For the past week or so I have been studying the C++ tutorials at cplusplus.com. I began with the tutorials on classes, because I have minimal experience with Object Oriented Programming. Next, I went on to study the rest of the C++ tutorials at this website.
For detailed information on how filters work, I recommend going to this URL:
The above mentioned website also has the best information I have found about how phase shift works. Here is the URL for said tutorial: