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A .wav file created from a .mp3 file has the same frequency domain plot as the mp3 file itself https://stackoverflow.com/questions/58706674/difference-between-frequency-domain-in-mp3-and-wav.

However, the .wav file created from .mp3 file has larger file size. According the post https://stackoverflow.com/questions/15593806/why-is-a-wav-file-created-from-a-mp3-file-much-larger-in-size, this is because the .wav file is storing much more data than the mp3 file is.

Now, is there any difference in the quality between the .wav file and .mp3 file?

Does the quality of .wav file sound better since it has more data stored?

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  • $\begingroup$ mp3 format is a compression method. It loses data which is supposed to be insignificant to the human ear. This means that no quality degradation is introduced. However, some listeners report that they do feel quality degradation. In any case, the conversion from mp3 back to wav cannot reinvent the lost information. If anything, any conversion process is a risk of introducing more noise (depending on the process). So, no, the quality of wav converted from mp3 is not better. $\endgroup$ – havakok Dec 2 at 8:55
  • $\begingroup$ Thanks @havakok. If so, what is the purpose of mp3 decoder since nowadays many devices do support mp3 format? $\endgroup$ – Cyan Dec 2 at 9:09
  • $\begingroup$ The purpose is compression. $\endgroup$ – havakok Dec 2 at 10:23
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    $\begingroup$ @Cyan "Amount of data" and "quality of data" are not always correlated. I can take lossy compressed data, stuff it with a bunch of random numbers to increase the "amount of data", but (as I hope you can see) the quality of the original data has not increased. $\endgroup$ – MBaz Dec 2 at 13:48
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MP3 is a lossy compression format, so encoding an uncompressed lossless WAV file to MP3 will lose some quality in the encoding process.

Decoding a MP3 file back to WAV file has at most the same quality as the MP3 file has, it is just as good or bad as the contents in the MP3 file was, it is not in any way different to decode it for saving into a file or decoding it for playback. Most importantly, you don't get the lost quality back when decoding, and basically the result actually depends on the quality of the decoder as well.

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No of course not... Indeed, every mp3 file must be converted to wav bit stream (pcm data) before being played back as audio; the process known as decoding the mp3 file;i.e. you cannot play back mp3 bit stream as a hearable (meaningful) audio...

A wav file bit stream (pcm data) may contain much higher quality audio depending on its originating source before it's decoded into a lossy format such as mp3, aac, ogg vorbis. However, the reverse process of decoding the compressed file back into a wav - pcm stream does not and cannot increase the quality.

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Well... maybe.

MP3 in its standard use is an a lossy audio compression format. It uses human auditory models to degrades data which the human ear is not (totally) sensitive too. Some sounds actually present in the audio file will not be heard because they are below the threshold of hearing, or they are masked by other sounds, nearby in time or frequency. This information that can be discarded is used to reduce the necessary size in bits to store the audio content.

So, information is lost, and a direct conversion to another audio format, whether lossless or not, will only cause minor changes (because of floating points operations on data and rounding, etc.). Unless in extreme cases (very high compression, very quiet sounds), those are unlikely to be heard.

However, compression standard tell how to decode compressed file streams, and do not disallow postprocessing that can improve the objective or subjective quality of the compressed file. For instance, an image renderer can process a decoded JPEG image to smooth out some border/checkerboard artifacts. The same may occur in audio, eg DSP-based audio post processing enhances audio quality. Based on some models, some processing might be able to compensate for what was lost in the initial MP3 coding.

Last: when original audio data contains noise, surprisingly, compression can enhance the quality, as noise can be discarded first while compressing. This is described in the influential paper (at least to me) Filtering Random Noise from Deterministic Signals via Data Compression by Natarajan in 1995. So, it is not impossible that converting a lossy format into another lossy format may actually improve quality.

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