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Will an MP3 file, encoded from a 16-bit, 44.1 kHz source sound better or worse than an MP3 file, encoded with identical settings, but from a 24-bit, 96 kHz source? Or will there be no audible difference?
I'm asking because obviously there is much more raw data to be compressed in the high-quality sample, so perhaps there's more compression artefacting to be expected than when converting from a well-downsampled source?
It is highly unlikely there will be any audible difference. The audio quality of an mp3 file is decided by it's bit rate and how good the encoder is.
In almost all cases you want to do as few re-samplings as possible, as it is a bit like making a copy in the analog world. In the case of mp3s, if you have a 96Khz source it has to be re-sampled to either 44.1 or 48Khz, as mp3 doesn't support 96kHz. A good decoder will probably not have to re-sample the bit rate before encoding, but that extra information will instead be thrown away during the encoding to make the data fit in the mp3 bit rate.
If there is an audible difference it's in that case because the decoder you use are bad at changing the sampling frequency from 96kHz to 44.1. In that case you might want to change the mp3 file to use 48kHz instead. But with modern encoders I find that unlikely as well. But should this be the case, re-sampling it to 44.1 or 48kHz in a program that does such re-samplings well could be an option. Re-sampling to 16bit from 24 shouldn't make a difference assuming your sources peak volume is reasonably close to max.
Should the peak level be extremely low, you may lose information that the mp3 encoding otherwise might have kept if you used the 24 bit source. But for that to happen I expect you would have to have a peak volume that is around 8 bits lower than max, which means that you could raise the volume 256 times (or 48db), which seems unlikely.
In the end though, all you can do is test both, and have a friend make a double blind test with you. :-) But if that doesn't work, just use the original source without re-encoding it first. It's likely to give the best results.
My personal experience: never let your MP3 encoder do any SRC (sample rate conversion) or truncation of bit resolution unless you are sure it is the best tool for that job. If you have better tools available for that purpose, use them. A good MPEG encoder doesn't necessarily mean a good sample rate converter.
One of the most valuable web sites I came across is http://src.infinitewave.ca/, which gives a very thorough comparison of sample rate converters. You can see that many DAWs are not as good as you expect them to be, and that the quality of a sample rate conversion is not always related to the price you pay for a product. I always use SoX to do my sample rate conversions.
So first dither, truncate and transcode, and then do the MPEG encoding on the result.
96 kHz downsampled to 48 kHz (the maximum supported by the .mp3 codec) will contain more information than 44.1 kHz.
As for bit depth (24 vs. 16 bits), this post says:
"When the MP3 is decoded to PCM it can be done as 24 bit integer, 32 bit float, etc., and with the proper hardware and software this added bit depth can be maintained through reproduction of the sound."
If that's true then the answer is yes, both the source bit depth and sampling rate are relevant for mp3 conversion, theoretically.
