[flac-dev] [PATCH] New apodization functions

[Martijn van Beurden]

Hi all,

This patch adds two new apodization functions that I developed. 
 From my own test results (on quite a diverse dataset) they 
outperform the current best apodizations by 0.05% - 0.1% 
(depending on the specifics) on compression.

Here's a selection of the test results

*Apodization functions*           ,Compres, Speed
partial_tukey(2) tukey(0.5)       , 56.50 , 37.2x
partial_tukey(3)                  , 56.51 , 37.0x
tukey(0.75) gauss(0.2) tukey(0.25), 56.54 , 35.8x
partial_tukey(2)                  , 56.55 , 50.5x
tukey(0.25) gauss(0.2)            , 56.57 , 49.6x
tukey(0.5)                        , 56.69 , 79.3x

Speed is in times realtime. Here "tukey(0.75) gauss(0.2) 
tukey(0.25)" was the best combination of three existing 
apodization functions I could find, and it is outperformed by 
"partial_tukey(2) tukey(0.5)" by 0.04 percentage points, which 
is 0.07%. It improves 0.19 percentage points or 0.33% on the 
default at the cost of halving in speed. By design, there is no 
decoding speed penalty nor are there any compatibility issues. 
The only trade-off is slower encoding.

This might not look much, but this is actually a better deal 
than using -8 over -5, which improves 0.23 percentage points at 
the cost of cutting the encoding speed to 1/3th and slightly 
slower decoding. The use and internals of these windows are 
explained in the documentation that is in the patch itself.

Note, this patch includes the patch I mailed a little more than 
a week ago, which fixes the triangle, bartlett and bartlett_hann 
windows.
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