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If we have an MP3 file and we decode it to an uncompressed WAV file and then later encode it to MP3 again at the same sample rate - why is it that the quality gets degraded?

This is a past exam question that I can't figure out. I know it has something to do with the fact that the MP3 codec uses lossy compression, but I can't figure out at what point it would remove more from it... - can anyone figure this out? Thanks in advance!

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2 Answers 2

When you encode a WAV file to an MP3, some information is irretrievably lost. When you decode the MP3 back to a WAV file, the decoder recreates something close to the original waveform, but not exact due to the lost information. When you re-encode the WAV file back to MP3 once again information is lost. The second MP3 file is of lesser quality than the original MP3 since the WAV file the second MP3 file was encoded from is of lesser quality than the original.

See this answer for an example of what happens to audio and video when you encode a video to a compressed format many times. Information is lost every time it is encoded.

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Each time you save (overwrite) your MP3 file, the "MP3 compression" applies. So, each time, you lose quality.

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Yeah, I understand that applying the MP3 compression is making it lose quality again - what I can't figure out is WHY that is happening - as in why the codec is removing more information from it... it is possible that this might be better to put on signal processing! –  user1058210 May 27 '12 at 15:04
    
That's just the way MP3 works, by removing non-audible frequencies. –  lewebdalex May 27 '12 at 16:14
    
The quality reduces every time you save the file with a lower compression as the original. That's how MP3 is actually able to save disk space, by removing audio content. If you take a full audio stream from a CD. That stream is written 44100 times per second with 16 bits to disk, which results in a certain amount of data stream. (kbps) Every time you encode in a lower quality, the quality is reduced. –  Zettt May 27 '12 at 16:46
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I think what the asker is getting at is that the psychoacoustical redundancies would have been removed during generation of the original MP3. When generating a WAV from MP3, technically the MP3 is a lossless compressed version of the generated WAV file, so why isn't the original MP3 produced when the generated WAV is compressed with the same parameters? I don't know any details but I remember reading that the MP3 encoder necessarily applies some sort of rounding off during quantization hence the further quality loss. –  Mulvya May 28 '12 at 18:36
    
Sound On Sound--Perceptual Coding: How Mp3 Compression Works is a really good, easy to follow, article on how MP3 works that you may find beneficial. It's old (May 2000), but the information is still relevant. –  Herbert Mar 15 '13 at 4:53
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