could Luke have made such accurate summary transcripts? Shorthand! It should be remembered that a rather sophisticated method of shorthand was in use during the first century. It was developed for the very purpose of taking down speeches by Cicero. In later times it was used in the church, and by physicians. Luke, a physician, may well have had a mastery of this skill which would have facilitated his ability to record the sermons while they were being delivered, and later to draw characteristic excerpts from those transcripts when including sermonic material in his narrative. (Tongues Aflame, 22)

This is especially interesting, as Wagner points out, because it means that the sermons are not only filled with apostolic content, but reflect original arrangement and style.