[Mp4-tech] How to convert 4X4 interger transform to equivalent dct transform

[乾]

X is the original 4 * 4 martrix,
Y is the DCT coefficient matrix
Y = AXA' and X = A'YA
    a   a   a   a
A = b   c  -c   b     ;          
    a  -a  -a   a
    c  -b   b  -c
a=1/2  ;  b=sqrt(1/2)cos(PI/8)  ; c = sqrt(1/2)cos(3*PI/8)
is can be equivalent as below：
Y ＝ ( CXC')#E
# means that to the result matrix's coefficient is to mutiply the two
coefficient at the response position.
Here, 
    1   1   1   1
C = 1   d  -d  -1      ;d = c/b =0.414,
    1  -1  -1   1
    d  -d   1  -d
for simplification and maintain orthogonality, made d = 0.5 and b = sqrt(2/5);
make the second line and forth line of C multiple with 2, so as the
second colomn and forth conomn. Named it as Cf
also make E corresponding Ef
to make Y = (CfXCf')#Ef
we get Cf and Ef:
    1   1   1   1
Cf= 2   1  -1  -2      
    1  -1  -1   1
    1  -2   2  -1
And:
    a*a     a*b/2   a*a    a*b/2
Ef= a*b/2   b*b/4   a*b/2  b*b/4      
    a*a     a*b/2   a*a    a*b/2
    a*b/2   b*b/4   a*b/2  b*b/4
H.264 make #Ef in quantification Process.
On 8/11/05, mp4-tech-request lists.mpegif.org
<mp4-tech-request lists.mpegif.org> wrote:
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>   1. How to convert 4X4 interger transform to equivalent dct
>      transform (tummala kalyani)
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> ----------------------------------------------------------------------
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> Message: 1
> Date: Wed, 10 Aug 2023 17:28:46 +0530
> From: tummala kalyani <tummalakalyani gmail.com>
> Subject: [Mp4-tech] How to convert 4X4 interger transform to
>        equivalent dct  transform
> To: mp4-tech lists.mpegif.org
> Message-ID: <13936ad5050810045829078b11 mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
> 
> can any one explain me to how to convert 4 X 4 integer transform used
> in H.264 to normal 4X4 dct transform matrix.
> 
> --
> Kalyani Tummala
> M.Tech CSE II year
> MBM Hall of Residence- #B2
> IIT Kharagpur - 721302
> mobile: 919932736720
> 
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