PSX YCbCr to yuv4mpeg2

PSX YCbCr

Given Y, Cb, and Cr color range of [-128, 127].

                              PSX
[ 1   0        1.402  ]   [ Y + 128 ]    [ r ]
[ 1  -0.3437  -0.7143 ] * [ Cb      ] =  [ g ]
[ 1   1.772    0      ]   [ Cr      ]    [ b ]

yuv4mpeg2 (i.e. Rec.601) YCbCr

Given Y color range of [16, 235] and Cb,Cr color range of [16, 240].

                              Rec.601
[ 1.164   0       1.59  ]   [ Y  - 16  ]     [ r ]
[ 1.164  -0.391  -0.813 ] * [ Cb - 128 ]  =  [ g ]
[ 1.164   2.018   0     ]   [ Cr - 128 ]     [ b ]

To convert a PSX YCbCr color to a Rec.601 YCbCr color:

[ 1  -3415973/13224846875  1242172/13224846875 ]
[ 0   105814197/105798775      -5608/105798775 ]
[ 0       19492/105798775  105791687/105798775 ]

Answer:  yuv4mpeg2^-1 * PSX =
[ 1  3415973/13225888625  -1242172/13225888625 ]
[ 0  105791687/105807109        5608/105807109 ]
[ 0     -19492/105807109   105814197/105807109 ]

Rec601_YCbCr = 
                                     PSX
                                     [Y + 128]   [ 16]
     Rec601_Matrix^-1 * PSX_Matrix * [Cb     ] + [128]
                                     [Cr     ]   [128]

Where

Rec601_Matrix^-1 * PSX_Matrix =

     [250/291 -488509/2660418030 -82738/1330209015]
     [0          4014411/4571165       164/4571165]
     [0            3673/27426990   8031459/9142330]

Thanks to toruvinn for refreshing me on matrix math, and this site and Maxima for saving me from lots of raw calculations.

Update 27Feb2010: Fixed.
Update 23Mar2010: Really fixed.