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The proliferation of Japanese animation (anime) in a worldwide audience, along with the advent of digital media editing tools have given way to the phenomenon known as the AMV or Anime Music Video. This usually refers to a clip of video that has been edited by a fan of some particular anime episode in such that the original audio is stripped out and their favorite music is inserted. The result is often a collaboration of multiple shots from different episodes of the anime title resulting in often powerful emotionally charged music videos.
A simple Google Search will return a few good sites to teach you what you will need to create your own. Sites like AnimeMusicVideos.org have many guides and a forum to help with the creation.