Does anyone know why, given a sampling rate of 48kHz per second for the .wav-file,
the long MDCT window in AAC has 49 scale factor bands and the short MDCT window has 14 ?
Is there a rule, based on critical bark bands or so, how to calculate the number of
scale factor bands, or is it a simple heuristic number? If I want to use an MDCT with,
say, 512 channels (instead of 1024, or 128) what would be the criteria to choose the number of scfbs?

It's a trade-off. The more scalfactors you have the more bits you need to code them which can't be spent anymore on the actual samples. Obviously there's a sweet spot somewhere. To cope with attacks and fight preecho you may use several short block groups (say 3) with different scalefactors within a frame, so you end up coding 3x14 scalefactors instead of 1x49. Thus you traded high spectral resolution of the noise floor for high temporal resolution.

Apart from that I'm clueless.

HTH,
SG

and of course, differentially coding the scalefactors helps to reduce their cost (mp3 vs aac)

Well, let's see.

There are some rules:

1) All scalefactors have to have a multiple of 4 lines in them
2) All scalefactors have to have no more than (I think 32?) lines in them, except the final band over 20kHz
3) All scalefactor bands should be close to ?1? critical band. (I've forgotten,but it was some %age of a critical band.)

I think those were the original criteria, at least.



Very much so, because of the Huffman coding.

Do you have any idea how hard a particular German organization fought against differential coding of scalefactors and Huffman coding of scalefactors.

Did you know that the scalefactor Huffman table is defective, and based on an unnecessary limit in the rate loop of the reference model?

On a related subject, perhaps one day you'll explain us what happened to the upper scalefactor within mp3. Did anyone stole it, or was it lost somewhere when traveling to an mpeg meeting?

Oh my ghu. You don't want to know.

Thank you very much.

I once read that it was common for the great mathematicians of the past, Gauss, Fermat, deMoivre, Leibnitz,
etc. to correspond particular formulas, which solve a mathematical equation, to their colleagues but they
did not describe how they achived their solutions. Everyone had to figure out by himself , how the
other one solved the problem.

Working on "the science" of audio coding sometimes reminds me of these times.

During the time of making the standard, not many people thought this information was important, in fact most people didn't want to use that many scalefactors, having misunderstood the tradeoff between side information and main information.

The maximum size of the scalefactor is directly related to the stereo/mono switching method. Is this a surprise?