@@ -307,6 +307,7 @@ For example: @-5~/~2 sup 1 = -3@ .bp .SUBSUBSECTION "the Residual" +.nr ZR \n% .PP Though the FLAC format allows for different forms of residual coding, two forms of partitioned Rice are the only ones @@ -708,7 +709,7 @@ delta's absolute value sum, below. .PP In this example, @\[*D] sup 1@'s value of 26 is the smallest. Therefore, when compressing this set of samples in a FIXED subframe, -it is best to use a predictor order of 1. +it's best to use a predictor order of 1. .PP The predictor order indicates how many warm-up samples to take from the PCM stream. @@ -731,3 +732,64 @@ Order:\^ 4:@"Residual" sub i = "Sample" sub i~~-~~((4 * "Sample" sub {i~-~1})~~-~~(6 * "Sample" sub {i~-~2})~~+~~(4 * "Sample" sub {i~-~3})~~-~~"Sample" sub {i~-~4})@ _ .TE +.\"In this example, the residual values are: -1 1 1 1 0 3 0 -4 -1 0 1 1 1 4 -3 1 4 -1 -1 +.bp +.SUBSUBSECTION "the Residual" +.PP +Given a stream of residual values, one must place them in one or more +partitions, each with its own Rice parameter, and prepended with a +small header.\(dg +.FS +\(dg See page \n(ZR for full details of how the residual is organized. +.FE +The residual's coding method is typically 0, unless one is encoding +audio with more than 16 bits-per-sample and one of the partitions +requests a Rice parameter higher than @2 sup 4@. +The residual's partition order is chosen exhaustively, which means +trying all of them within a certain range (e.g. 0 to 5) such that +the residuals can be divided evenly between them and then the partiton +order which uses the smallest estimated amount of space is chosen. +.PP +Choosing the best Rice parameter is a matter of selecting the smallest +value of `x' such that: +.EQ +"sample count" * {2 sup x}~~>~~{sum from {i = 0} to {"residual count"~-~1} +|{"residual" sub i}|} +.EN +.LP +Again, this is easier to understand with a block of example residuals, +19 in total: +.TS +tab(:); +| c | c | c | +| c | r | r |. +_ +index:@residual sub i@:@|~{residual sub i}~|@ += +0:-1:1 +1:1:1 +2:1:1 +3:1:1 +4:0:0 +5:3:3 +6:0:0 +7:-4:4 +8:-1:1 +9:0:0 +10:1:1 +11:1:1 +12:1:1 +13:4:4 +14:-3:3 +15:1:1 +16:4:4 +17:-1:1 +18:-1:1 +_ +@|~{roman "sum"}~|@::29 +_ +.TE +@19 * {2 sup 0}@ is not larger than 29. +.br +@19 * {2 sup 1}@ is larger than 29, so the best Rice parameter +for this block of residuals is 1. docs/codec_flac.ms f41dc759e876f20a6c6e8695b778372b88112caa Brian Langenberger bjl@usa.net http://github.com/tuffy/python-audio-tools/commit/2e7139d403f8fd8b6a265b2a2147e430fe9c6606 2e7139d403f8fd8b6a265b2a2147e430fe9c6606 2008-05-10T12:47:04-07:00 2008-05-10T12:47:04-07:00 Added some documentation on determining Rice partition orders from a list of residuals. aa40fce5b55a53f03fbd6fd1ccce3cde04cf5307 Brian Langenberger bjl@usa.net