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There are volumes written about both audio and video compression on a yearly basis. New codecs and file processes come in and out of fashion even faster than the temporary technology that supports them. This trip toward advanced singularity relies on a few basic principles that set up what compression is within this digital information system.
Many people assume that compression of video and audio files is the exact same process. This assumption comes from the idea that we just take the central file and then remove information, thus making it smaller. Though it is very much simplified, this is the general idea behind video compression. Here small fragments of the video information are taken out to make the final amount of data smaller. This will affect the over all video quality and resolution, but the idea is that the video compression will not be so profound as to make the video unwatchable. Almost every transfer format that you see a video in, such as most data files or DVDs, are all compressed video.
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Audio compression, on the other hand, is an entirely different process all together. Instead of simply taking out these pieces of information the audio compression process wants to actually shrink the availability of possible frequencies.
All sound has what is called a dynamic range. This dynamic range is simply the range from the absolute loudest to the absolute quietest. Each piece of audio independently has its own dynamic range that goes from high to low. What audio compression attempts to do is to shrink that audio piece's dynamic range to a smaller average over all. This can generally lower the audio peaks, and raise up the quieter parts. This is the general rule for almost all broadcast formats, especially radio or television.
There is a huge range of audio compression types that will work with the file, and are used to alter the sound itself. Audio compression is by no means only used to shrink the files, though that can be a factor. For example, MP3s are a compressed audio file that loses quite a bit of information. They were constructed so they could be transferred more easily.
Basic Differences Between Audio and Video Compression
Here are different articles on video compression.